TAFE Queensland Learner Guide - MSL30122/MSL20122 PDF

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Description: TAFE Queensland logo and cover background +-----------------+-----------------+-----------------+-----------------+ | Unit version | Document | Release date | Comments/action | | | version | | s | +=================+=================+=================+=================+ | MSL973001A | 1.1 | Feb 2016 | New Document | | | | | | | MSL973002A | | | | | | | | | | MSL922002A | | | | +-----------------+-----------------+-----------------+-----------------+ | MSL973013 | 1.2 | Feb 2017 | Updated to new | | | | | unit codes and | | MSL973014 | | | minor changes | | | | | | | MSL922001 | | | | +-----------------+-----------------+-----------------+-----------------+ | MSL973013 | 1.3 | Feb 2018 | Updated to new | | | | | template | | MSL973014 | | | | | | | | | | MSL922001 | | | | +-----------------+-----------------+-----------------+-----------------+ | MSL973013 | 1.4 | Jan 2019 | Updated to new | | | | | template | | MSL973014 | | | | | | | | | | MSL922001 | | | | +-----------------+-----------------+-----------------+-----------------+ | MSL973013 | 1.5 | July 2019 | Unit codes | | | | | updated to new | | MSL973014 | | | units. | | | | | | | MSL922001 | | | | +-----------------+-----------------+-----------------+-----------------+ | MSL973013 | 1.6 | Jan 2020 | Updated to new | | | | | template | | MSL973014 | | | | | | | | | | MSL922001 | | | | +-----------------+-----------------+-----------------+-----------------+ | MSL973013 | 1.7 | July 2020 | General Updates | | | | | | | MSL973014 | | | | | | | | | | MSL922001 | | | | +-----------------+-----------------+-----------------+-----------------+ | MSL973013 | 1.8 | January 2021 | General Updates | | | | | | | MSL973014 | | | | | | | | | | MSL922001 | | | | +-----------------+-----------------+-----------------+-----------------+ | MSL973013 | 2.0 | March 2021 | Renamed file | | | | | | | MSL973014 | | | | | | | | | | MSL922001 | | | | +-----------------+-----------------+-----------------+-----------------+ | MSL973013 | 2.1 | March 2021 | Reviewed, Minor | | | | | changes | | MSL973014 | | | | | | | | | | MSL922001 | | | | +-----------------+-----------------+-----------------+-----------------+ | MSL973013 | 2.2 | December 2022 | Reviewed, Minor | | | | | changes | | MSL973014 | | | | | | | | | | MSL922001 | | | | +-----------------+-----------------+-----------------+-----------------+ | MSL922002 | 3 | January 2024 | Unit Codes have | | | | | changed, | | MSL973025 | | | document | | MSL973026 | | | updated | | | | | accordingly | +-----------------+-----------------+-----------------+-----------------+ | MSL922002 | 4 | July 2024 | Reviewed, major | | | | | changes, | | MSL973025 | | | corrections, | | MSL973026 | | | update of | | | | | learning | | | | | materials and | | | | | examples. | +-----------------+-----------------+-----------------+-----------------+ : Document version control table **\ ** **Copyright** © TAFE Queensland 2024 Copyright protects this material. Except as permitted by the Copyright Act 1968 (Cth), reproduction by any means (photocopying, electronic, mechanical, recording or otherwise), making available online, electronic transmission or other publication of this material is prohibited without the prior written permission of TAFE Queensland. Inquiries must be addressed to the TAFE Queensland Copyright Officer, Office of the Chief Academic Officer, TAFE Queensland, PO Box 16100, CITY EAST QLD, 4002, or Email. **Disclaimer** Every effort has been made to provide accurate and complete information. However, TAFE Queensland assumes no responsibility for any direct, indirect, incidental, or consequential damages arising from the use of information in this document. Data and case study examples are intended to be fictional. Any resemblance to real persons or organisations is coincidental. If you believe that information of any kind in this publication is an infringement of copyright, in material in which you either own copyright or are authorised to exercise the rights of a copyright owner, and then please advise us by contacting the TAFE Queensland Copyright Officer, Office of the Chief Academic Officer, TAFE Queensland, PO Box 16100, CITY EAST QLD, 4002, or Email. **Acknowledgement** This resource was compiled by Katrina Mengede from: *MSL922002A Record and present data Learner Guide* originally produced by SBIT Applied Science team using *PMLDATA200A Record and present data Learning and assessment guide* Commonwealth of Australia, Australian Training Products Ltd Melbourne 2006. Copyright Commonwealth of Australia reproduce by permission. *MSL973002A Prepare working solutions Learner Guide* originally produced by SBIT Applied Science team using *PMLTEST303B Prepare working solutions Learning and assessment guide* Commonwealth of Australia, Australian Training Products Ltd Melbourne 2006. Copyright Commonwealth of Australia reproduce by permission. Unless otherwise stated, images are from the above sources. Introduction ============ This Learner Guide has been developed to support you as a resource for your study program. It contains key information relating to your studies including all the skills and knowledge required to achieve competence. What will I learn? ------------------ *MSL973025 Perform basic tests* This unit/cluster will provide you with the ability to prepare samples and perform tests and measurements using standard methods with access to readily available advice from supervisors. This unit of competency is applicable to laboratory/field assistants working in all industry sectors. In general, they do not calibrate equipment and make only limited adjustments to the controls. They do not interpret or analyse results or troubleshoot equipment problems. *MSL973026 Prepare working solutions* This unit/cluster will provide you with the ability to prepare working solutions and to check that existing stocks of solutions are suitable for use. Working solutions include those required to perform laboratory tests. Personnel are required to calculate quantities and make dilutions. This unit of competency is applicable to laboratory assistants working in all industry sectors. *MSL922002 Record and present data* This unit/cluster will provide you with the ability to record and store data, perform simple calculations of scientific quantities and present information in tables and graphs. The unit of competency requires personnel to solve predictable problems using clear information or known solutions. Where alternatives exist, they are limited or apparent. This unit of competency is applicable to production operators, field assistants and laboratory assistants working in all industry sectors. Are there any special requirements? ----------------------------------- The student will need to have access to a calculator and or computer to perform the necessary calculations TAFE Queensland student rules ----------------------------- TAFE Queensland student rules are designed to ensure that learners are aware of their rights as well as their responsibilities. All learners are encouraged to familiarise themselves with the TAFE Queensland student rules, specifically as they relate to progress of study and assessment guidelines. A full guide to student rules can be found at Student rules[^1^](#fn1){#fnref1.footnote-ref}. Information to support your learning and assessment --------------------------------------------------- There's always someone to help you. Undertaking further study can bring both excitement and challenges. Our Student Services, Learning Support and Library staff can help you make the most of your time at TAFE. Callout panels -------------- A number of panels have been designed to help guide you to important information and actions throughout this Learner Guide. The full choice of panels you are likely to encounter to support you in your studies are included below. NB: not all the panels will be used in every learner guide.  Contents {#contents.TOCHeading} ======== [Maths and Chemistry - Theory 1](file:///D:%5CD%20Drive%5CTAFE_2024_Sem1%5CMSL30122_Cert%203_LabSkills%5CCert%203%20Data%20Testing%20and%20solutions%20cluster%5CMSL922002_MSL973025_MSL973026_LG_MC_TQB_F2F_V3.docx#_Toc155689996) [Introduction 5](#section) [What will I learn? 5](#what-will-i-learn) [Are there any special requirements? 5](#are-there-any-special-requirements) [TAFE Queensland student rules 6](#_Toc155690000) [Information to support your learning and assessment 6](#_Toc155690001) [Callout panels 6](#callout-panels) [Welcome 10](#welcome) [Required resources 12](#required-resources) [Section 1 -- Basic Calculations 13](#section-1-basic-calculations) [Section outline 13](#_Toc155690006) [Basic Operation with numbers 14](#_Toc155690007) [Order of operations 15](#order-of-operations) [Equality and inequality 15](#equality-and-inequality) [Addition and Subtraction 16](#addition-and-subtraction) [Multiplication and Division 16](#multiplication-and-division) [Algebra 18](#algebra) [Fractions 20](#fractions) [Decimals 26](#decimals) [Converting between fractions and decimals 26](#converting-between-fractions-and-decimals) [Ratio 28](#_Toc155690017) [Percentage 29](#_Toc155690017) [Converting from fraction or decimal to percentage 29](#converting-from-fraction-or-decimal-to-percentage) [Finding a percentage of a quantity 30](#section-13) [Percentage difference 32](#percentage-difference) [Square root 33](#square-root) [Section 2 -- Measurement and Data Recording 35](#_Toc155690022) [Section outline 35](#section-outline-1) [Recording and enter data 36](#recording-and-enter-data) [Recording data 36](#recording-data) [Data traceability and coding 37](#data-traceability-and-coding) [Check data to identify transcription errors or atypical entries 39](#check-data-to-identify-transcription-errors-or-atypical-entries) [Rectify errors in data using standard procedures 40](#rectify-errors-in-data-using-standard-procedures) [Scientific notation and Powers (indices) 42](#_Toc155690029) [Rounding 46](#rounding) [The use of significant figures in measurements and uncertainties 46](#the-use-of-significant-figures-in-measurements-and-uncertainties) [Rule for adding and subtracting 48](#_Toc155690032) [Rule for multiplying or dividing 49](#rule-for-multiplying-or-dividing) [Why are units important? 51](#_Toc155690034) [The SI unit system 52](#the-si-unit-system) [Derived units 53](#derived-units) [SI prefixes 55](#section-15) [Converting SI units 56](#converting-si-units) [Multiples and submultiples 56](#multiples-and-submultiples) [Converting from multiples and submultiples 58](#_Toc155690040) [Section 3 -- Statistics and Graphing 61](#section-3-statistics-and-graphing) [Section outline 61](#section-outline-2) [Statistical calculations 62](#statistical-calculations) [Measures of central tendency 62](#measures-of-central-tendency) [Variation of data 65](#variation-of-data) [Accuracy and precision 68](#accuracy-and-precision) [Accuracy 68](#accuracy) [Precision 68](#precision) [Bias 68](#bias) [Measurement Uncertainty 68](#measurement-uncertainty) [Geometry calculations..............................................................................\....70](#geometry-calculations) [Estimating answers to check calculations 74](#estimating-answers-to-check-calculations) [Tables and Graphs 77](#tables-and-graphs) [Line graphs 80](#_Toc155690054) [Reading line graphs 81](#reading-line-graphs) [Plotting the points 85](#plotting-the-points) [Interpreting line graphs 88](#interpreting-line-graphs) [Reading from a graph 88](#reading-from-a-graph) [Recognise and report obvious features and trends in data 88](#recognise-and-report-obvious-features-and-trends-in-data) [Section 4 -- Introductory Chemistry 92](#_Toc155690061) [Section outline 92](#section-outline-3) [Introductory chemistry 93](#_Toc155690063) [Atoms 93](#_Toc155690064) [Ions 94](#ions) [Molecules 94](#molecules) [Elements and compounds 94](#elements-and-compounds) [Symbols of the elements 94](#symbols-of-the-elements) [Periodic table 96](#periodic-table) [Types of compounds and chemical formulae 102](#types-of-compounds-and-chemical-formulae) [Ionic compounds 102](#_Toc155690071) [Polyatomic compounds 104](#polyatomic-compounds) [Other compounds, names and formulae 106](#other-compounds-names-and-formulae) [Prefixes used in binary molecular compounds 107](#_Toc155690074) [Organic Compounds 108](#organic-compounds) [The mole concept 109](#the-mole-concept) [Calculating the mass of a mole of pure substance 110](#calculating-the-mass-of-a-mole-of-pure-substance) [Concentration calculations 113](#concentration-calculations) [Calculating the quantity of solute (compound) 113](#calculating-the-quantity-of-solute-compound) [Revision: Concentration of Solutions 123](#revision-concentration-of-solutions) Welcome ======= [Welcome to the MSL973025 Perform basic tests. ] By completing this unit you will be able to: - accurately interpreting workplace procedures and standard methods - preparing samples using at least three (3) different processes - performing at least five (5) basic tests or measurements using standard methods and procedures - checking test equipment before use - completing all tests within the required timeline without sacrificing safety, accuracy or quality - demonstrating close attention to the accuracy and precision of measurements and the data obtained - calculating simple quantities using appropriate equations, units, uncertainties and precision - recording and presenting results accurately and legibly - maintaining the security, integrity and traceability of all samples, data/results and documentation - Following procedures for working safely and minimising environmental impacts.. [Welcome to the MSL973026 Prepare working solutions] By completing this unit you will be able to: - safely preparing at least five (5) examples of correctly labelled working solutions, including calculation of the quantities involved and any dilutions required - checking that existing stocks of working solutions and identifying those unfit for use, including: - noting turbidity to exclude absorption of moisture - noting deposits to exclude microbial contamination or chemical degradation - noting crystals to exclude evaporation - noting colour changes indicating a pH shift with solutions containing indicators - checking expiry dates on solution containers - following workplace procedures for the safe use of hazardous chemicals, laboratory glassware and equipment - accurately labelling and storing solutions in accordance with workplace procedures - safely cleaning up spills and collecting/disposing of waste in accordance workplace procedures - recording and presenting data accurately and legibly. [Welcome to the MSL922002 Record and present data] By completing this unit you will be able to: - accurately coding, checking, recording and storing data in the required format - Performing simple calculations involving scientific quantities, with or without a calculator or computer software. The following must be performed: - decimals, fractions, ratios, proportions and percentages - unit conversion, multiples and submultiples - use of significant figures, rounding off, estimation and approximation - substitution of data in formulae - conversions between SI units - performing at least five (5) of the following calculations: - perimeters - angles - areas (m2) and volumes (mL, L, m3) of regular shapes (e.g. packaging and moulds) - average mass, mass %, density, specific gravity, moisture, relative and absolute humidity - ratios, such as mass to mass, mass to volume and volume to volume percentages - industry specific ratios, such as g/cm^2^, kg/m2 - concentration (e.g. g/100mL, mg/L, mg/L) - dilution - statistical values, such as mean, median, mode and standard deviation - average count, colonies per swab surface and cell counts (live and dead/total) - process variables, such as pressure, velocity and flow rates - \% content of moisture, ash, fat, protein, alcohol, sulphur dioxide and trace metals, such as calcium or zinc - food properties, such as % concentration (dry), friability, bitterness, brix, free amino nitrogen, diastatic power, calorific content and yeast viability - preparing and interpreting straightforward tables, graphs and charts of data - recognising obvious features and trends in data, including: - maximum and minimum values - spread of data - increasing/decreasing data, rate of change - outliers, data beyond control limits or normal range - presenting accurate results in the required format - Maintaining the confidentiality of data in accordance with workplace and regulatory requirements. Required resources ------------------ - To complete these units, you will need to do all activities in the learner guide, all practice quiz's online and the assessments associated with these units. **\ ** Section 1 -- Basic Calculations =============================== ### Section outline This section covers the basic mathematical concepts required for the Certificate III in Laboratory Skills. More advanced maths will be introduced in the next section and in the Testing, Calibrations and Sampling Laboratory Manual. The notes in this section are not designed as a detailed learning tool, rather as a refresher for concepts you should already be familiar with. Please contact your teacher if you require additional assistance with the activities in this section. Topics covered in this section are: - Basic operations with numbers - Basic concepts of algebra - Fractions - Decimals - Ratios - Percentage - Square root **[Note:]\ The activities in this section do not need to be submitted for marking as you can self-check your answers using the answers available online on Connect.** **\ ** Basic Operation with numbers ---------------------------- The basic mathematical operators are addition, subtraction, division and multiplication: - Addition (+) is the adding of two numbers to give a sum. - Subtraction (-) is subtracting one number from another to give a difference. - Division () is dividing one number by another number resulting in a quotient. Division can also be written as one term over another which is known as a fraction. - Multiplication (x) is multiplying two numbers to give a product. Multiplication is also known as *times*. These operations can be written in numerical equations or in word form. For example: ### Order of operations It is important that operations are evaluated in the proper order; otherwise an incorrect answer will result. The correct order of operations can be determined using the acronym BEDMAS: 1. 2. 3. 4. ### ### Equality and inequality **Equal symbol =** Denotes equality, that the left expression is equal to the right expression e.g. 7 = 7, 6 + 1 = 7 **Less than symbol** \< Denotes that the value to the left of the symbol is less than the value on the right e.g. 3 \< 5 **Less than or equal to symbol** Denotes that the value to the left of the symbol is less than or equal to the value on the right e.g. 3 ≤ 5, 5 ≤ 5 **Greater than symbol** \> Denotes that the value to the left of the symbol is greater than the value on the right e.g. 5 \> 3 **Greater than or equal to symbol** Denotes that the value to the left of the symbol is greater than or equal to the value on the right e.g. 5 ≥ 3, 5 ≥ 5 **Not equal to symbol** Denotes that the value to the left of the symbol is not equal to the value on the right e.g. 2 ≠ 3 **Approximately equal to symbol** or Denotes that the value to the left of the symbol is approximately equal to the value on the right e.g. 1.001 ≈ 1 ### ### Addition and Subtraction Numbers (or integers) may be positive (+) or negative (-). If a number has no sign in front of it, it is a positive number e.g. 2 = +2 In an expression, brackets may be written around a number to make it easier to determine the sign of the number e.g. (- 9). When adding and subtracting numbers, first simplify the expression. Two symbols together can be replaced by a single symbol. If the symbols are the same, then they are replaced with +. If the symbols are different, they are replaced by -. See the examples below. 2 + (+2) = 2 + 2 3 -- (-2) = 3 + 2 Two positive signs = positive Two negative signs = positive 4 + (-2) = 4 -- 2 4 -- (+2) = 4 -- 2 Positive and negative = negative Negative and positive = negative ### Multiplication and Division When multiplying or dividing two numbers that have the same sign (either positive or negative), the answer is a positive number. If the two numbers have different signs, then the answer is a negative number. 2 x (+2) = 4 -6 ÷ (-2) = 3 Positive x positive = positive Positive ÷ positive = positive Negative x negative = positive Negative ÷ negative = positive 2 x (-2) = -4 6 ÷ (-2) = -3 -9 ÷ 3 = -3 Positive x negative = negative Negative x positive = negative Positive ÷ negative = negative Negative ÷ positive = negative When multiplying or dividing more than two numbers: - if there is an odd number of negative numbers, the answer will be negative - if there is an even number of negative numbers, the answer will be positive. -4 x 6 x (-8) = 192 -4 x (-6) x (-8) = -192 10 ÷ (-2) x (-6) = 30 +-----------------------------------+-----------------------------------+ | Activity-01 | Activity 1 : Evaluating equations | +===================================+===================================+ | 1. 7 + 8 x 6 -- 2 | | | | | | -- | | | -- | | | | | | 2. 4 - 2^2^ + 8 | | | | | | -- | | | -- | | | | | | 3. 36 ÷ 3 -- 2 x (7-2) | | | | | | -- | | | -- | | | | | | 4. 7 + 9 ÷ 3 -- 2 | | | | | | -- | | | -- | | | | | | 5. (9 + 3) x 8 -- 2 | | | | | | -- | | | -- | | +-----------------------------------+-----------------------------------+ Algebra ------- Algebra is solving equations that have unknown quantities or variables. A variable or unknown value is represented as a symbol, usually a letter of the alphabet. Variables are used mathematically in the same manner as the values they represent. When numbers and variables are multiplied, the multiplication is often omitted e.g. 6 x a = 6a. Sometimes a dot is used for multiplication (6.a) although this can get confused with a decimal point. The concept of using variables can be seen in the use of formulas. For example, the area of a rectangle is given by: where the variable *L* represents the length of the rectangle and the variable *W* represents the width of the rectangle. *L* and *W* are variables as their values will vary depending on the length and width of the rectangle being considered. **Figure 1.1:** The width and length of the rectangle may change depending on the size of the rectangle being measured; this is why we use variables. If we know that, the width is 4 cm and the length is 8 cm we can use the formula to determine the area Note that we have to square the units, cm x cm = cm^2^. You will learn more about units in the next section. Now, what if we know that the area = 45 cm^2^ and the width = 5 cm. How do we determine the length of the rectangle? Therefore 45 cm^2^ = L x 5 cm 45 cm^2^/5 cm = L x 5 cm/5 cm 9 cm = L It is important that you know how to manipulate a formula. +-----------------------------------+-----------------------------------+ |  | Activity 2 : Equations with | | | variables | +===================================+===================================+ | 1. *a* x *b* where *a* = 4 and | | | *b* = 2 | | | | | | -- | | | -- | | | | | | 2. 2*y* where *y* = 7 | | | | | | -- | | | -- | | | | | | 3. 42 -- 4*x* where *x* = 3 | | | | | | -- | | | -- | | | | | | 4. 7 (*n* + 2) where *n* = 4 | | | | | | -- | | | -- | | | | | | 5. 4*n* + 5*x* where *x* = 5 and | | | *n* = 2 | | | | | | -- | | | -- | | +-----------------------------------+-----------------------------------+ Fractions --------- A fraction is a number that is not a whole number. It looks like this: The denominator tells how many pieces or parts, something is divided into and the numerator tells how many pieces you have. data200frac1  **Figure 1.2** - - +-----------------------------------+-----------------------------------+ | Tip-01 | Tip | +===================================+===================================+ | The concept to remember when | | | working with fractions is that | | | any fraction where the numerator | | | and denominator are the same, | | | equals 1. | | | | | | This is why we can multiply or | | | divide both the numerator and | | | denominator by the same number in | | | order to perform fraction | | | operations, without changing the | | | value of the fraction. We are | | | only multiplying by 1. | | +-----------------------------------+-----------------------------------+ | [\$\\frac{2}{3} \\times \\ | | | \\frac{4}{4\\ } = \\ | | | \\frac{2}{3}\\ \\times 1\\ | | | \$]{.math.inline} We use this | | | when making equivalent fractions | | | | | | Equivalent fractions are used | | | when adding and subtracting | | | fractions. | | +-----------------------------------+-----------------------------------+ #### #### Equivalent fractions Equivalent fractions are fractions of the same value but have different numerators and denominators. Equivalent fractions can be found by multiplying or dividing the numerator and denominator by the same whole number. The following examples are equivalent fractions. is equivalent to = and is equivalent to [\$\\frac{1\\ }{5}\$]{.math.inline} x [\$\\frac{3}{3}\$]{.math.inline} = [\$\\frac{3}{15}\$]{.math.inline} is equivalent to = #### #### Reducing fractions to the simplest form Fractions should be expressed in their simplest form. This requires the denominator and numerator to be reduced to the smallest possible integers. This is achieved by dividing both the numerator and denominator by the same integer. In the fraction both the numerator (2) and the denominator (8) are divisible by 2. = = Therefore, is in its simplest form. A fraction is in its simplest form when there is no whole number that can be divided into both the numerator and denominator. = = in its simplest form. is in its simplest form as there is no whole number that can be divided into both 10 and 13. +-----------------------------------+-----------------------------------+ |  | Activity 3A: Simplest forms | +===================================+===================================+ | 1 | | | --- -- -- | | | 2 | | | 3 | | | 4 | | | 5 | | +-----------------------------------+-----------------------------------+ #### Multiplying fractions Multiplication is the easiest operation to perform on fractions. Simply keep the numerators and denominators separate and carry out the operation as normal. That is, multiply all the numerators together and then multiply all the denominators together. [\$\\frac{3}{7} \\times \\ \\frac{3}{8\\ }\\ = \\ \\frac{9}{56}\$]{.math.inline} [\$\\frac{1}{4} \\times \\ \\frac{- 5}{6\\ }\\ = \\ \\frac{- 5}{2\\ 4}\$]{.math.inline} #### Reciprocals or inverse To get the reciprocal of a fraction, you invert it so the numerator becomes the denominator and the denominator becomes the numerator. That is, you turn the fraction upside down. Reciprocal of [\$\\frac{2}{5} = \\ \\frac{5}{2}\$]{.math.inline} Reciprocal of [\$\\frac{7}{3} = \\ \\frac{3}{7}\$]{.math.inline} Reciprocal of [\$4 = \\ \\frac{1}{4}\$]{.math.inline} (as 4 is the same as [\$\\frac{4}{1}\\ \$]{.math.inline}) #### Dividing fractions To divide by a fraction, you multiply by its reciprocal [\$5 \\div \\ \\frac{3}{4}\\ = \\ \\frac{5}{1}\\ \\times \\frac{4}{3}\\ \\ = \\ \\frac{20}{3\\ \\ } = 6\\frac{2}{3}\\ \$]{.math.inline} +-----------------------------------+-----------------------------------+ | Activity-01 | Activity 3B : Multiplying and | | | dividing fractions | +===================================+===================================+ | 1 | | | --- -- -- | | | 2 | | | 3 | | | 4 | | +-----------------------------------+-----------------------------------+ #### Adding and subtracting fractions To be able to perform an addition or subtraction with two or more fractions, they must first be converted to a common denominator. Then, the addition or subtraction operations are carried out on the numerator. [\$\\frac{4}{5} + \\ \\frac{3}{10\\ } + \\frac{1}{15}\\ \$]{.math.inline} Step 1: Get all fractions to their simplest form. (this is already done for the above equation) Step 2: Convert all fractions to the lowest common denominator. This means the lowest number that all the denominators are factors of (i.e. divide into). This cannot be smaller than the largest denominator (once it is in its simplest form). So, for the above example, we know our lowest common denominator cannot be less than 15. For the above example we can see that 5, 10 and 15 are all factors of 30, so 30 will be our new denominator. To convert all fractions to the lowest common denominator, we multiply both the numerator and denominator by the factor required to get the new denominator. That is, we make equivalent fractions having the same denominator. [\$\\frac{4}{5} \\times \\ \\frac{6}{6\\ } = \\frac{24}{30}\$]{.math.inline} [\$\\frac{3}{10} \\times \\ \\frac{3}{3} = \\frac{9}{30}\$]{.math.inline} [\$\\frac{1}{15} \\times \\ \\frac{2}{2} = \\frac{2}{30}\$]{.math.inline} The fraction can now be written as this: [\$\\frac{24 + 9 + 2}{30}\$]{.math.inline} Step 3: Add (or subtract) the numerators and keep the denominator the same [\$\\frac{35}{30}\$]{.math.inline}\ Step 4: Simply the fraction [\$\\frac{35}{30}\\ \\div \\frac{5}{5} = \\ \\frac{7}{6}\$]{.math.inline} or +-----------------------------------+-----------------------------------+ |  | Example | +===================================+===================================+ | [\$\\frac{3}{4} - \\ | | | \\frac{1}{5}\$]{.math.inline} | | | lowest common denominator is 20 | | +-----------------------------------+-----------------------------------+ Note-01 Note --------- ------ +-----------------------------------+-----------------------------------+ |  | Activity 4 : Adding and | | | subtracting fractions | +===================================+===================================+ | 1 | | | --- -- -- | | | 2 | | | 3 | | | 4 | | +-----------------------------------+-----------------------------------+ Decimals -------- A decimal, like a fraction, is not a whole number. Decimals can be terminating where they have a certain number of decimal places; or they are recurring where they repeat continuously. The fraction 2/3, when written as a decimal, is recurring 0.666666666666**^.^**. Note the raised ^**.**^ to show the recurrence. Decimals are usually rounded to a set number of decimal places for practicality. Decimals look like this: 1.2, 0.19 and 2.1416852 Whilst many scientific calculators allow you to input fractions, the answers are generally supplied in the form of decimal numbers. This means you will need to convert between fractions and decimals. ### Converting between fractions and decimals To change a fraction to a decimal, you just need to divide the numerator by the denominator. **Fraction to a decimal** (that is, 3 ÷ 6) = 0.5 (that is, 1 ÷ 8) = 0.125 +-----------------------------------+-----------------------------------+ | Activity-01 | Activity 5 : Converting fractions | | | to decimals | +===================================+===================================+ | 1 | | | --- -- -- | | | 2 | | | 3 | | | 4 | | +-----------------------------------+-----------------------------------+ #### Decimal to a fraction **Step 1** **Step 2** **Step 3** +-----------------------------------+-----------------------------------+ |  | Example | +===================================+===================================+ | Convert 0.028 to a fraction | | +-----------------------------------+-----------------------------------+ +-----------------------------------+-----------------------------------+ | Activity-01 | Activity 6 : Converting decimals | | | to fractions | +===================================+===================================+ | 1 0.35 | | | --- ------- -- | | | 2 0.2 | | | 3 0.125 | | | 4 0.6 | | +-----------------------------------+-----------------------------------+ Ratio ----- A ratio compares the size of two quantities that have the same units. A ratio has no units and can be written in word form or quantity:quantity. **Word a:b notation Parts in total** Ratio of 15 g to 28 g 15:28 43 Ratio of 23 cm to 100 cm 23:100 123 **Note**: To obtain the total number of parts, add the components of the ratio together. +-----------------------------------+-----------------------------------+ |  | Example: Ratios | +===================================+===================================+ | A cleaning solution is used for | | | mopping the laboratory room | | | floor. The direction for making | | | this solution is one part | | | detergent to seven parts water. | | | | | | The ratio of detergent to water | | | used in making the solution is | | | 1:7. This is read as 'one to | | | seven'. In the diluted solution | | | [\$\\frac{1\\ }{8}\$]{.math | | |.inline} would be detergent | | | and[\$\\ \\frac{7\\ }{8}\$]{.math | | |.inline} would be water. That is | | | for every litre of detergent, you | | | will need to add seven litres of | | | water, which is 8 litres in | | | total. | | | | | | If you only wanted to make 4 | | | litres of cleaning solution you | | | would need ½ litre of detergent | | | and 3 ½ litres of water. This is | | | still in the ratio of 1:7. | | +-----------------------------------+-----------------------------------+ +-----------------------------------+-----------------------------------+ |  | Activity 7 : Ratios | +===================================+===================================+ | Complete the following table | | | | | | ------------------------ ------ | | | ------------- ------------------- | | | ---- ------ | | | In words Quanti | | | ty:quantity Fraction of each pa | | | rt | | | ratio of 7 to 8 | | | | | | | | | 57.5:6 | | | 0.2 | | | | | | | | | 7/10 | | | 3/10 | | | 24 metres to 31 metres | | | | | | | | | 220:27 | | | 0 | | | | | | ------------------------ ------ | | | ------------- ------------------- | | | ---- ------ | | +-----------------------------------+-----------------------------------+ Percentage ---------- Percentages provide the same information as a ratio or fraction. The term percentage comes from 'per cent' meaning 'out of 100' or 'parts per 100 parts. The percent symbol % is written after a number that gives the number of parts per 100. Example-01 Example: Percentage ------------ --------------------- +-----------------------------------+-----------------------------------+ |  | Activity 8 : Converting | | | percentages to fractions and | | | decimals | +===================================+===================================+ | 1 25% | | | --- ------ -- | | | 2 83% | | | 3 120% | | | 4 0.5% | | +-----------------------------------+-----------------------------------+ ### Converting from fraction or decimal to percentage To convert a fraction or decimal to a percentage, you multiply by 100. **Convert a fraction to a percentage** **Convert a decimal to a percentage** +-----------------------------------+-----------------------------------+ | Activity-01 | Activity 9 : Fractions and | | | decimals to percentages | +===================================+===================================+ | 1 0.125 | | | --- ------- -- | | | 2 1/8 | | | 3 0.75 | | | 4 3/4 | | | 5 1/3 | | | 6 0.008 | | +-----------------------------------+-----------------------------------+ ### ### Finding a percentage of a quantity The simplest way to find a percentage of a quantity is to write the percent as a fraction (or decimal), replace the word *of* by the multiplication sign X, and then calculate the equation. So, to find 30% of 50, the equation becomes x 50 = 15 (You can use either the fraction or decimal form of percent) +-----------------------------------+-----------------------------------+ |  | Example: Percentage of a quantity | | | \#1 | +===================================+===================================+ | - | | +-----------------------------------+-----------------------------------+ | Example-01 | Example: Percentage of a quantity | | | \#2 | +-----------------------------------+-----------------------------------+ | | | +-----------------------------------+-----------------------------------+ +-----------------------------------+-----------------------------------+ |  | Activity 10 : Calculating the | | | percentage of a quantity | +===================================+===================================+ | -- | | | -- | | +-----------------------------------+-----------------------------------+ Percentage difference --------------------- To determine the percentage difference, first work out the absolute difference and then convert this to a percentage of the original value. To do this, write the change as a fraction of the original amount and then multiply by 100 to get a percent. For example, a change of 7 to an original amount of 20 is a 7/20 x 100 = 35% change. Example-01 Example: Percentage difference ------------ -------------------------------- +-----------------------------------+-----------------------------------+ |  | Activity 11 : Percentage change | +===================================+===================================+ | -- | | | -- | | +-----------------------------------+-----------------------------------+ Square root ----------- The square root of a number, shown by the symbol is a value when multiplied by itself gives the original number. For example, the square root of 4 (written as) is 2 (that is, ); the square root of 28.09 () is 5.3 (that is, ). Note that the square root of 1 is 1 (that is,). From the work on multiplying and dividing negative numbers earlier in this chapter, you should note that the square root of a positive number could also be a negative number. That is, -2 x -2 = 4 and -1 x -1 = 1 etc. Unless relevant to the application or specifically stated, we usually accept the answer to be the positive number. Note: You cannot calculate the square root of a negative number as no number multiplied by itself will give a negative number, it will always be positive, as the signs are the same. +-----------------------------------+-----------------------------------+ | Activity-01 | Activity 12 : Square Root | +===================================+===================================+ | 1 62 | | | --- ------ -- | | | 2 3 | | | 3 0.75 | | | 4 1/9 | | | 5 4/9 | | | 6 7/9 | | +-----------------------------------+-----------------------------------+ Section 2 -- Measurement and Data Recording =========================================== Section outline --------------- **This section covers data and measurement concepts required for the Certificate III in Laboratory Skills. More advanced maths will be introduced in the next section.** **Please contact your teacher if you require additional assistance with the activities in this section.** Topics covered in this section are: - Data recording - Error correction - Scientific notation - Rounding - Significant figures - Units **[Note:]\ The activities in this section do not need to be submitted for marking as you can self-check your answers using the answer booklet available online via Connect** **\ ** Recording and enter data ------------------------ - Quantitative - data is measurements and is written as numbers. - ### Recording data - - the name of the person responsible for the sampling, testing or calibration - the time and/or date of when the sampling, testing or calibration was done - the results (may not be applicable to sampling data). - a pH recorded as 5.8 is reported as 5.8 - temperature recorded and reported from a digital thermometer is 4.7 °C - - A count of bacteria colonies on an agar plate usually needs to be processed to take into account the volume of sample used.  Important: Data entry ------------------------------------ ----------------------- ### Data traceability and coding It is critical that data is recorded in such a way that it clearly links to the relevant samples, sampling points, patients, batches or processing records. A sample is worthless unless its origin and/or history are recorded. The origin of a sample is the place and time where it was taken, such as a particular work area, site, batch or patient. The history of a sample is a record of how the sample was taken and what has been done to test it. Data must be coded to easily link it in some way to its origin and history. This is done by the use of sample numbers or IDs and clearly labelling samples to avoid confusion. The same applies to instruments like thermometers that are calibrated. These are labelled or coded so that useful calibration records can be kept. Careful coding will give you an audit trail. An audit trail is a way that you can trace any sample or result back to its source. Traceability is particularly important for two reasons: - In a quality system, you must be able to prove the reliability of your test results by being able to trace back from the result to find out exactly how tests were done and how the samples were collected. - If there is a problem with a result, it may be necessary to take some form of corrective action. For example: - If there was a food poisoning outbreak caused by salami, it would be necessary to know exactly which batch of salami caused the problem. - If a supervisor questioned the reliability of the results of your testing, you must be able to show exactly how the results were obtained, what equipment was used and whether it was in proper working order at the time. Having traceability in laboratory processes enables a laboratory to identify the original material from which the results were produced. +-----------------+-----------------+-----------------+-----------------+ | 1. **Wheat | | | | | Central | | | | | Testing | | | | | Laboratory* | | | | | * | | | | +-----------------+-----------------+-----------------+-----------------+ | **Sample | Date | **15/2/2024** | | | Record** | | | | +-----------------+-----------------+-----------------+-----------------+ | Project No. | BR-1234 | Location: | Rockbank | +-----------------+-----------------+-----------------+-----------------+ | Sample No. | **D155** | Sampled by: | **T. Brown** | +-----------------+-----------------+-----------------+-----------------+ | Sample Location | **Silo 10** | Sampling time | **1530 hrs** | +-----------------+-----------------+-----------------+-----------------+ | Comments | | | | +-----------------+-----------------+-----------------+-----------------+ +-----------------+-----------------+-----------------+-----------------+ | 2. **Wheat | | | | | Central | | | | | Testing | | | | | Laboratory* | | | | | * | | | | +-----------------+-----------------+-----------------+-----------------+ | **Moisture | Date | **15/2/2024** | | | content** (AS | | | | | 1289.2.1.6) | | | | +-----------------+-----------------+-----------------+-----------------+ | Project No. | BR-1234 | Location: | Rockbank | +-----------------+-----------------+-----------------+-----------------+ | Sample No. | **D155** | Tested by: | **J. Smith** | +-----------------+-----------------+-----------------+-----------------+ | Description: | | | | | **Silo 10** | | | | +-----------------+-----------------+-----------------+-----------------+ | Determination | **1** | **2** | **3** | | No. | | | | +-----------------+-----------------+-----------------+-----------------+ | Moisture | **9.3** | | | | content (%) | | | | +-----------------+-----------------+-----------------+-----------------+ ### Check data to identify transcription errors or atypical entries Data is only useful if it is correct and presented in the appropriate format. The quality of data relies on firstly producing or collecting accurate data and secondly, on recording and reporting this data correctly. Errors made while producing or collecting the data can be referred to as *experimental errors*. These are errors relating to sample collection, the design of surveys, instrument calibration, reagents, test procedure etc. Experimental errors can be avoided by: - ensuring that the sample is suitable for testing or processing - ensuring that the correct tests were performed on the sample - checking associated quality control data is within limits - getting test results checked for validity by a supervisor. You will learn more about how to reduce experimental errors during your practicals' sessions. [Things to remember when recording data:] - - - - - - Tip-01 Tip ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ ----- A common expression in the computer industry is **'garbage in, garbage out!'** The computer cannot fix poor data. It will just process that data to produce 'garbage' results. **Adopt the habit of always double-checking data.** +-----------------------------------+-----------------------------------+ |  | Activity 13 : Quality of data | +===================================+===================================+ | 1. Give two examples where poor | | | data will cause problems in | | | your workplace. | | | | | | -- | | | -- | | | | | | 2. List three things you can do | | | to avoid making transcription | | | errors. | | | | | | -- | | | -- | | +-----------------------------------+-----------------------------------+ ### Rectify errors in data using standard procedures Only by acknowledging errors and investigating them can we begin to understand the causes of problems. When you know what the causes of the problems are, you can put work procedures in place to ensure that, in future, the quality system works more effectively. There are a number of golden rules for handling errors in data that must be followed for an enterprise to function properly. They are not difficult rules to understand or apply and can be summed up as: 1. 2. 3. 4. +-----------------------------------------------------------------------+ | ~ZZ\ 15/07/2024~ | | | | ~~Misteak~~ Correct Answer | +-----------------------------------------------------------------------+ 5. The person making the correction must have the authority to do so and must ***sign*** the correction. 6. ***Learn*** from the error and amend processes to prevent this happening again. There are reasons why the incorrect data is not removed or completely blacked out. These are: - - - Important-01 Important --------------------------------------------------------------------------------------------------------------------------------------------------------- ----------- Honesty is always the best policy when it comes to errors in data. **Never cover up an error and always report the error promptly to your supervisor!** +-----------------------------------+-----------------------------------+ |  | **Activity 14 : Rectify errors in | | | data** | +===================================+===================================+ | -- | | | -- | | +-----------------------------------+-----------------------------------+ Scientific Notation and Powers (indices) ---------------------------------------- **Scientific notation (or standard form) expresses any number as:** +-----------------------------------+-----------------------------------+ | DidYouKnow-01 | Did you know? | +===================================+===================================+ | An easy but less technical way is | | | to move the decimal point in the | | | original number to 'make' a | | | number between 1 and 9.99999\... | | | The power of 10 is always equal | | | to the number of places the | | | decimal point has | | | moved -- positive if the decimal | | | point moves to the left, negative | | | if it moves to the right. | | +-----------------------------------+-----------------------------------+ Number 10000 1000 100 10 1 0.1 0.01 0.001 0.0001 10power 104 103 102 101 100 10-1 10-2 10-3 10-4 etc. Example: Scientific Notation 3.456 × 10-4 = 0.0003456 (divide by 10 000 or move the decimal 4 places to the left). +-----------------------------------+-----------------------------------+ | Activity-01 | **Activity 15 : Scientific | | | Notation** | +===================================+===================================+ | i. Express the following in | | | Scientific Notation (Standard | | | Form). | | | | | | 1 270 000 | | | ---- ------------- -- | | | 2 430 | | | 3 0.00008 | | | 4 0.5 | | | 5 803 000 000 | | | 6 0.000469 | | | 7 0.0205 | | | 8 0.0530 | | | 9 866 300 | | | 10 0.674 | | | | | | ii. Express as decimal numbers. | | | | | | +---------+---------+---------+ | | | | 1 | 3 × | | | | | | | 10^4^ | | | | | +=========+=========+=========+ | | | | 2 | 2 × | | | | | | | 10-^3^ | | | | | +---------+---------+---------+ | | | | 3 | 2.6 × | | | | | | | 10-^1^ | | | | | +---------+---------+---------+ | | | | 4 | 95. × | | | | | | | 10- | | | | | | | ^5^ | | | | | +---------+---------+---------+ | | | | 5 | 7.32 × | | | | | | | 10^4^ | | | | | +---------+---------+---------+ | | | | 6 | 4.3 × | | | | | | | 10^0^ | | | | | +---------+---------+---------+ | | | | 7 | 4.60 × | | | | | | | 10-^2^ | | | | | +---------+---------+---------+ | | | | 8 | 8.91 × | | | | | | | 10^3^ | | | | | +---------+---------+---------+ | | | | 9 | 1.34 × | | | | | | | 10^5^ | | | | | +---------+---------+---------+ | | | | 10 | 7.020 × | | | | | | | 10-^4^ | | | | | +---------+---------+---------+ | | +-----------------------------------+-----------------------------------+ Rounding -------- -- -- -- -- ### The use of significant figures in measurements and uncertainties - - - If a result is reported as 4.0 g (2 significant figures) this means it is not 4.1 g and not 3.9 g. However, if it was reported as 4 g (1 significant figure) we can assume that it may in fact be 3.8 g or perhaps 4.3 g as the single number 4 indicates it has been rounded to the nearest whole. - - Looking at data set A, it would be correct to assume that 1000 has 4 significant figures as it looks like results have been reported to the nearest whole number. In data set B however, it appears that results have been reported to the nearest 100. Therefore, 1000 would have 2 significant figures (as would 1200 and 1100). That is, the last 2 zeros are not significant but a result of rounding. The above guidelines show how significant figures play an important role in portraying the accuracy of a result. In a laboratory, knowledge of significant figures it is important when following methods or procedures as well as reporting results. If the procedure for preparing a reagent says weigh 4.322 g of potassium sulphate, you should get the weight as close as possible to this figure on an analytical balance. If on the other hand it says weigh 4.3 g, a top pan balance should be sufficient to weigh between 4.25 and 4.35 g. This is accurate to 2 significant figures. +-----------------------------------+-----------------------------------+ |  | **Activity 16 : Significant | | | figures** | +===================================+===================================+ | a. 183 b) 1024 c) 0.04 d) 15.301 | | | | | | -- -- -- -- | | | | | | -- -- -- -- | | | | | | -- -- -- -- | | | | | | -- -- -- -- | | +-----------------------------------+-----------------------------------+ | | | +-----------------------------------+-----------------------------------+ ### Rule for adding and subtracting ### Rule for multiplying or dividing +-----------------------------------+-----------------------------------+ | Example-01 | Example: Significant figures, | | | multiplying and dividing | +===================================+===================================+ | Thickness of one piece of paper = | | | = 0.029167 cm | | | | | | Thickness of one piece of paper = | | | 0.029 cm | | +-----------------------------------+-----------------------------------+ | | | +-----------------------------------+-----------------------------------+ +-----------------------------------+-----------------------------------+ |  | **Activity 17 : Correct use of | | | significant figures in | | | calculations** | +===================================+===================================+ | a. | | | | | | -- | | | -- | | | | | | b. | | | | | | -- | | | -- | | | | | | c. | | | | | | -- | | | -- | | | | | | d. | | | | | | -- | | | -- | | | | | | e. | | | | | | -- | | | -- | | | | | | f. | | | | | | -- | | | -- | | | | | | g. | | | | | | -- | | | -- | | | | | | h. | | | | | | -- | | | -- | | | | | | i. | | | | | | -- | | | -- | | | | | | j. | | | | | | -- | | | -- | | +-----------------------------------+-----------------------------------+ +-----------------------------------+-----------------------------------+ | Activity-01 | **Activity 18 : Significant | | | figures** | +===================================+===================================+ | 1. Round the answer to the | | | correct number of significant | | | figures. | | | | | | -- | | | -- | | | | | | 2. Comment on the usefulness of | | | weighing the ore so | | | accurately and then using a | | | measuring cylinder rather | | | than more accurate glassware. | | | | | | -- | | | -- | | +-----------------------------------+-----------------------------------+ | | | +-----------------------------------+-----------------------------------+ In reporting the results of testing or analysis, often the procedure states how many significant figures or decimal places to quote in the result. For example, a beverage procedure may specify to record the pH of the sample to one decimal place. Though you may be technically correct to quote to two decimal places, all that is required (probably at the request of the users of the data) is one place. Avoid recording results that use unnecessary (or unwarranted) precision for the purpose of the result. []{#_Toc155690034.anchor}**Why are units important?** Numbers are used frequently in everyday life and in the workplace. For these numbers to be meaningful, they must be accompanied by the correct unit. For example, if you buy a length of wood from a hardware store, you give the assistant both a number and a unit. You may ask for two metres of wood. In this case the unit is metres. If you were to leave out the unit and ask for 'two of that', the assistant would not know if you meant two metres or two yards or two feet and so on. The SI unit system ------------------ **Table 2.1: SI base units** --------------------- --------------- ------------ **Quantity** **Base Unit** **Symbol** length metre m mass kilogram kg time second s temperature kelvin K amount of substance mole mol luminous intensity candela cd electric current ampere A --------------------- --------------- ------------ You should also be familiar with the rules for using units: - - - - ### Derived units Sometimes, base units are combined. For example, area is measured in units of (metres x metres) or m2. This type of unit is called a derived unit. Some of these units are named after famous scientists. This makes the names of the units less complex. For example, in terms of base units, the unit for force would be (\[kilograms x metres\] / \[seconds x seconds\]). For simplicity, this unit is known as the newton. Some common examples of derived SI units are given in the table below. Note that the litre is not an official SI unit. The SI unit for volume is the m^3^, but the litre has been widely accepted for use within the SI system. It can have either the symbol of the uppercase or lowercase L. The symbol L avoids confusion with the number 1. **Table 2.2: A selection of SI derived units** +-----------------------+-----------------------+-----------------------+ | **Quantity** | **Derived SI unit** | **Symbol** | +-----------------------+-----------------------+-----------------------+ | volume | cubic metre | m3 | +-----------------------+-----------------------+-----------------------+ | pressure | pascal | Pa | +-----------------------+-----------------------+-----------------------+ | energy | joule | J | +-----------------------+-----------------------+-----------------------+ | force | newton | N | +-----------------------+-----------------------+-----------------------+ | power | watt | W | +-----------------------+-----------------------+-----------------------+ | density | kilogram per cubic | kg/m3 | | | metre | | +-----------------------+-----------------------+-----------------------+ | area | square metre | m2 | +-----------------------+-----------------------+-----------------------+ | velocity | metre per second | m/s | +-----------------------+-----------------------+-----------------------+ | voltage | volt | V | +-----------------------+-----------------------+-----------------------+ | electrical resistance | ohm | Ω | +-----------------------+-----------------------+-----------------------+ | electrical | siemens | S | | conductance | | | +-----------------------+-----------------------+-----------------------+ | electrical charge | coulomb | C | +-----------------------+-----------------------+-----------------------+ | electrical | farad | F | | capacitance | | | +-----------------------+-----------------------+-----------------------+ | frequency | hertz | Hz | +-----------------------+-----------------------+-----------------------+ | inductance | henry | H | +-----------------------+-----------------------+-----------------------+ | magnetic flux | weber | Wb | +-----------------------+-----------------------+-----------------------+ | magnetic flux density | tesla | T | +-----------------------+-----------------------+-----------------------+ |  | Significant figures** | | +-----------------------+-----------------------+-----------------------+ | Complete the table | | | | below. Include the | | | | symbol e.g. a litre | | | | of volume (L), a | | | | hectare of area (ha) | | | | and an atmosphere of | | | | pressure (atm). | | | | Record whether the | | | | unit is an SI unit or | | | | not. | | | | | | | | ------------------- | | | | ----- --------------- | | | | ------------- ------- | | | | ----- ------------- - | | | | - -- -- -- | | | | **Quantity** | | | | **Unit used in | | | | workplace** **Symbo | | | | l** **SI Unit** | | | | | | | | amount of substance | | | | | | | | | | | | | | | | | | | | area | | | | | | | | | | | | | | | | | | | | density | | | | | | | | | | | | | | | | | | | | electric current | | | | | | | | | | | | | | | | | | | | electrical capacita | | | | nce | | | | | | | | | | | | | | | | electrical conducta | | | | nce | | | | | | | | | | | | | | | | electrical resistan | | | | ce | | | | | | | | | | | | | | | | energy | | | | | | | | | | | | | | | | | | | | force | | | | | | | | | | | | | | | | | | | | frequency | | | | | | | | | | | | | | | | | | | | inductance | | | | | | | | | | | | | | | | | | | | length | | | | | | | | | | | | | | | | | | | | luminous intensity | | | | | | | | | | | | | | | | | | | | magnetic flux | | | | | | | | | | | | | | | | | | | | magnetic flux densi | | | | ty | | | | | | | | | | | | | | | | mass | | | | | | | | | | | | | | | | | | | | pressure | | | | | | | | | | | | | | | | | | | | power | | | | | | | | | | | | | | | | | | | | temperature | | | | | | | | | | | | | | | | | | | | time | | | | | | | | | | | | | | | | | | | | velocity | | | | | | | | | | | | | | | | | | | | voltage | | | | | | | | | | | | | | | | | | | | volume | | | | | | | | | | | | | | | | | | | | ------------------- | | | | ----- --------------- | | | | ------------- ------- | | | | ----- ------------- - | | | | - -- -- -- | | | +-----------------------+-----------------------+-----------------------+ ### ### SI prefixes After performing Activity 19, you have probably found that you do not always use SI units in the workplace. This is sometimes because the SI unit is not of an appropriate size. For example, if you were dispensing liquids, cubic metres would not be a convenient unit to use. SI units can be made more convenient by the use of standard SI prefixes which indicate the multiples or submultiples of the unit. For example, a small length can be measured in units of millimetres (mm). The prefix milli (measuring one thousandth) together with the standard unit (metre) now represents the smaller, convenient unit of length. That is, 1 mm = one thousandth of a metre (1/1000 m). A list of commonly used standard SI prefixes is given in the table below. It is important to write prefixes correctly. For example, km not Km. **Table 2.3: Standard SI prefixes** ------------ ------------ -------------------------------------------- **Prefix** **Symbol** **Factor** giga G 10^9^ (one thousand million) 1 000 000 000 mega M 10^6^ (one million) 1 000 000 kilo k 10^3^ (one thousand) 1000 milli m 10^-3^ (one thousandth) micro μ 10^-6^ (one millionth) nano n 10^-9^ (one thousand millionth) ------------ ------------ -------------------------------------------- +-----------------------------------+-----------------------------------+ | Activity-01 | **Activity 20 : Prefixes in your | | | workplace** | +===================================+===================================+ | Did you use any of these prefixes | | | in your laboratory sessions? It | | | may help you to look at your | | | answers to the previous activity. | | | | | | List the prefixes you used. | | | | | | -- | | | -- | | +-----------------------------------+-----------------------------------+ ### ### Converting SI units There are two types of conversion we can make. These are: - from the SI unit to the multiple/submultiple - from the multiple/submultiple to the SI unit. We will discuss each of these in turn. Before we do this, it is worthwhile noting that Australian Standard AS ISO 1000 - 1998 *The International system of units (SI) and its application* suggests numbers are expressed in the range 0.1- 1000 for convenience. For example, 27 MPa not 27,000 kPa. When doing calculations however, errors are more easily avoided if all quantities in the calculation are expressed in SI units with scientific notation instead of using prefixes. Expressing numbers correctly therefore involves being able to convert between appropriate prefixes. ### Multiples and submultiples -------------------------------------------------------------------------  Di