Numerical Values and Metric Systems PDF

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Qalqilia Secondary Industrial School

Dr. Yahia A. Kaabi

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numerical values metric systems laboratory math science

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This document provides an introduction to numerical values and metric systems, specifically for clinical laboratory settings. It covers topics such as unit conversion, significant figures, scientific notation, and more.

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Numerical Values and Metric Systems Introduction The clinical laboratory uses measurements in almost all aspects of its operations. Measurements commonly made in the lab include: Concentration of substances Volume of a solution Weight of a substance or object Numbe...

Numerical Values and Metric Systems Introduction The clinical laboratory uses measurements in almost all aspects of its operations. Measurements commonly made in the lab include: Concentration of substances Volume of a solution Weight of a substance or object Numbers of cells Size or length of an object Temperature Time Use of Measurements Measurements made in the clinical laboratory have a direct impact on the quality of patient care. Laboratory results can be a basis for establishing a diagnosis and are also used to follow the course of disease and prescribe appropriate treatment. The measurements must be reliable, accurate, precise, and easily standardized. Introduction Test results report measurements of concentration, number, weight, volume, and size when indicating numbers and types of cells or indicating quantities of substances in a patient’s blood, serum, or other body fluids. These measurements are then compared to reference (normal) values to aid in assessing a patient’s condition Quantitative laboratory results Meaningful quantitative laboratory results most have two main component: 1.6 g/dL Unit of Number express ion Define physical quantity or dimension Numeric value (e.g. mass, length, or volume) Number, Figure and Digit Digit: each individual symbol (or character) that makes a number. 0 1 2 3 4 5 6 7 8 9 Number: one or more than one digits together used to describe quantity 7 - 2507 2,507.38 Figure: representative number used to explain data and must be a result of a calculation. 15,000 people 2,000 km 31.5$ Decimals Decimal place value A decimal number system is used to express the whole number and fraction of one together. Tenth place Whole number part Hundredths place Thousands 1,445.871 place Decimal/fractional number part Thousands Separator Comma Decimal Point The dot in a decimal number is called a decimal point. Digits following the decimal point show a value smaller than one. Question: The digit 9 in which number represents a value of 0.009? A- 1.739 B- 3.097 9.871 Significant Figures The significant figures are digits of a number that contribute to the accuracy and precision of the measured value. It in a measurement include all of the digits that are known, plus a last digit that is estimated. The higher the significant figures the higher accuracy of the measured value. Significant Figures The width of the door can be expressed as: 0.8 m for meter stick “a” because 0 is known and.8 is estimated 0.77 m for meter stick “b” because 0.7 is known and 0.07 is a. estimated 0.772 m for meter b. stick “c” because 0.77 is known and.2 is c. estimated Significant Figures Rules 1. All non-zero digits are always significant. 647.23 cm 76 m 12.1 g 2. Zeros between non-zero digits are always significant. 7,003 mmole 5,085 g 3. Leading zeros are never significant. 0.000045 m (45x10-6) 0091 kg 4. Trailing zeros are not significant, EXCEPT if the number contains a decimal point. 2000 mm (2 m) 0.00500 kg 2.30 x 10-5 s 100.000 s Which ZERO digits are NOT significant figures? Leading zeros before real numbers Example 0.000231 Trailing zeros after real numbers if no decimal is written- Example 1,000,000 Significant Figures Each of these measurements has only two significant figures: 0.0071 meter = 7.1 x 10-3 meter 0.42 meter = 4.2 x 10-1 meter 0.000099 meter = 9.9 x 10-5 meter These are All digits are leading zeros significant using scientific notation Significant Figures The zeros in these measurements are not significant: WHY? 300 meters (one significant figure) 7,000 meters (one significant figure) 27,210 meters (four significant figures) No captured zeros nor trailing zeros, no decimal points! Question: How many significant figures are in each measurement? a. 123 m 3 b. 40,506 mm 5 c. 9.8000 x 104 m 5 d. 0.007 g 1 e. 0.07080 m 4 f. 98,000 m 2 Rounding Often necessary to round off numbers when performing calculation in clinical lab especially if hand calculators are used in order to produce a lab result with appropriate number of digits or signification figures. Calculated results are more precise than measured data, thus, measurements must always be reported to the correct number of significant figures. Example: Suppose measured blood glucose for a patient is 122 g/dL and you want to express data in mmole/L, the conversion factor is 18.018. 122 / 18.018 = 6.771006771 mmole/L However, blood glucose usually expressed in two sig-fig in mmole/L format (e.g. 7.0, 5.8, or 3.1), therefore rounding to 2 sig-fig is needed. 6.8 mmole/L is the most appropriate result to report Rules for Rounding Off 1. If the number to be dropped is 5, the preceding number raised by one. 3. If the number to be dropped equals 5: - and the preceding number is ODD, the preceding number raised by one. - and the preceding number is EVEN, the preceding number remains the same. Rounding Measurements To round a number, first decide how many significant figures the answer should have. Example: Round off each measurement to the number of significant figures shown. a. 314.721 meters (four) 314.7 b. 0.001 775 meter (two) 0.001 8 m 1.8x10-3 m 1.8 mm c. 8792 grams (two) 8800 g 8.8x103 g 8.8 kg SI Units The 200 years old, Système International d'Unités (SI), adopted internationally in 1960, is the most commonly used system of units. The SI provide a uniform method of describing physical quantities. The SI metric system composed of seven fundamental SI units and additional derived and accepted Non-SI units. SI Units Prefixes The SI units most commonly used in medicine are the Liter (L) gram (g) meter (m) mole (mol) A prefix used to identify multiples of the original unit or fractions of the original unit. Larger units kilo means 1000. Therefore, a kilometer (km) is 1000 meters or 10³ meters, a kilogram (kg) is 1000 grams, a kiloliter (kL) is 1000 liters. Although “kilo” is the prefix most commonly used for large units, “Deca” can be used to indicate the unit times 10, as in decaliter. “Hecto” indicates the unit times 100. The prefixes and their definitions are the same for the three basic units. Smaller Units In laboratory analyses, it is more common to measure units smaller than the basic units. milli, which means one-thousandth (0.001 or 10-3) centi, which means one-hundredth (0.01 or 10-2) deci, which means one-tenth (0.1 or 10 -1). A milliliter is 0.001 liter, or 10-3 liter Micro, denotes one-millionth or 10-6 Nano, 10-9 pico, 10-12 femto, 10-15 Small samples are measured in microliters Converting Units To convert smaller to larger units, e.g grams to kilograms or milliliters to liters, divide by the difference between the values of the prefixes or move the decimal point to the left places by the number of zeros. Example: Convert 50.0 g to …. Kg 50 / 1000 = 0.050 kg Convert 19125.0 ng to.. mg 0.19125/1,000,000= 0.019125 mg =19.1 x10-3 mg To convert larger to smaller units multiply by the value of the prefix or move the decimal point to the right by the same number of zeros. Example: Convert 0.05110 g to … mg 0.05110 x 1,000 = 51.10 mg Convert 43 x10-4 L to …. uL 43 x 100 = 4300 uL SI Units and English Units Equivalent Quantitiy SI unit English Unit 1 m = 3.281 feet (ft) 1.6 km= 1 mile (mi) Length Meter (m) 0.9 m = 1 yard (yd) 2.54 cm = 1 inch (in) 454 g = 1 pound (lb) Mass Gram (g) 28 g = 1 ounce (oz) 3.78 L = 1 gallon (gal) 0.95 L = 1 quart (qt) Volume Liter (L) 30 mL = 1 fluid ounce (fl oz) 5 mL = 1 teaspoon (tsp) Temperature and time units Temperature is measured using either the Fahrenheit (F) scale or the Celsius (C) scale. The Fahrenheit temperature scale has a boiling point of 212° F and a freezing point of 32° F. The Fahrenheit scale is used most commonly in the US. The Celsius scale, used in most countries other than US, has a boiling point of 100° C and a freezing point of 0° C. It is used for making most scientific temperature measurements e.g. Reaction temperature, incubation, and boiling points. To convert from F to C use the formula: C = 5/9 (F- 32) To convert from C to F use the formula: F = 9/5 (C) + 32 Temperature conversion Question 1: Convert 98.6°F (normal body temperature) to Celsius (C) degrees. C = 5/9 (98.6 – 32) C= 5/9 (66.6) C= 36.99 or 37 ºC Question 2: Convert 37°C to Fahrenheit (F) degrees. F= 9/5 (37) + 32 F= 66.6 + 32 F= 98.6 ºF Standardized reporting of laboratory results The Clinical and Laboratory Standards Institute (CLSI) has published guidelines for uniform reporting of clinical laboratory results using SI units. Blood cell counts have traditionally been expressed as the number of cells per cubic millimeter (cu mm) of blood. In the SI system, however, cell counts are expressed as number of cells per liter of blood. Chemical substances such as bilirubin, protein or glucose, which are expressed as milligrams per deciliter (dL) or per 100 mL, now recommended to be reported as milligrams or grams per liter or as micromoles (µmol) or millimoles (mmol) Laboratory Math and Reagents Preparation Dr. Yahia A. Kaabi Solution Preparation Lab math and calculations is especially needed when preparing solutions in clinical laboratory. There are several methods of preparing laboratory solutions, including dilutions, ratios, percent solutions, and molar solutions. Follow all safety rules and quality assessment guidelines when preparing solutions. Use volumetric and glassware sensitive balances capable of weighing +- 0.0001 g quantities will ensure that the reagent will be the expected range of calculated concentration. Use appropriate significant figures will yield a realistic estimate of the expected concentration range. Changing Concentrations Sometimes it is necessary to prepare a diluted solution from a concentrated stock solution. The following formula can be used: V1 x C1 = V2 x C2 Where; V1 = Volume of stock solution V2 = volume of the new solution required C1 = Concentration of the stock solution C2 = Concertation of the solution to be prepared Prepare 100 mL of 0.1 M HCl using a 1 M HCl stock solution. (V1) (1 M) = (100 mL) (0.1 M) V1= (100 x 0.1) / 1 = 10 mL 10 mL of 1M HCl is added to 90 mL of H 2O to make 100 mL of 0.1 M HCl solution. Changing Concentrations Prepare 250.0 mL of a 0.435 M solution of HNO 3 by diluting a stock concentrated HNO3 with molarity of 15.7 M. V1 x C1 = V2 x C2 V1 x 15.7 = 250 x 0.435 V1 = (250 x 0.435) / 15.7 = 6.93 mL HNO3 stock. Dilutions Sometimes it necessary to make sample dilutions, especially for serum sample who are lipemic or have higher values a specific analyte exceeding the capacity of the instrument to read. A dilution is usually expressed as a ratio, proportion, or fraction. For example, if a serum has been diluted 1:5, it means that 1 part of the serum has been combined with 4 parts of a diluent to create 5 total parts. A simple formula for calculating dilutions: = C A = volume of substance being diluted B = volume of diluent added C = The dilution factor, expressed as a fraction (A and B must be in the same units of volume) Dilutions Example : Patient sample from the morning glucose run was out of the linear range of the assay (>600 mg/dL). Make 1:3 dilution of the sample and reanalyze the sample and report the result? Add 0.1 mL of sample to 0.2 mL of saline to give total volume of 0.3 mL. 0.1/(0.1+0.2) = 1/3 (dilution factor) Suppose the new results was 364 mg/dL what is the glucose value in the patient sample? Multiply the new result x dilution factor  1092 mg/dL Serial Dilutions In a serial dilution, a sample is diluted number of times by the same dilution factor. Usually used in immunology or microbiology labs to find the titer of a particular component in the sample. The titer is the measure of reactivity or strength of the component and is reported as the reciprocal of the highest dilution giving a reaction. If a tube containing a 1/16 dilution is the last one showing a reaction, the titer is 16. Titers are often used in immunology to indicate the level of a particular antibody in a serum sample. Dilutions of serum are used in certain tests such as measuring levels of antibodies the rheumatoid factor (RF) test for rheumatoid arthritis. Serial Dilutions Example to make two fold dilution of serum Set up 9 tubes, each containing one mL of diluent. Transfer one mL of patient serum to tube 1. Mix serum and diluent, and transfer one mL of the mixture to tube 2. Repeat the procedure, transferring one mL each time after mixing with diluent. Discard one mL from the last tube. When dilution series is complete, each of the nine tubes should contain one mL. The titer, 1ml Serum 1ml 1ml ml 1ml 1ml 1ml the reciprocal of1mlthe highest 1ml 1ml 1m dilution giving the desired reaction, would be reported as 64. Discard Serum 1:2 1:4 1:8 1:16 1:32 1:64 1:128 1:256 1:512

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