Numerical Values and Metric Systems PDF

**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 subst...

**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:  Number, Figure and Digit ======================== - ***Digit***: each individual symbol (or character) that makes a number. - ***Number***: one or more than one digits together used to describe quantity - ***Figure*:** representative number used to explain data and must be a result of a calculation. **15,000 people 2,000 km 31.5\$** Decimals ======== - A decimal number system is used to express the whole number and fraction of - The dot in a decimal number is called a decimal point. - Digits following the decimal point show a value smaller than one. - The digit 9 in which number represents a value of 0.009? 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 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" - 0.772 m for meter stick "c" Significant Figures Rules ------------------------- 1. All non-zero digits are always significant. 2. Zeros between non-zero digits are always significant. 7,003 mmole 5,085 g 3. Leading zeros are never significant. **0.0000**45 m (45x10-6) **00**91 kg 4. Trailing zeros are not significant, EXCEPT if the number contains a - 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 ------------------- 0.000099 meter = 9.9 x 10^-5^ meter Significant Figures ------------------- a. 123 m b. 40,506 mm c. 9.8000 x 104 m d. 0.007 g e. 0.07080 m f. 98,000 m 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: 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. - To round a number, first decide how many significant figures the answer should have. a. 314.721 meters (four) b. 0.001775 meter (two) c. 8792 grams (two) - 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 (µL) - Wavelengths of light are measured in nanometers (nm) ### 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. - 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. ### SI Units and English Units Equivalent +-----------------------+-----------------------+-----------------------+ | | Meter (m) | 1 m = 3.281 feet (ft) | | | | | | | | 1.6 km= 1 mile (mi) | | | | | | | | 0.9 m = 1 yard (yd) | | | | | | | | 2.54 cm = 1 inch (in) | +-----------------------+-----------------------+-----------------------+ | | Gram (g) | 454 g = 1 pound (lb) | | | | | | | | 28 g = 1 ounce (oz) | +-----------------------+-----------------------+-----------------------+ | | Liter (L) | 3.78 L = 1 gallon | | | | (gal) | | | | | | | | 0.95 L = 1 quart (qt) | | | | | | | | 30 mL = 1 fluid ounce | | | | (fl oz) 5 mL = 1 | | | | teaspoon (tsp) | +-----------------------+-----------------------+-----------------------+ - Temperature is measured using either the Fahrenheit (F) scale or the Celsius - The Fahrenheit temperature scale has a boiling point of 212° F and a - The Fahrenheit scale is used most commonly in the US. - The Celsius scale, used in most countries other than US, has a boiling point - 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: - To convert from C to F use the formula: Temperature conversion ====================== - Question 1: Convert 98.6°F (normal body temperature) to Celsius #### C = 5/9 (98.6 -- 32) - Question 2: Convert 37°C to Fahrenheit (F) degrees. F= 9/5 (37) + 32 #### F= 66.6 + 32 ### 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) per liter. Dr. Yahia A. Kaabi Solution Preparation -------------------- - Lab math and calculations is especially needed when preparing solutions - 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; Changing Concentrations ======================= 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: ^𝐴^Τ𝐴+𝐵 = C Dilutions ========= 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 - 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 - 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, the reciprocal of the highest dilution giving the desired reaction, would be reported as 64. Discard