1. Unit #3 - Basic Clinical Laboratory Math
Author:
Cecile Sanders, M.Ed., MLS(ASCP),
Revised 11/03/2016

2. Metric System Most countries use the metric system for measurement
Examples:
Gasoline by liter
Body weight in kilograms
Distance in meters or kilometers
U.S. uses English system of measurement in everyday life
Gasoline in gallons
Weight in pounds
Distance in miles

3. Metric System
English system of measurement is not accurate enough for most scientific measurements
Because metric system is a decimal system, it can be used for very small quantities with accuracy
International System of Units (SI) is a form of the metric system adopted for use by the worldwide scientific community.

4. Units of Metric System Base Units
Distance = meter (m)
Mass or Weight = gram (g)
Volume = liter (L)
Prefixes are used to indicate larger or smaller quantities of the base units above

5. Common Metric Prefixes
Kilo (k) = 1000 x base unit
Centi (c) = .01 x base unit
Milli (m) = .001 x base unit
Micro (µ) = x base unit
Nano (n) = x base unit
Pico (p) = x base unit

6. Converting within Metric System
Move decimal to left Move decimal to right
King Henry Dances BOLDLY Down Center Main * * Micro
(kilo)(hecto)(deca) BASE (deci) (centi) (milli)* * (micro)
Example:
Convert Kilograms to Grams: Move decimal 3 places to right
Convert Centimeters to Meters: Move decimal 2 places to left

7. Converting between English and Metric Systems
Mile x 1.6 = kilometers
Pound x = kilograms
Quart x 0.95 = liters
Kilometer x 0.6 = miles
Meter x 3.3 = feet
Meter x = inches
Centimeter x 0.4 = inches
Gram x = pounds
Liter x 1.06 = quarts

8. SI System (International System)
Base Units of the SI System
Length = Meter (m)
Mass = Kilogram (kg)
Time = Second (s)
Amount of Substance = Mole (mol)
Electric Current = Ampere (A)
Temperature = Kelvin (K)*
Luminous Intensity = Candela (cd)
Volume = Liter (L)**
*Although Kelvin is the SI unit, Celsius (C) is used almost exclusively in the clinical laboratory.
**Liter (L) was not included in the list of base units in the SI system because the liter is a unit derived from other units. However, the liter has been accepted for use in measuring volume.

9. SI System (International System)
All units in the SI system can be qualified by standard prefixes (as shown on slide #5) that serve to convert values to more convenient forms, depending on the size of the object being measured.
Commas are not used as spacers in recording large numbers; instead, groups of three digits are separated by spaces.

10. SI System (International System)
Non-SI units accepted in the clinical laboratory
Minutes (min)
Hours (hr)
Days (d)
Liter (L)
Pressure (mm Hg)
Enzyme Activity (IU) – International Unit

11. Temperature Conversion
To convert from Fahrenheit to Centigrade:
C0 = 5/9(F0-32)
To convert from Centigrade to Fahrenheit:
F0 = 9/5(C0) + 32

12. Dilutions for the Clinical Laboratory
Dilution = making weaker solutions from stronger ones
Example: Making orange juice from frozen concentrate. You mix one can of frozen orange juice with three (3) cans of water.

13. Dilutions for the Clinical Laboratory (cont’d)
Dilutions are expressed as the volume of the solution being diluted per the total final volume of the dilution
In the orange juice example on the previous slide, the dilution would be expressed as 1/4, for one can of O.J. to a TOTAL of four cans of diluted O.J. When saying the dilution, you would say, in the O.J. example: “one in four”.

14. Dilutions for the Clinical Laboratory (cont’d)
Another example:
If you dilute 1 ml of serum with 9 ml of saline, the dilution would be written 1/10 or said “one in ten”, because you express the volume of the solution being diluted (1 ml of serum) per the TOTAL final volume of the dilution (10 ml total).

15. Dilutions for the Clinical Laboratory (cont’d)
Another example:
One (1) part of concentrated acid is diluted with 100 parts of water. The total solution volume is 101 parts (1 part acid parts water). The dilution is written as 1/101 or said “one in one hundred and one”.

16. Dilutions for the Clinical Laboratory (cont’d)
Notice that dilutions do NOT have units (cans, ml, or parts) but are expressed as one number to another number
Example: 1/10 or “one in ten”

17. Dilutions for the Clinical Laboratory (cont’d)
Dilutions are always expressed with the original substance diluted as one (1). If more than one part of original substance is initially used, it is necessary to convert the original substance part to one (1) when the dilution is expressed.

18. Dilutions for the Clinical Laboratory (cont’d)
Example:
Two (2) parts of dye are diluted with eight (8) parts of diluent (the term often used for the diluting solution). The total solution volume is 10 parts (2 parts dye + 8 parts diluent). The dilution is initially expressed as 2/10, but the original substance must be expressed as one (1). To get the original volume to one (1), use a ratio and proportion equation, remembering that dilutions are stated in terms of 1 to something:
______2 parts dye = ___1.0___
10 parts total volume x
2 x =
x =
The dilution is expressed as 1/5.

19. Dilutions for the Clinical Laboratory (cont’d)
The dilution does not always end up in whole numbers.
Example:
Two parts (2) parts of whole blood are diluted with five (5) parts of saline. The total solution volume is seven (7) parts (2 parts of whole blood + 5 parts saline). The dilution would be 2/7, or, more correctly, 1/3.5. Again, this is calculated by using the ratio and proportion equation, remembering that dilutions are stated in terms of 1 to something:
__2 parts blood_____ = ___1.0___
7 parts total volume x
2 x =
x =
The dilution is expressed as 1/3.5

20. Dilutions for the Clinical Laboratory (cont’d)
Dilution Factor – used to correct for having used a diluted sample in a lab test rather than the undiluted sample. The result (answer) using the diluted sample must be multiplied by the RECIPROCAL of the dilution made.
The RECIPROCAL of a 1/5 dilution is 5.

21. Dilutions for the Clinical Laboratory (cont’d)
Correction for using a diluted sample
Example: A technician performed a laboratory analysis of patient’s serum for a serum glucose (blood sugar) determination. The patient’s serum glucose was too high to read on the glucose instrument. The technician diluted the patient’s serum 1/2 and re-ran the diluted specimen, obtaining a result of 210 g/dl. To correct for the dilution, it is necessary to multiply the result by the dilution factor (in this case x 2). The final result is 210 g/dl x 2 = 420 g/dl.

22. Dilutions for the Clinical Laboratory (cont’d)
Sometimes it is necessary to make a dilution of an existing solution to make it weaker.
Example: A 100 mg/dl solution of substrate is needed for a laboratory procedure. All that is available is a 500 mg/dl solution of substrate. A dilution of the stronger solution of substrate is needed.

23. Dilutions for the Clinical Laboratory (cont’d)
To make a weaker solution from a stronger one, use this formula:
V1 x C1 = V2 x C2
Example: To make 100 ml of the 100 mg/dl solution from the 500 mg/dl solution needed in the previous example:
V1 = 100 ml V2 = V2 (unknown)
C1 = 100 mg/dl C2 = 500 mg/dl
100 ml x 100 mg/dl = V2 x 500 mg/dl
V2 = 20 ml
Dilute 20 ml of 500 mg/dl solution up to 100 ml with water to obtain 100 ml of 100 mg/dl substrate solution

24. Serial Dilutions
Dilutions can be made singly (as shown previously) or in series, in which case the original dilution is diluted further. A general rule for calculating the dilution of solutions obtained by diluting in a series is to MULTIPLY the original dilution by subsequent dilutions.

25. Serial Dilutions (cont’d)
Example of a serial dilution:

26. Serial Dilutions (cont’d)
In the serial dilution on the previous slide, 1 ml of stock solution is mixed with 9 ml of diluent, for a 1/10 dilution. Then 1 ml of the 1/10 dilution is mixed with another 9 ml of diluent. The second tube also has a 1/10 dilution, but the concentration of stock in the second tube is 1/10 x 1/10 for a 1/100 dilution.

27. Serial Dilutions (cont’d)
Continuing with the serial dilution, in the third tube, you mix 1 ml of the 1/100 dilution from the second tube with 9 ml of diluent in the third tube. Again you have a 1/10 dilution in the third tube, but the concentration of stock in the third tube is 1/10 x 1/10 x 1/10 for a 1/1000 dilution.
This dilution could be carried out over many subsequent tubes.

28. Serial Dilutions (cont’d)
Serial dilutions are most often used in serological procedures, where technicians need to make dilutions of patient’s serum to determine the weakest concentration that still exhibits a reaction of some type. The RECIPROCAL of the weakest concentration exhibiting a reaction is called a “titer”.

29. Serial Dilutions (cont’d)
Example of determining a titer:
A technician makes a serial dilution using patient serum:
Tube #1 = 1/10
Tube #2 = 1/100
Tube #3 = 1/1000
Tube #4 = 1/10,000
Tube #5 = 1/100,000
Reactions occur in tubes 1 through 3, but NOT in tubes 4 or 5. The titer = 1000.

30. Rounding Off Numbers
Sometimes it is necessary to round off insignificant digits in order not to imply an accuracy greater than the test is capable of delivering.
When the digit next to the last one to be retained is less than 5, the last digit should be left unchanged.
Example: is rounded off to 7.86

31. Rounding Off Numbers (cont’d)
When the digit next to the last one to be retained is greater than 5, the last digit is increased by 1.
Example: is rounded off to 7.867
If the additional digit is 5, the last digit reported is changed to the nearest even number.
Example: is rounded off to 23.2
Example: is rounded off to 23.4

32. Basic Clinical Laboratory Math Assignment
The assignment for this Clinical Laboratory Math unit is found in the “Assignments” folder at the bottom of the menu. All instructional material may be used for this assignment. Please complete it by the deadline listed on the Schedule.
As always, for help, or call or

33. Basic Clinical Laboratory Math
Resources
Mathematics for the Clinical Laboratory, Doucette, L. J., Saunders, Third Edition, 2016
Essential Laboratory Mathematics, Johnson, Timmons, and Hall, Waveland Press, Second Edition, 2010