Unit #3 - Basic Clinical Laboratory Math Cecile Sanders, M.Ed., MLS(ASCP)

Unit #3 - Basic Unit #3 - Basic Clinical Laboratory Clinical Laboratory

MathMathCecile Sanders, M.Ed., MLS(ASCP)Cecile Sanders, M.Ed., MLS(ASCP)

Metric SystemMetric System

– Most countries use the metric system for Most countries use the metric system for measurementmeasurement Examples:Examples:

– Volume in litersVolume in liters– Weight in grams or kilograms Weight in grams or kilograms – Distance in meters or kilometersDistance in meters or kilometers

– U.S. uses English system of measurement in U.S. uses English system of measurement in everyday lifeeveryday life Examples:Examples:

– Volume in pints, quarts or gallonsVolume in pints, quarts or gallons– Weight in ounces or poundsWeight in ounces or pounds– Distance in feet or milesDistance in feet or miles

Metric SystemMetric System

– English system of measurement is not English system of measurement is not accurate enough for most scientific accurate enough for most scientific measurementsmeasurements

– Because metric system is a decimal Because metric system is a decimal system, it can be used for very small or system, it can be used for very small or very large quantities with accuracyvery large quantities with accuracy

– International System of Units (SI) is a International System of Units (SI) is a form of the metric system adopted for form of the metric system adopted for use by the worldwide scientific use by the worldwide scientific community.community.

Units of Metric SystemUnits of Metric System

– Base UnitsBase Units Distance = meter (m)Distance = meter (m) Mass or Weight = gram (g)Mass or Weight = gram (g) Volume = liter (L)Volume = liter (L)

– Prefixes are used to indicate larger or Prefixes are used to indicate larger or smaller quantities of the base units smaller quantities of the base units aboveabove

Common Metric PrefixesCommon Metric Prefixes

– Kilo (k) = 1000 x base unitKilo (k) = 1000 x base unit– Centi (c) = .01 x base unitCenti (c) = .01 x base unit– Milli (m) = .001 x base unitMilli (m) = .001 x base unit– Micro (µ) = .000001 x base unitMicro (µ) = .000001 x base unit– Nano (n) = 10 Nano (n) = 10 -9 -9 x base unitx base unit– Pico (p) = 10Pico (p) = 10-12-12 x base unit x base unit

Converting within Metric Converting within Metric SystemSystem

There are many different formulas used to convert units within the metric system. You may have learned one in a math class, perhaps in high school or at ACC.

Please feel free to use whatever system you may already know and be comfortable with. If, however, you are NOT comfortable with a system, consider using the diagram on the next following page. It includes a mnemonic (a sentence that helps to remember a list, such as the prefixes for the metric system).


The mnemonic for the prefixes for the metric system is “King Henry Dances Boldly Down Center Main”. The first letter of each word refers to a metric prefix, such as the “K” in King refers to “kilo”, the “H” in Henry refers to “hecto”, etc.

The word “Boldly” is used to refer to the metric “base” used, which is METER, LITER, or GRAM. (See slide 4 in this presentation)

Since the prefixes between “milli”, as in “Main” in the mnemonic, and “micro” are seldom used, I have inserted two asterisks (* *) so you will remember to add two more decimal spaces when converting to or from the “micro” metric unit.


Move decimal to leftMove decimal to left Move decimal to rightMove decimal to right

King Henry Dances BOLDLY Down Center Main * * MicroKing Henry Dances BOLDLY Down Center Main * * Micro (kilo)(hecto)(deca) BASE (deci) (centi) (milli)* * (micro)(kilo)(hecto)(deca) BASE (deci) (centi) (milli)* * (micro)

Example:Example:Convert Kilograms to Grams: Move decimal 3 places to rightConvert Kilograms to Grams: Move decimal 3 places to rightExample:Example:Convert Centimeters to Meters: Move decimal 2 places to leftConvert Centimeters to Meters: Move decimal 2 places to leftExample:Example:Convert Microliters to Centiliters: Move decimal 4 places to the Convert Microliters to Centiliters: Move decimal 4 places to the

leftleft

Converting between English Converting between English and Metric Systemsand Metric Systems

Mile x 1.6 = kilometersMile x 1.6 = kilometers Pound x 0.454 = kilogramsPound x 0.454 = kilograms Quart x 0.95 = litersQuart x 0.95 = liters Kilometer x 0.6 = milesKilometer x 0.6 = miles Meter x 3.3 = feetMeter x 3.3 = feet Meter x 39.37 = inchesMeter x 39.37 = inches Centimeter x 0.4 = inchesCentimeter x 0.4 = inches Gram x .0022 = poundsGram x .0022 = pounds Liter x 1.06 = quartsLiter x 1.06 = quarts

SI SystemSI System (International System) (International System)

Base Units of the SI SystemBase Units of the SI System– Length = Meter (m)Length = Meter (m)– Mass = Kilogram (kg)Mass = Kilogram (kg)– Time = Second (s)Time = Second (s)– Amount of Substance = Mole (mol)Amount of Substance = Mole (mol)– Electric Current = Ampere (A)Electric Current = Ampere (A)– Temperature = Kelvin (K)*Temperature = Kelvin (K)*– Luminous Intensity = Candela (cd)Luminous Intensity = Candela (cd)– Volume = Liter (L)**Volume = Liter (L)**

*Although Kelvin is the SI unit, Celsius (C) is used almost *Although Kelvin is the SI unit, Celsius (C) is used almost exclusively in the clinical laboratory.exclusively in the clinical laboratory.

**Liter (L) was not included in the list of base units in the SI **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. system because the liter is a unit derived from other units. However, the liter has been accepted for use in measuring However, the liter has been accepted for use in measuring volume.volume.


All units in the SI system can be All units in the SI system can be qualified by standard prefixes (as shown qualified by standard prefixes (as shown on slide #5) that serve to convert values on slide #5) that serve to convert values to more convenient forms, depending on to more convenient forms, depending on the size of the object being measured.the size of the object being measured.

Commas are not used as spacers in Commas are not used as spacers in recording large numbers; instead, recording large numbers; instead, groups of three digits are separated by groups of three digits are separated by spaces.spaces.


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

Temperature ConversionTemperature Conversion

To convert from Fahrenheit to Centigrade:To convert from Fahrenheit to Centigrade:

CC00 = 5/9(F = 5/9(F00-32)-32)(Remember to do the math function (Remember to do the math function

INSIDE parentheses FIRST – That is, INSIDE parentheses FIRST – That is,

subtract 32 from degrees Fahrenheit FIRST;subtract 32 from degrees Fahrenheit FIRST;

then multiply by 5/9)then multiply by 5/9)

To convert from Centigrade to Fahrenheit:To convert from Centigrade to Fahrenheit:

FF00 = 9/5(C = 9/5(C00) + 32) + 32(Multiply degrees Centigrade by 9/5 FIRST; then add (Multiply degrees Centigrade by 9/5 FIRST; then add 32)32)

Dilutions for the Clinical Dilutions for the Clinical LaboratoryLaboratory

Dilution = making weaker solutions Dilution = making weaker solutions from stronger onesfrom stronger ones

Example: Making orange juice from Example: Making orange juice from frozen concentrate. You mix one can frozen concentrate. You mix one can of frozen orange juice with three (3) of frozen orange juice with three (3) cans of water.cans of water.

Dilutions for the Clinical Dilutions for the Clinical Laboratory (cont’d)Laboratory (cont’d)

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


Another example:Another example:

If you dilute 1 ml of serum with 9 ml If you dilute 1 ml of serum with 9 ml of saline, the dilution would be of saline, the dilution would be written 1/10 or said “one in ten”, written 1/10 or said “one in ten”, because you express the volume of because you express the volume of the solution being diluted (1 ml of the solution being diluted (1 ml of serum) per the TOTAL final volume of serum) per the TOTAL final volume of the dilution (10 ml total).the dilution (10 ml total).


Another example:Another example:

One (1) part of concentrated acid is One (1) part of concentrated acid is diluted with 100 parts of water. The diluted with 100 parts of water. The total solution volume is 101 parts (1 total solution volume is 101 parts (1 part acid + 100 parts water). The part acid + 100 parts water). The dilution is written as 1/101 or said dilution is written as 1/101 or said “one in one hundred and one”.“one in one hundred and one”.


Notice that dilutions do NOT have Notice that dilutions do NOT have units (cans, ml, or parts) but are units (cans, ml, or parts) but are expressed as one number to another expressed as one number to another numbernumber

Example: 1/10 or “one in ten”Example: 1/10 or “one in ten”


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


Example:Example:Two (2) parts of dye are diluted with eight (8) parts of Two (2) parts of dye are diluted with eight (8) parts of diluent (the term often used for the diluting solution). diluent (the term often used for the diluting solution). The total solution volume is 10 parts (2 parts dye + The total solution volume is 10 parts (2 parts dye + 8 parts diluent). The dilution is initially expressed as 8 parts diluent). The dilution is initially expressed as 2/10, but the original substance must be expressed 2/10, but the original substance must be expressed as one (1). To get the original volume to one (1), use as one (1). To get the original volume to one (1), use a ratio and proportion equation, remembering that a ratio and proportion equation, remembering that dilutions are stated in terms of 1 to something:dilutions are stated in terms of 1 to something:____________2 parts dye 2 parts dye = ___ = ___1.0___1.0___ 10 parts total volume x10 parts total volume x

2 x = 102 x = 10 x = 5x = 5

The dilution is expressed as 1/5.The dilution is expressed as 1/5.


The dilution does not always end up in whole numbers.The dilution does not always end up in whole numbers.Example:Example:Two parts (2) parts of whole blood are diluted with Two parts (2) parts of whole blood are diluted with five (5) parts of saline. The total solution volume is five (5) parts of saline. The total solution volume is seven (7) parts (2 parts of whole blood + 5 parts seven (7) parts (2 parts of whole blood + 5 parts saline). The dilution would be 2/7, or, more saline). The dilution would be 2/7, or, more correctly, 1/3.5. Again, this is calculated by using correctly, 1/3.5. Again, this is calculated by using the ratio and proportion equation, remembering that the ratio and proportion equation, remembering that dilutions are stated in terms of 1 to something: dilutions are stated in terms of 1 to something: ____2 parts blood_____2 parts blood_____ = ___ = ___1.0___1.0___ 7 parts total volume x7 parts total volume x

2 x = 72 x = 7 x = 3.5x = 3.5The dilution is expressed as 1/3.5The dilution is expressed as 1/3.5


Dilution Factor – used to correct for Dilution Factor – used to correct for having used a diluted sample in a lab having used a diluted sample in a lab test rather than the undiluted test rather than the undiluted sample. The result (answer) using sample. The result (answer) using the diluted sample must be the diluted sample must be multiplied by the RECIPROCAL of the multiplied by the RECIPROCAL of the dilution made. dilution made.

The RECIPROCAL of a 1/5 dilution is The RECIPROCAL of a 1/5 dilution is 5.5.


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


Sometimes it is necessary to make a Sometimes it is necessary to make a dilution of an existing solution to dilution of an existing solution to make it weaker. make it weaker. Example: A 100 mg/dl solution of Example: A 100 mg/dl solution of substrate is needed for a laboratory substrate is needed for a laboratory procedure. All that is available is a procedure. All that is available is a 500 mg/dl solution of substrate. A 500 mg/dl solution of substrate. A dilution of the stronger solution of dilution of the stronger solution of substrate is needed.substrate is needed.


To make a weaker solution from a stronger one, use this To make a weaker solution from a stronger one, use this formula:formula:

VV1 1 x C x C11 = V = V2 2 x Cx C22

Example: To make 100 ml of the 100 mg/dl solution from Example: To make 100 ml of the 100 mg/dl solution from the 500 mg/dl solution needed in the previous example:the 500 mg/dl solution needed in the previous example:

VV11 = 100 ml = 100 ml VV22 = V = V22 (unknown) (unknown)CC11 = 100 mg/dl = 100 mg/dl CC22 = 500 mg/dl = 500 mg/dl100 ml x 100 mg/dl = V100 ml x 100 mg/dl = V22 x 500 mg/dl x 500 mg/dlVV2 2 = 20 ml = 20 ml

Dilute 20 ml of 500 mg/dl solution up to 100 ml with Dilute 20 ml of 500 mg/dl solution up to 100 ml with water to obtain 100 ml of 100 mg/dl substrate solutionwater to obtain 100 ml of 100 mg/dl substrate solution

Serial DilutionsSerial Dilutions

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

Serial Dilutions (cont’d)Serial Dilutions (cont’d)

Example of a serial dilution:Example of a serial dilution:


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


Continuing with the serial dilution, in the Continuing with the serial dilution, in the third tube, you mix 1 ml of the 1/100 third tube, you mix 1 ml of the 1/100 dilution from the second tube with 9 ml of dilution from the second tube with 9 ml of diluent in the third tube. Again you have a diluent in the third tube. Again you have a 1/10 dilution in the third tube, but the 1/10 dilution in the third tube, but the concentration of stock in the third tube is concentration of stock in the third tube is 1/10 x 1/10 x 1/10 for a 1/1000 dilution.1/10 x 1/10 x 1/10 for a 1/1000 dilution.

This dilution could be carried out over This dilution could be carried out over many subsequent tubes.many subsequent tubes.


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

Serial Dilutions (cont’d)Serial Dilutions (cont’d) Example of determining a titer:Example of determining a titer:

A technician makes a serial dilution using A technician makes a serial dilution using patient serum:patient serum:Tube #1 = 1/10Tube #1 = 1/10Tube #2 = 1/100Tube #2 = 1/100Tube #3 = 1/1000Tube #3 = 1/1000Tube #4 = 1/10,000Tube #4 = 1/10,000Tube #5 = 1/100,000Tube #5 = 1/100,000Reactions occur in tubes 1 through 3, but Reactions occur in tubes 1 through 3, but NOT in tubes 4 or 5. The titer = 1000. NOT in tubes 4 or 5. The titer = 1000.

Rounding Off NumbersRounding Off Numbers

Sometimes it is necessary to round Sometimes it is necessary to round off insignificant digits in order not to off insignificant digits in order not to imply an accuracy greater than the imply an accuracy greater than the test is capable of delivering.test is capable of delivering.

When the digit next to the last one to When the digit next to the last one to be retained is less than 5, the last be retained is less than 5, the last digit should be left unchanged.digit should be left unchanged.

Example: 7.863 is rounded off to Example: 7.863 is rounded off to 7.867.86

Rounding Off Numbers (cont’d)Rounding Off Numbers (cont’d)

When the digit next to the last one to When the digit next to the last one to be retained is greater than 5, the last be retained is greater than 5, the last digit is increased by 1.digit is increased by 1.Example: 7.866 is rounded off to 7.87Example: 7.866 is rounded off to 7.87

If the additional digit is 5, the last If the additional digit is 5, the last digit reported is changed to the digit reported is changed to the nearest even number.nearest even number.Example: 23.25 is rounded off to 23.2Example: 23.25 is rounded off to 23.2Example: 23.35 is rounded off to 23.4Example: 23.35 is rounded off to 23.4

Basic Clinical Laboratory Math Basic Clinical Laboratory Math AssignmentAssignment

The assignment for this Clinical Laboratory The assignment for this Clinical Laboratory Math unit is found in the “Assignments” Math unit is found in the “Assignments” folder at the bottom of the menu. All folder at the bottom of the menu. All instructional material may be used for this instructional material may be used for this assignment. Please complete it by the assignment. Please complete it by the deadline listed on the Schedule.deadline listed on the Schedule.

As always, for help, email As always, for help, email [email protected] or call 393-1307 or call 393-1307 or 512-396-1501. or 512-396-1501.

Unit #3 - Basic Clinical Laboratory Math Cecile Sanders, M.Ed., MLS(ASCP)

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