Transcript PowerPoint

Unit #3 - Basic
Clinical Laboratory
Math
Cecile Sanders, M.Ed., MT(ASCP),
CLS (NCA)
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

Examples:
– Gasoline in gallons
– Weight in pounds
– Distance in miles
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.
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
Common Metric Prefixes
–
–
–
–
–
–
Kilo (k) = 1000 x base unit
Centi (c) = .01 x base unit
Milli (m) = .001 x base unit
Micro (µ) = .000001 x base unit
Nano (n) = 10 -9 x base unit
Pico (p) = 10-12 x base unit
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
Example:
Convert Centimeters to Meters: Move decimal 2 places to
left
Converting between English and
Metric Systems

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Mile x 1.6 = kilometers
Pound x 0.454 = kilograms
Quart x 0.95 = liters
Kilometer x 0.6 = miles
Meter x 3.3 = feet
Meter x 39.37 = inches
Centimeter x 0.4 = inches
Gram x .0022 = pounds
Liter x 1.06 = quarts
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.
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.
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
Temperature Conversion
To convert from Fahrenheit to
Centigrade:
0
0
C = 5/9(F -32)
To convert from Centigrade to
Fahrenheit:
0
0
F = 9/5(C ) + 32
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.
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”.
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).
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 + 100 parts water). The dilution is
written as 1/101 or said “one in one
hundred and one”.
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”
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.
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
2x
=
10
x
=
5
The dilution is expressed as 1/5.
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
2x
=
7
x
=
3.5
The dilution is expressed as 1/3.5
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.
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.
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.
Dilutions for the Clinical
Laboratory (cont’d)

To make a weaker solution from a stronger one, use
this formula:
V1 x C 1 = V 2 x C 2
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
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.
Serial Dilutions (cont’d)
 Example
of a serial dilution:
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.
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.

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”.
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.
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: 7.863 is rounded off to 7.86
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: 7.866 is rounded off to 7.867
 If the additional digit is 5, the last digit
reported is changed to the nearest even
number.
Example: 23.25 is rounded off to 23.2
Example: 23.35 is rounded off to 23.4
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, email
[email protected] or call 393-1307 or
512-396-1501.

Basic Clinical Laboratory Math

Resources
– Mathematics for the Clinical Laboratory,
Doucette, Lorraine J., Saunders, Second
Edition, 2011
– Essential Laboratory Mathematics,
Johnson, Timmons, and Hall, Waveland
Press, Second Edition, 2010