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In everyday life we are limited to a range of numbers usually embraced by the range 1 to several thousands. Rarely do we calculate with very large numbers and even more rarely with extremely small fractions or decimals.
The body is a container of solvents, mainly water, in which various substances (solutes) are present in dilute to extremely dilute amounts or concentrations. To cope with the numeracy of physiology we have to accustom ourselves to dealing with extremely small numbers.
The following table illustrates the dimension and terminology commonly used in expressing measurements in clinical medicine.
Table 1 Common measures and notations in clinical medicine
|
Name
|
Fraction
|
Decimal
|
Abbreviation
|
|
Weight
|
|
Gram
|
1
|
1
|
g
|
|
Kilogram
|
1000
|
1 x 103
|
kg
|
|
Milligram
|
1/1000
|
1 x 10-3
|
mg
|
|
Microgram
|
1/1,000,000
|
1 x 10-6
|
mg
|
|
Nanogram
|
1/1,000,000,000
|
1 x 10-9
|
ng
|
|
Picogram
|
1/1,000,000,000,000
|
1 x 10-12
|
pg
|
|
Volume
|
|
Liter
|
1
|
1
|
l
|
|
Deciliter
|
1/100
|
1 x 10-2
|
dl
|
|
Milliliter
|
1/1000
|
1 x 10-3
|
ml
|
|
Microliter
|
1/1,000,000
|
1 x 10-6
|
ml
|
|
Nanoliter
|
1/1,000,000,000
|
1 x 10-9
|
nl
|
|
Picoliter
|
1/1,000,000,000,000
|
1 x 10-12
|
pl
|
|
Femtoliter
|
1/1,000,000,000,000,000
|
1 x 10-15
|
fl
|
|
Molarity
|
|
Mole
|
1
|
1
|
Mol
|
|
Millimole
|
1/1000
|
1 x 10-3
|
mmol
|
|
Micromole
|
1/1,000,000
|
1 x 10-6
|
mmol
|
|
Nanomole
|
1/1,000,000,000
|
1 x 10-9
|
nmol
|
|
Picomole
|
1/1,000,000,000,000
|
1 x 10-12
|
pmol
|
Proper attention must be paid to mathematical conventions when calculating with and expressing mass, volume and concentration with such small numbers.
In general, the largest appropriate unit is used. We would not express a mass as 1,340,000 ng, but as 1.34 mg or 1,340 mg. A volume of 1800 ml is best expressed as 1.8 l if at the same time we are expressing a concentration as units per liter. A concentration of 0.0000001 mol/l is better expressed as 10 mmol/l, etc.
When calculating, it is imperative to always ensure that the same units are used for each element in an equation. Adherence to mathematical notation (e.g., 10-3, 104, 10-7) reduces the chance of error. A classic example using mixed units is found in the calculation of creatinine clearance where plasma creatinine is reported as mg/dl, urinary creatinine as mg/l and urinary volume as liters.
Creatinine clearance = [Urinecreatinine x Urine volume ]/[ Plasmacreatinine x time]
Urinecreatinine = 2300 mg/l; Urine Volume = 2l; Plasmacreatinine = 1.2 mg/dl
UV/Pt = [2300 x 2]/[1.2 x 1440] = 2.7 ml/min (error: mixed units of concentration)
UV/Pt = [2.3 x 2000]/[ 0.12 x 1440] = 27 ml/min (correct)
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