## Expressing Numbers, Fractions, and Decimals

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. 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 M 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 μg. 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 mole/L is better expressed as 10 mmole/L, etc.

When performing calculations, 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 of an error due to using mixed units is found in the incorrect calculation of creatinine clearance shown below.  In this case, plasma creatinine is reported as mg/dL, urinary creatinine as mg/L and urinary volume as liters. The correct calculation is also shown below.

#### (1) Incorrect calculation

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 min] = 2.7 mL/min

Here, 2300 mg/L and 1.2 mg/dL were not converted to the mg/mL.

#### (2) Correct calculation

UV/Pt = [2.3 mg/mL x 2000 mL]/[ 0.12 mg/mL x 1440 min] = 27 mL/min

P/N 101817-01 Rev B 02/2021