The Metric System

The metric system is the international standard for medication dosing and clinical measurement. Unlike household measurements, the metric system is decimal-based. Everything scales by powers of 10, making conversions straightforward.

Powers of ten

A power of ten means 10 multiplied by itself a set number of times: 10³ = 1000, 10² = 100, 10¹ = 10. In the metric system you only ever multiply or divide by 1000 (10³) when moving one prefix step. New to this? See Whole Numbers — Powers of Ten.

Base Units in Nursing

The base unit is an unscaled unit. Use it as a baseline conversion factor.

Measurement	Base Unit	Abbreviation
Weight	gram	g
Volume	liter	L
Length	meter	m

Prefixes

Prefixes modify the base unit by a power of 10.

Prefix	Symbol	Meaning	Example
kilo	k	× 1000	1 kg = 1000 g
(base)	—	× 1	1 g
milli	m	× 0.001	1 mg = 0.001 g
micro	mc or µ	× 0.000001	1 mcg = 0.001 mg

Memory Tip

Create a chain of the units and prefixes, as shown below.

\[\text{kg} \rightarrow \text{g} \rightarrow \text{mg} \rightarrow \text{mcg}\]

Moving to the right takes you from a larger to smaller unit. Multiply by 1000 for each step.

Moving to the left takes you from a smaller to larger unit. Divide by 1000 for each step.

Key Weight Conversions

\[ 1 \text{ kg} = 1000 \text{ g} \]

\[ 1 \text{ g} = 1000 \text{ mg} \]

\[ 1 \text{ mg} = 1000 \text{ mcg} \]

Key Volume Conversions

\[1 \text{ L} = 1000 \text{ mL}\]

\[1 \text{ dL} = 100 \text{ mL}\]

Each equality is a factor pair

Every conversion you just memorized can be written as a fraction two ways — both equal 1:

\[\frac{1000 \text{ mg}}{1 \text{ g}} \quad \text{or} \quad \frac{1 \text{ g}}{1000 \text{ mg}}\]

You choose the orientation that cancels the unit you want to remove. This is how every metric conversion is set up in dimensional analysis.

Abbreviation Safety

mcg vs mg

Do not abbreviate microgram as µg in handwritten orders. It can be misread as mg, resulting in a 1000x overdose. Always write mcg in full.

Units of Insulin

Never abbreviate units as U for insulin orders. U can be misread as a zero, turning 4U into 40 units. Always write units in full.

Clinical Application

Example 1: A medication order reads 0.5 g. Stock is labeled in mg. What is the equivalent dose in mg?

\[0.5 \text{ g} \times \frac{1000 \text{ mg}}{1 \text{ g}} = 500 \text{ mg}\]

Example 2: A patient weighs 75 kg. A weight-based dose requires the weight in grams. Convert:

\[75 \text{ kg} \times \frac{1000 \text{ g}}{1 \text{ kg}} = 75{,}000 \text{ g}\]

Example 3: A lab value is reported as 1500 mcg. Convert to mg:

\[1500 \text{ mcg} \times \frac{1 \text{ mg}}{1000 \text{ mcg}} = 1.5 \text{ mg}\]

Practice Problems

Problem 1

Convert 2.5 g to mg.

Answer

\[2.5 \text{ g} \times 1000 = 2500 \text{ mg}\]

Problem 2

Convert 750 mg to g.

Answer

\[750 \text{ mg} \div 1000 = 0.75 \text{ g}\]

Problem 3

Convert 0.25 mg to mcg.

Answer

\[0.25 \text{ mg} \times 1000 = 250 \text{ mcg}\]

Problem 4

Convert 2500 mL to L.

Answer

\[2500 \text{ mL} \div 1000 = 2.5 \text{ L}\]

Problem 5

An order reads 0.125 mg. Stock is labeled in mcg. What is the equivalent dose?

Answer

\[0.125 \text{ mg} \times 1000 = 125 \text{ mcg}\]

Clinical Tip

When converting between metric units always ask yourself — am I going to a smaller or larger unit? Smaller unit = larger number. Larger unit = smaller number. If your answer goes the wrong direction, recheck your work.