Nursing math & unit conversions: practice problems with step-by-step solutions

1Why nurses convert units

A prescription, a drug label and a patient chart do not always use the same units. A dose is ordered in grams but the tablets are labelled in milligrams; a weight is given in pounds but the dose is per kilogram; a parent measures medicine with a teaspoon.

Every medication calculation starts by putting all quantities in the same units. This topic practises exactly that step:

• Metric units (kg, g, mg, mcg and L, mL), pounds and kilograms, and household measures.
• Temperature, the 24-hour clock and rounding to the precision a question asks for.
• Dimensional analysis: chains of conversions, for example from mcg/min to mg/h.

2Metric units: steps of 1000

Mass goes kg → g → mg → mcg, and every step is a factor of 1000. Volume goes L → mL, also a factor of 1000.

• Going to a smaller unit, the number gets bigger: multiply by 1000 (move the decimal point three places to the right). 0.25 g = 250 mg.
• Going to a larger unit, the number gets smaller: divide by 1000. 125 mcg = 0.125 mg.

Write doses safely: always a zero before the decimal point (0.5 mg, never .5 mg), never a trailing zero (5 mg, never 5.0 mg), and write mcg and units in full instead of µg and U.

3Weight, length and household measures

Nursing exams use rounded equivalents. The question normally states the ones you need:

• 1 kg = 2.2 lb and 1 lb = 16 oz.
• 1 inch = 2.54 cm and 1 ft = 12 in.
• 1 tsp = 5 mL, 1 tbsp = 15 mL, 1 fl oz = 30 mL and 1 cup = 8 fl oz = 240 mL.

Write the conversion as a fraction so that the unit you do not want cancels:

A newborn of 7 lb 4 oz is not 7.4 lb: the ounces are sixteenths of a pound, so 4 oz = 0.25 lb and the baby weighs 7.25 lb = 3.30 kg.

4Temperature and the 24-hour clock

Temperature conversions use two formulas. Watch the order of the steps:

A quick check: 37 °C is 98.6 °F, and a change of 1 °C is a change of 1.8 °F.

Hospitals chart times on the 24-hour clock to avoid AM/PM mix-ups. From 1 PM onwards add 12 to the hour: 3:45 PM is 15:45. Midnight to 12:59 AM is 00:00–00:59, and noon to 12:59 PM stays 12:00–12:59.

To find a duration that crosses midnight, split it: first up to 24:00, then from 00:00 on. From 21:40 to 02:10 is 140 min + 130 min = 270 min.

5Rounding and dimensional analysis

Round only the final answer, and only to the precision the question or the local rule asks for. To round, look at the digit just after the place you keep: 5 or more rounds up, 4 or less leaves it.

Common exam rules: volumes of 1 mL or more to the nearest tenth, volumes below 1 mL to the nearest hundredth, drip rates to whole drops, weights to one decimal.

For a rate with two units to change, multiply by one conversion fraction for each unit:

6Common mistakes

• Multiplying when the unit gets larger, or dividing when it gets smaller.
• Moving the decimal point two places instead of three.
• Reading 7 lb 4 oz as 7.4 lb.
• Adding 32 before multiplying when going from °C to °F.
• Treating 2 h 30 min as 2.30 h instead of 2.5 h.
• Rounding in the middle of a calculation, or rounding a cylinder or bottle count the unsafe way.

7How exam questions look

• Easy: metric, weight and household units. Convert between g, mg and mcg or L and mL, pounds and kilograms, and teaspoons, tablespoons, ounces and cups; and pick the safely written dose.
• Medium: temperature, the 24-hour clock and rounding. Convert °F and °C, click the matching time on the other clock, convert infant weights and heights, and round to a stated rule.
• Hard: dimensional analysis chains. Add up an oral intake, convert dose rates, work out the volume to dispense, count time across midnight and convert laboratory units with a given factor.