SI Units for EDAIC: Avoid Factor-of-Ten Errors

The safest way to convert units in an EDAIC calculation is to write the units throughout and multiply by a conversion fraction that equals one. The unwanted unit should cancel. Guessing whether to move a decimal left or right is less reliable, especially when a concentration and a time unit change together.

These examples use hypothetical laboratory quantities and flows. They practise arithmetic and dimensional reasoning, rather than recommending a medicine dose or a clinical setting. The BIPM SI Brochure is the authoritative starting point for SI units and prefixes.

Keep prefixes attached to their units

Kilo represents 10³, milli 10⁻³ and micro 10⁻⁶. A milligram is therefore one thousand micrograms. A prefix changes the size of a unit, not the physical amount being described.

Write the destination unit before calculating. If the task is to express 0.24 mg in micrograms, the target is a smaller unit, so the numerical answer should be larger:

0.24 mg × 1,000 micrograms/mg = 240 micrograms.

The mg units cancel. As a reverse check, 240 micrograms divided by 1,000 returns 0.24 mg. A result of 0.00024 micrograms fails both the direction check and the reverse calculation.

Volume: do not cube the wrong factor

One litre equals 1,000 mL, and one millilitre equals one cubic centimetre. NIST's volume guide distinguishes these relationships from conversions between lengths.

Consider a cube with each side 1 cm. Its volume is 1 cm³. Each side is also 10 mm, so the same volume is 10 × 10 × 10 = 1,000 mm³. Converting a volume requires cubing the length conversion, not merely replacing cm with mm and multiplying once.

Now express 250 mL in litres: 250 × 1 L/1,000 mL = 0.250 L. The amount is unchanged. If you obtain 250,000 L, the conversion fraction was inverted.

This distinction matters whenever a formula contains radius squared or cubed. Before substituting a length, check whether the formula's other quantities expect metres, centimetres or another consistent system.

Original concentration example

A fictional non-clinical solution contains 18 mg of a substance in a final volume of 6 mL. Assume the substance is evenly distributed.

Its concentration is 18/6 = 3 mg/mL. Expressed in micrograms per millilitre, it is 3,000 micrograms/mL. Expressed in milligrams per litre, it is 3,000 mg/L.

The two answers share a number but have different units. They are equivalent descriptions of the same concentration, not interchangeable labels in a calculation.

For example, the amount in 0.4 mL is:

3 mg/mL × 0.4 mL = 1.2 mg.

Using the microgram form gives 3,000 micrograms/mL × 0.4 mL = 1,200 micrograms. Converting that result back to milligrams confirms agreement. This second route is especially useful when an answer looks plausible but may conceal a thousand-fold error.

Combine volume and time deliberately

An imaginary pump used on a bench moves water at 90 mL/h. To express the flow per minute, multiply by 1 h/60 min:

90 mL/h × 1 h/60 min = 1.5 mL/min.

To express it in litres per second, change both units:

90 mL/h × 1 L/1,000 mL × 1 h/3,600 s = 0.000025 L/s.

The small number is reasonable because the destination describes litres delivered during one second, rather than millilitres delivered over a whole hour. A small numerical result is not automatically an error; judge it alongside its units and scale.

Notation is part of the calculation

Unit symbols are case-sensitive, and compound units should be written unambiguously. NIST's notation rules explain how prefixes and products or quotients of units are represented.

In revision notes, write 0.5 rather than .5, and keep the unit visible beside the number. Use parentheses when multiple divisions could be misunderstood. A clear expression such as mg/(kg·min) is easier to inspect than a sequence of slashes with an uncertain denominator.

Also distinguish a fraction from a percentage. A saturation of 97% becomes 0.97 when a formula expects a fraction. Substituting 97 into the same formula creates a hundred-fold change without any physiology changing.

Self-test: show the cancelling units

1. Express 0.08 g in mg.
2. Express 2.4 L/min in mL/s.
3. A sample contains 12 mg in 8 mL. How much is present in 2 mL?
4. Express 2 cm³ in mm³.

Answers: 80 mg; 40 mL/s; 3 mg; 2,000 mm³. For the third answer, calculate the concentration first: 1.5 mg/mL. For the fourth, cube the tenfold length conversion.

If one answer was wrong, record whether the error involved a prefix, denominator, time conversion or power. Practise that category with changed numbers rather than repeating the same result from memory.

The EDAIC physics overview places units within the wider syllabus. Use AnesCORE calculation questions with the units written out, even when mental arithmetic feels quicker.

Sources

• BIPM: The International System of Units
• NIST: SI Units—Volume
• NIST: Rules and style conventions for units

Prepared with AI assistance for examination revision; this article is not a patient-care protocol or a substitute for current primary guidance. Sources checked 7 October 2026.