# Expressing quantities

The International Bureau of Weights and Measures (BIPM) has developed a set of guidelines on how to properly use and apply the International System of Units (SI). These guidelines describe how unit symbols and names, including prefix symbols should be written and used, and how the values of quantities should be expressed.

### BIPM brochure

Cover image from the brochure *The International System of Units (SI)* issued by Bureau International des Poids et Mesures (BIPM).

**Rights:**Image reproduced with permission of the BIPM, which retains full internationally protected copyright.

## Symbols and names

Use normal fonts for numbers, unit and prefix symbols, and chemical element symbols. Use italic letters for quantity symbols.

mL (millilitres) not ml (l is a quantity symbol for length)

Do not add an ‘s’ for plurals or place a full stop after a symbol unless it ends a sentence.

kg (kilograms) not kg. or kgs

Units named in honour of a person have capitalised symbols.

MJ (megajoules) not Mj or MJs (the joule is named after James Joule)

Leave a space between the number and the unit symbol. (This guideline is often ignored.)

25 m not 25m

Units are common nouns, not proper nouns, so do not capitalise a spelled-out name.

50 newtons not 50 Newtons

Do not mix symbols with spelled-out names in the same expression.

35 km/h not 35 km per hour or 35 kilometres/hour

## Values of quantities

Use decimals not fractions or mixed numbers with all units.

35.5 °C not 35 1/2 °C

Write a zero in front of a leading decimal point so that it is not ‘lost’ or overlooked.

0.4 mm not .4 mm

Use a prefix that gives a number between 0.1 and 1000 and only one prefix per unit.

5 km not 5000 m

20 nm not 20 mµm (millimicrometres)

When writing long numbers, use spaces to separate digits into groups of three, counting both left and right from the decimal point, as in some countries, the comma is used to indicate a decimal point. (This guideline is often ignored.)

7.498 564 not 7.498564

38 921 324 not 38,921,324 or 38921324

To multiply unit symbols in formally written scientific papers, use a middle dot (•) and to divide use a slash (/), horizontal bar (—) or negative exponent. (The use of the middle dot is often ignored.)

Fifty newton metres is represented as 50 N•m.

Eighty kilometres per hour is written as 80 km/h or 80 km•h-1

## Rounding

When multiplying or dividing quantities, round the final answer to the same number of significant figures as the least precise original data.

3 m x 2.12 m = 6.36 m2 – since the quantity 3 m has only one significant figure, the final answer can only claim one significant figure, so 6.36 m2 has to be rounded down to the final answer of 6 m2.

8.8 m / 0.134 s = 65.67 m•s-1 – since the quantity 8.8 m has only two significant figures, this must be reflected in the final answer, so 65.67 m•s-1 has to be rounded up to the final answer of 66 m•s-1.

When adding or subtracting quantities, round the final answer to the same place value as the least precise original data.

6.54 g – 2.6 g = 3.94 g – since the quantity 2.6 g has only one decimal place, the final answer must have this place value, so 3.94 g has to be rounded down to the final answer of 3.9 g.

## Related content

Measurement of any quantity involves comparison with some precisely defined unit value of the quantity. Measurement systems have developed over the years. The system that is used in the scientific community is called Système International d’Unités, abbreviated to SI – find out more about SI base units and SI derived units.

Powers of 10 explains the prefix names and symbols for decimal multiples and submultiples of SI units.

## Activity idea

Precision and accuracy provides various datasets for students to judge precision and accuracy in scientific settings.

## Nature of science

Science demands and relies upon evidence frequently gathered by taking measurements. Since every measurement consists of two parts (a number and a unit), it is essential that a set of rules be devised that govern the writing and recording of measurements. Adherence to such a set of rules allows for the successful communication of results across national, language and cultural barriers.

## Useful link

See the BIPM brochure on the International System of Units.

**Published:**17 August 2011