E5.1 Units of measure

Learning objectives

E5.1.1Use metric units of mass, length, area, volume and capacity in• Use metric units of mass, length, area, volume and capacity in practical situations and convert quantities into larger or smaller units. Units include: • mm, cm, m, km • mm², cm², m², km² • mm³, cm³, m³ • ml, l • g, kg. Conversion between units includes: • between different units of area, e.g. cm² ↔ m² • between units of volume and capacity, e.g. m³ ↔ litres.

A metric conversion uses the linear scale factor once for length, squared for area and cubed for volume; the numerical value grows when the unit becomes smaller.

Quantity	Metric equivalence	Conversion factor
length	$1\text{ m}=100\text{ cm}=1000\text{ mm}$ ; $1\text{ km}=1000\text{ m}$	use the linear factor
area	$1\text{ m}^2=10\,000\text{ cm}^2$ ; $1\text{ km}^2=1\,000\,000\text{ m}^2$	square the linear factor
volume	$1\text{ m}^3=1\,000\,000\text{ cm}^3$	cube the linear factor
capacity	$1\text{ litre}=1000\text{ ml}=1000\text{ cm}^3$ ; $1\text{ m}^3=1000\text{ litres}$	use the stated equivalence
mass	$1\text{ kg}=1000\text{ g}$	factor $1000$

First identify the quantity type from the unit exponent. Write one exact equivalence, raise its linear factor to the same exponent, then multiply when converting to smaller units or divide when converting to larger units. Keep the target unit beside the result and check that the size change is sensible.

To convert $0.17\text{ m}^2$ to $\text{cm}^2$ , use $1\text{ m}^2=100^2\text{ cm}^2$ : $0.17\times10\,000=1700\text{ cm}^2$ . To convert $8500\text{ cm}^3$ to litres, use $1000\text{ cm}^3=1$ litre: $8500\div1000=8.5$ litres.

Do not use a length factor unchanged for area or volume: $1\text{ m}^2$ is not $100\text{ cm}^2$ , and $1\text{ m}^3$ is not $100\text{ cm}^3$ . Capacity equivalences connect cubic units to litres; they are not ordinary linear conversions.

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