Converting lengths and masses

The conversion-table method

To convert a length or a mass, we use a table where each column represents a place value (as with decimal numbers). We place the reference unit (m or g) in the center, then the multiples to the left (km, hm, dam) and the submultiples to the right (dm, cm, mm).

km	hm	dam	m	dm	cm	mm
			1	2	5	0

This table represents 1.250 m, that is, 1 m, 2 dm, 5 cm, and 0 mm.

Conversion example

Convert 3.5 km to m: we multiply by 1000 (kilo = x1000), so 3.5 km = 3500 m.

Convert 250 g to kg: we divide by 1000 (kilo = x1000, so to go back to grams we divide), so 250 g = 0.250 kg.

Summary table

Conversion	Operation	Example
km -> m	x 1000	2 km = 2000 m
m -> cm	x 100	1.5 m = 150 cm
g -> kg	/ 1000	500 g = 0.5 kg
cm -> mm	x 10	4 cm = 40 mm

Common pitfall

When moving from a large unit to a small unit (for example km to m), the number gets bigger: we multiply. When moving from a small unit to a large unit (for example g to kg), the number gets smaller: we divide. Many students mix up multiplication and division: always remember to check whether the result should be bigger or smaller than the starting number.