Unit Conversion

How the SAT tests this, with worked examples — plus the 4 skills it covers. Free to read, no account needed.

Conversion questions are solved by multiplying by fractions that equal one, arranged so the unwanted units cancel.
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The rule for building each fraction is simple: put the unit you want on top and the unit you have on the bottom. Then the unit you have cancels, exactly as a common factor cancels in algebra.
Chains work the same way. To convert kilometres per hour into metres per second, multiply by 1000 m1 km\frac{1000\ \text{m}}{1\ \text{km}} and then by 1 h3600 s\frac{1\ \text{h}}{3600\ \text{s}}, and both unwanted units disappear.
When a question involves area or volume, the conversion factor must be raised to the same power. There are 100100 centimetres in a metre but 1002=10,000100^2 = 10{,}000 square centimetres in a square metre.
If you are unsure whether to multiply or divide, write the units out and let them decide. The arrangement that cancels correctly is the right one, and it needs no judgement.

Worked examples

Convert 9090 kilometres to metres.
Want metres on top, kilometres on the bottom
90 km×1000 m1 km=90,000 m{90\ \text{km} \times \frac{1000\ \text{m}}{1\ \text{km}} = 90{,}000\ \text{m}}
Convert 7272 km/h into m/s.
Chain the two conversions so both unwanted units cancel
72×10001×13600=20 m/s{72 \times \frac{1000}{1} \times \frac{1}{3600} = 20\ \text{m/s}}
How many square centimetres are in 33 square metres?
  • A300300
  • B30,00030{,}000
The length factor is 100100, so the area factor is 1002=10,000100^2 = 10{,}000, giving 30,00030{,}000. (B) is correct; (A) uses the length factor by mistake.

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All the skills in Unit Conversion