A prefix such as kilo or milli stands for a power of ten. To convert, replace the prefix with its power of ten, and square or cube it when the unit is squared or cubed.
This lesson is part of SPM Physics measurement. Next, see distinguishing scalar and vector quantities.
Which prefixes do you need?
| Prefix | Symbol | Power of ten |
|---|---|---|
| giga | G | 10⁹ |
| mega | M | 10⁶ |
| kilo | k | 10³ |
| centi | c | 10⁻² |
| milli | m | 10⁻³ |
| micro | µ | 10⁻⁶ |
| nano | n | 10⁻⁹ |
Worked conversions
Length. 350 mm = 350 × 10⁻³ m = 0.350 m. And 2.4 km = 2.4 × 10³ m = 2 400 m.
Area. 5 cm² = 5 × (10⁻²)² m² = 5 × 10⁻⁴ m² = 0.0005 m².
Volume. 500 cm³ = 500 × (10⁻²)³ m³ = 500 × 10⁻⁶ m³ = 5 × 10⁻⁴ m³.
Speed. 72 km/h = 72 × 1 000 m ÷ 3 600 s = 20 m/s.
The mistake that costs marks
The common slip is to use the length factor once for an area. Students write 5 cm² = 5 × 10⁻² m², which is 100 times too large.
| Conversion | Wrong | Right |
|---|---|---|
| 5 cm² to m² | 5 × 10⁻² m² | 5 × 10⁻⁴ m² |
| 500 cm³ to m³ | 5 × 10⁻² m³ | 5 × 10⁻⁴ m³ |
A size check catches it. A square of side 1 cm is 0.01 m by 0.01 m, which has an area of 0.0001 m². So 1 cm² cannot be 10⁻² m².
How do you handle standard form?
Write the number as A × 10ⁿ with A between 1 and 10. For 0.00045 m, move the decimal point four places to give 4.5 × 10⁻⁴ m. A negative power means a number smaller than 1.
Check yourself
Convert (a) 4 500 mm² to m², and (b) 90 km/h to m/s.
Answer
(a) 1 mm = 10⁻³ m, so 1 mm² = 10⁻⁶ m². 4 500 mm² = 4 500 × 10⁻⁶ = 4.5 × 10⁻³ m².
(b) 90 × 1 000 ÷ 3 600 = 90 ÷ 3.6 = 25 m/s.
Size check for (a): 4 500 mm² is 45 cm², a small area, and 0.0045 m² is also small.
What to study next
Continue with distinguishing scalar and vector quantities. Then use the measurement practice set to test conversions alongside the other skills.
The units and significant-figure checker lets you test conversions. If you want a teacher to review your conversion steps, see online one-to-one Physics tuition.