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Prefixes and conversion

Prefixes such as kilo, milli and micro are powers of ten placed in front of a unit, so we avoid writing very large or very small numbers. Before you substitute numbers into a formula, convert everything to SI base units: meters, kilograms and seconds, not km, grams or minutes.

1\ \mathrm{km/h} = \dfrac{1}{3.6}\ \mathrm{m/s}

speed converted to SI

1\ \mathrm{m^2} = 10^4\ \mathrm{cm^2}

area scales with the square of the length factor

1\ \mathrm{m^3} = 1000\ \mathrm{L}

volume, since 1 L = 1 dm³

Symbols

$k$	kilo prefix, times a thousand
$m$	milli prefix, a thousandth
$\mu$	micro prefix, a millionth

Example

A car drives at $90$ km/h. In SI that is $90/3.6 = 25$ m/s. A tank holds $2.0$ m³ of oil, which is $2.0\cdot 1000 = 2000$ L.

Multiply or divide by a fraction equal to 1, for example

1000\ \mathrm{m}/1\ \mathrm{km}

, to change units without making mistakes.

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← SI units · Significant figures →

Part of Foundations of Physics: Quantities, units and measurement.