km to um Converter - Kilometer to Micrometer

Conversion derivation

Express both km and um in the same base unit m (meter), then cancel the shared base unit.

1. 1

   Rewrite km in the base unit

   $$1\mathrm{km}=1,000\mathrm{m}$$
2. 2

   Rewrite um in the base unit

   $$1\mathrm{um}=0.000001\mathrm{m}$$
3. 3

   Forward conversion

   $$\begin{array}{rl}1\mathrm{km}& =\frac{1,000\cancel{\mathrm{m}}}{0.000001\cancel{\mathrm{m}}}\times 1\mathrm{um}\\ & =\frac{1,000}{0.000001}\mathrm{um}\\ & =1\times 10^9\mathrm{um}\end{array}$$
4. 4

   Reverse conversion

   $$\begin{array}{rl}1\mathrm{um}& =\frac{0.000001\cancel{\mathrm{m}}}{1,000\cancel{\mathrm{m}}}\times 1\mathrm{km}\\ & =\frac{0.000001}{1,000}\mathrm{km}\\ & =1\times 10^{-9}\mathrm{km}\end{array}$$