m a nm convertitore - Metro a Nanometro

Conversion derivation

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

1. 1

   Rewrite m in the base unit

   $$1\mathrm{m}=1\mathrm{m}$$
2. 2

   Rewrite nm in the base unit

   $$1\mathrm{nm}=1\times 10^{-9}\mathrm{m}$$
3. 3

   Forward conversion

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

   Reverse conversion

   $$\begin{array}{rl}1\mathrm{nm}& =\frac{1\times 10^{-9}\cancel{\mathrm{m}}}{1\cancel{\mathrm{m}}}\times 1\mathrm{m}\\ & =\frac{1\times 10^{-9}}{1}\mathrm{m}\\ & =1\times 10^{-9}\mathrm{m}\end{array}$$