g to ug Converter - Gram to Microgram

Conversion derivation

Express both g and ug in the same base unit kg (kilogram), then cancel the shared base unit.

1. 1

   Rewrite g in the base unit

   $$1\mathrm{g}=0.001\mathrm{kg}$$
2. 2

   Rewrite ug in the base unit

   $$1\mathrm{ug}=1\times 10^{-9}\mathrm{kg}$$
3. 3

   Forward conversion

   $$\begin{array}{rl}1\mathrm{g}& =\frac{0.001\cancel{\mathrm{kg}}}{1\times 10^{-9}\cancel{\mathrm{kg}}}\times 1\mathrm{ug}\\ & =\frac{0.001}{1\times 10^{-9}}\mathrm{ug}\\ & =1,000,000\mathrm{ug}\end{array}$$
4. 4

   Reverse conversion

   $$\begin{array}{rl}1\mathrm{ug}& =\frac{1\times 10^{-9}\cancel{\mathrm{kg}}}{0.001\cancel{\mathrm{kg}}}\times 1\mathrm{g}\\ & =\frac{1\times 10^{-9}}{0.001}\mathrm{g}\\ & =0.000001\mathrm{g}\end{array}$$