# How do you complete the following metric conversion problem: 3.5 mg = ? mug?

Jan 23, 2017

$3.5 \cdot m g \equiv 3500 \cdot \mu g$. Why and how?

#### Explanation:

$1 \cdot m g = 1 \times {10}^{-} 3 \cdot g$

$1 \cdot \mu g = 1 \times {10}^{-} 6 \cdot g$

$3.5 \cdot m g = \frac{3.5 \times {10}^{-} 3 \cdot \cancel{g}}{{10}^{-} 6 \cdot \cancel{g} \cdot \mu {g}^{-} 1}$

$= {10}^{6} \times 3.5 \times {10}^{-} 3 \cdot \mu g = 3.5 \times {10}^{3} \times \cancel{{10}^{3}} \times \cancel{{10}^{-} 3} \mu g$

$= 3500 \cdot \mu g$.

Just a note on the arithmetic, $\frac{1}{10} ^ - 3 \equiv \frac{1}{\frac{1}{10} ^ 3} = \frac{1}{\frac{1}{1000}} = 1000$. Why? Because there are a $\text{thousands}$ $\text{one thousandths}$ in $\text{one}$. Confused yet? If you don't see it, then try it on a calculator.