# How do you write 4times10^-4 in standard form?

Mar 25, 2017

$x \times {10}^{- 4} = \textcolor{g r e e n}{\frac{1}{2500}}$ or $\textcolor{g r e e n}{0.0004}$

#### Explanation:

It depends upon what you (or your instructor) means by "standard form" for a number. (I have seen it used to mean "scientific notation" but that is obviously not the intent in this case).

As a rational fraction:
$\textcolor{w h i t e}{\text{XXX}} 4 \times {10}^{- 4} = 4 \times \frac{1}{{10}^{4}} = \frac{4}{10000} = \frac{1}{2500}$

As a decimal fraction:
$\textcolor{w h i t e}{\text{XXX}} 4 \times {10}^{- 4} = 0.4 \times {10}^{- 3} = 0.04 \times {10}^{- 2} = 0.004 \times {10}^{- 1} = 0.0004 \times {10}^{0} = 0.0004$