# How do you write 10^-4 as both a decimal and a fraction?

Jan 11, 2017

See explanation.

#### Explanation:

To write the number as a fraction we can use the following identity:

## ${a}^{-} b = \frac{1}{a} ^ b$

${10}^{-} 4 = \frac{1}{10} ^ 4 = \frac{1}{10000}$

To change the fraction whose denominator is a power of $10$ to a decimal you can write the numerator and then move the decimal point as many places to the left as the number of zeros is which appear in the fraction's denominator.

$\frac{1}{10000} = 0.0001$