# How do you express 0.0042 in scientific notation?

Jan 28, 2017

$42 \cdot {10}^{-} 4$

#### Explanation:

Scientific notation was created for when numbers are too large to write down, particularly when many digits are zeros. In our case,

$0.0042 = \frac{42}{10000} = \frac{42}{10} ^ 4 = 42 \cdot \frac{1}{10} ^ 4$

Recall that $\frac{1}{a} ^ b = {a}^{-} b$ and vice versa,

so we can write $42 \cdot \frac{1}{10} ^ 4 = 42 \cdot {10}^{-} 4$.