Question

What exponent would complete this equation 0.005 = 5 x 10?
To the ? Power

Answer 1

-3

Explanation:

0.005 = 5 *
`10^?`

0.005 = 5 * 0.001

Thus, to find what 10 should be raised to, we should find which exponent of 10 gives us 0.001

We can do this by just testing a few numbers from 10^1 and down:

`10^1 = 10\\10^0 = 1\\10^(-1) = 0.1\\10^(-2) = 0.01\\10^(-3) = 0.001`

As we can see,
`10^(-3)` = 0.001, thus the exponent in our equation is -3

A shorthand of this is counting the number of zeroes, 10^-1 has one zero, 10^-2 has two zeroes, and 10^-3 has three zeroes.

Since we were looking for 0.001, which has 3 zeroes, we can see that the correct exponent should be -3.