Question

Question #c7863

Answer 1

To find the multiplicative inverse, convert the number to a fraction and flip it over.

Explanation:

Make fraction

`0.1=1/10`

Flip

`1/10rarr10/1`

Simplify

`10/1=10`

Answer 2

`10`

Explanation:

First, note that `0.1` just has a `1` in the `10^"th"s` position. As a fraction, then, we can represent it as `0.1 = 1/10`

Next, remember that the multiplicative inverse of any nonzero number is the number whose product with the original number is `1`. So, for any nonzero number `x`, the multiplicative inverse of `x` is `1/x`. This is because `x xx 1/x = x/x = 1`

So, if we want the multiplicative inverse of `0.1`, we look at `1/0.1` and get

`1/0.1 = 1/(1/10)`

`=1/(1/10) xx 10/10`

(multiplying the numerator and denominator by the same number doesn't change our value)

`=10/((1/10)xx10)`

`=10/1`

`=10`

So the multiplicative inverse of `0.1` is `10`.

As a side note, it's a useful trick to remember that `1/(1/x) = x` for any nonzero `x`. Multiplying by `x/x = 1` shows it to be true, as done above.