# Indices and decimal places

What is `10^0.2` ?

The way to tackle these problems is (if you can) turn the decimal into a fraction.

So `10^0.2=10^(2/10)`

And we now know this equals

`10^(2/10)=(root10\10)^2`

Which reads

What do we have to multiply by itself `10` times to get `10` then multiply the answer by itself `2` times.

In this case:

`root10\10=1.259` (see logarithms)

And `(1.259)^2 = 1.259\times1.259`

`= 1.585`

**Answer:**

`10^0.2= 1.585`