# 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

Work out what 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

10^0.2= 1.585