Question

Find the decimal form of $\frac{1}{5}+\frac{1}{25}+\frac{1}{125}$.

Answer 1

Given operation is $\frac{1}{5}+\frac{1}{25}+\frac{1}{125}$
By factorising the denominators,
$\frac{1}{5}+\frac{1}{25}+\frac{1}{125}=\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}$

To convert a fraction into decimal form, make the denominator in terms of multiples of 10.

$\Rightarrow (\frac{1}{5}\times \frac{2}{2})+(\frac{1}{5^2}\times \frac{2^2}{2^2})+(\frac{1}{5^3}\times \frac{2^3}{2^3})$
$=\frac{2}{10}+\frac{4}{100}+\frac{8}{1000}$
= 0.248