Question

The decimal form of $\frac{1}{5}+\frac{1}{25}+\frac{1}{16}$ is ____

• A. 0.3025
• B. 0.2425
• C. 0.2625
• D. 0.6625

Answer 1

The correct option is A 0.3025

Given operation is $\frac{1}{5}+\frac{1}{25}+\frac{1}{16}$
By factorising the denominators,
$\frac{1}{5}+\frac{1}{25}+\frac{1}{16}=\frac{1}{5}+\frac{1}{5^2}+\frac{1}{2^4}$

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

$\Rightarrow (\frac{1}{5}\times \frac{2}{2})+(\frac{1}{5^2}\times \frac{2^2}{2^2})+(\frac{1}{2^4}\times \frac{5^4}{5^4})$
$=\frac{2}{10}+\frac{4}{100}+\frac{625}{10000}$
$=0.2+0.04+0.0625$
$=0.3025$