Question

Find the decimal form of $\frac{1}{2}+\frac{1}{8}+\frac{1}{16}$.

• A. 0.5865
• B. none of the above
• C. 0.6875
• D. 0.5275

Answer 1

The correct option is C 0.6875

Given operation is $\frac{1}{2}+\frac{1}{8}+\frac{1}{16}$
By factorising the denominators,
$\frac{1}{2}+\frac{1}{8}+\frac{1}{16}=\frac{1}{2}+\frac{1}{2^3}+\frac{1}{2^4}$

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

$\Rightarrow (\frac{1}{2}\times \frac{5}{5})+(\frac{1}{2^3}\times \frac{5^3}{5^3})+(\frac{1}{2^4}\times \frac{5^4}{5^4})$
$=\frac{5}{10}+\frac{125}{1000}+\frac{625}{10000}$
$=0.5+0.125+0.0625$
$=0.6875$