Question

The decimal expansion of $\frac{1}{32}$ is

• A. 0.03125
• B. 0.15625
• C. 0.3125
• D. 0.00625

Answer 1

Answer: (A)

0.03125

Consider the number $\frac{1}{32}$
$\frac{1}{32}=\frac{1}{2^5}$
$=\frac{1}{2^5}\times \frac{5^5}{5^5}$

$=\frac{5^5}{2^5\times 5^5}$

$=\frac{5^5}{(2\times 5{)}^5}$
$=\frac{5^5}{(10{)}^5}$
$=\frac{3125}{100000}$
$=0.03125$
Hence, the decimal expansion of $\frac{1}{32}$ is $0.03125$