Question

State true or false.

$\frac{6}{200}$ has non terminating repeating decimal expansion.

• A. True
• B. False

Answer 1

The correct option is B False

$\frac{p}{q}$ is terminating if $q$ is of the form $2^n{5}^m$ in the simplest ratio possible $\frac{p}{q}$ where $p$ and $q$ are co-primes.

($m$ and $n$ are non-negative integers)

Consider $\frac{6}{200}$

$\left(i\right)6$ and $200$ are not co-prime

$\because$ HCF$(6,200)=2$

$\frac{6}{200}=\frac{3\times 2}{100\times 2}$
$\frac{3}{100}=0.03$

Hence $\frac{6}{200}=0.03$ has terminating decimal expansion.