Question

Consider the fraction $\frac{m}{n}$ where $m$ is an integer. Choose the value of $\text{n}$ which will always result in terminating decimal number.

• A. $32$
• B. $30$
• C. $\frac{2}{3}$

Answer 1

Answer: (A), (C)

$\frac{2}{3}$

Givem fraction is $\frac{m}{n}$ where $m$ is an integer.

For $\frac{m}{n}$ to be a terminating decimal number, $\text{n}$ should be a power of $2,$ $5$ or multiplication of power of $2$ and $5.$

When $\text{n}=32$:

$32=4\times 8=(2\times 2)\times (2\times 2\times 2)$

Hence, $32$ is a possible value of $\text{n}.$

When $\text{n}=30$:

$30=3\times 10\to 3$ in the denominator may not get canceled out and result in a non-terminating decimal number.

When $\text{n}=\frac{2}{3}$:

$\frac{m}{n}=\frac{m}{\frac{2}{3}}=\frac{3\times m}{2}$

The denominator is a power of $2,$ hence, this value of $\text{n}$ will result in a terminating decimal number.