Question

Identify the fraction(s) which will result in non-terminating decimal number(s).

• A. $\frac{6}{54}$
• B. $\frac{27}{54}$
• C. $\frac{3}{75}$
• D. $\frac{9}{225}$

Answer 1

Answer: (B), (C), (D)

$\frac{9}{225}$

Concept: If denominator of a fraction is a multiple of only 2 or only 5 or both 2 and 5 then the fraction can be converted into a terminating decimal nmber.

Let's simplify each fraction one by one.

$\frac{6}{54}=\frac{6}{6\times 9}=\frac{1}{9}$

The denominator of the reduced form is a multiple of $3.$
Hence, it will result in a non-terminating decimal number.

$\frac{27}{54}=\frac{27}{2\times 27}=\frac{1}{2}$

The denominator is a multiple of 2 only, hence it can be converted into a terminating decimal number.

$\frac{3}{75}=\frac{3}{3\times 25}=\frac{1}{25}$

The denominator is a multiple of 5 only, hence it can be converted into a terminating decimal number.

$\frac{9}{225}=\frac{9}{9\times 25}=\frac{1}{25}$

The denominator is a multiple of 5 only, hence it can be converted into a terminating decimal number.