Question

Which of the following has a terminating decimal representation?

• A. $\frac{13}{44}$
• B. $\frac{81}{30}$
• C. $\frac{29}{12}$
• D. $\frac{31}{75}$

Answer 1

The correct option is B $\frac{81}{30}$

For a fraction to have a terminating decimal representation, its denominator should be of the form $2^m\times 5^n.$

$\frac{13}{44}\to 44=2^2\times 11$
$\frac{81}{30}=\frac{27}{10}\to 10=2\times 5$
$\frac{29}{12}\to 12=2^2\times 3$
$\frac{31}{75}\to 75=3\times 5^2$
Thus, among the given options, only $\frac{81}{30}$ has a terminating decimal representation.