Question

Determine whether the given expression will result in a terminating or non-terminating decimal number.

$\frac{1}{13}\times \frac{26}{5}-\frac{1}{4}÷\frac{2}{17}$

• A. Terminating decimal number.
• B. Non-terminating decimal number.
• C. Cannot be determined.

Answer 1

The correct option is A Terminating decimal number.

Let's follow the PEMDAS rule and simplify it.

We know multiplication and division are of the same priority, followed by subtraction.

$\frac{1}{13}\times \frac{26}{5}-\frac{1}{4}÷\frac{2}{17}$
$=\frac{1}{13}\times \frac{2\times 13}{5}-\frac{1}{4}\times \frac{17}{2}$
(canceling $13$ from numerator and denominator)
$=\frac{2}{5}-\frac{17}{8}$
Without solving further, we can infer that the denominator is a multiple of both 2 and 5 only.
$\therefore$ It will result in a terminating decimal number.