Question

Alan rewrites a fraction less than las a decimal. The numerator is a whole number greaterthan 0. For which denominator will the fraction always convert to a terminating decimal?121316

Answer 1

A terminating decimal is usually defined as a decimal number that contains a finite number of digits after the decimal point.

Usually, numbers with factors of 3 and prime numbers (numbers that are only divisible by 1 and itself) as the denominator of the fraction will have a case where the decimal does not terminate.

Let us check each option:

FIRST OPTION: 12

12 has a factor of 3. Hence it would have a non-terminating decimal.

To check, consider 1/12

$\frac{1}{12}=0.08\bar{3}$

Therefore, this option is INCORRECT.

SECOND OPTION: 9

9 has a factor of 3. Hence it would have a non-terminating decimal.

To check, consider 1/9

$\frac{1}{9}=0.\bar{1}$

Therefore, this option is INCORRECT.

THIRD OPTION: 13

13 is a prime number. Hence it would have a non-terminating decimal.

To check, consider 1/13

$\frac{1}{13}=0.0\bar{769230}$

Therefore, this option is INCORRECT.

FOURTH OPTION: 16

This should always give a terminating decimal. We can check as follows:

$\begin{gathered} \frac{1}{16}=0.0625 \\ \frac{2}{16}=0.125 \\ \frac{3}{16}=0.1875 \\ \frac{4}{16}=0.25 \\ \frac{5}{16}=0.3125 \\ \frac{6}{16}=0.375 \\ \frac{7}{16}=0.4375 \\ \frac{8}{16}=0.5 \\ \frac{9}{16}=0.5625 \end{gathered}$

Therefore, this option is CORRECT.