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

`(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

`(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

`(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} (1)/(16)=0.0625 \\ (2)/(16)=0.125 \\ (3)/(16)=0.1875 \\ (4)/(16)=0.25 \\ (5)/(16)=0.3125 \\ (6)/(16)=0.375 \\ (7)/(16)=0.4375 \\ (8)/(16)=0.5 \\ (9)/(16)=0.5625 \end{gathered}`

Therefore, this option is CORRECT.