Question

alan rewrites a fraction less than 1 as a decimal. the numerator is a whole number greater than 0. for which denominator will the fraction always convert to a terminating decimal? 13 12 9 16

Explanation:

Step1: Recall terminating decimal rule

A fraction in simplest form converts to a terminating decimal if and only if its denominator has no prime factors other than 2 and 5.

Step2: Factor each denominator

• $13$: Prime factor is $13$ (not 2/5)
• $12$: $12=2^2\times3$ (has factor 3)
• $9$: $9=3^2$ (has factor 3)
• $16$: $16=2^4$ (only factor 2)

Step3: Verify the valid denominator

Only 16 has prime factors limited to 2, so any fraction with denominator 16 (in simplest form) will terminate.

Answer:

16