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 16 9

Explanation:

Step1: Recall terminating decimal rule

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

Step2: Factor each denominator

• For 13: Prime factor is 13 (not 2 or 5), so fractions with denominator 13 may not terminate.
• For 12: Prime factors are \(2^2 \times 3\) (has 3, not allowed), so fractions with denominator 12 may not terminate.
• For 16: Prime factor is \(2^4\) (only 2), so fractions with denominator 16 will always terminate.
• For 9: Prime factor is 3 (not 2 or 5), so fractions with denominator 9 may not terminate.

Answer:

16