Which fraction has a terminating decimal representation?

Which fraction has a terminating decimal representation?

• A. 1/3
• B. 1/7
• C. 1/2
• D. 5/6

Answer: (C)

A fraction has a terminating decimal representation when, after reducing to lowest terms, the denominator has only the prime factors 2 and 5. This works because decimal notation is based on powers of 10 (which equals 2×5), so you can rewrite the fraction with a denominator that's a power of 10, giving a finite number of decimal places. - 1/3 has denominator 3, which is not 2 or 5, so the decimal repeats (0.333…). - 1/7 has denominator 7, so the decimal repeats (0.142857…). - 1/2 has denominator 2, which fits the rule, so it terminates as 0.5. - 5/6 has denominator 6 = 2×3, and the presence of 3 makes the decimal repeat (0.8333…). So the fraction that terminates is 1/2, which equals 0.5.

A fraction has a terminating decimal representation when, after reducing to lowest terms, the denominator has only the prime factors 2 and 5. This works because decimal notation is based on powers of 10 (which equals 2×5), so you can rewrite the fraction with a denominator that's a power of 10, giving a finite number of decimal places.

• 1/3 has denominator 3, which is not 2 or 5, so the decimal repeats (0.333…).

• 1/7 has denominator 7, so the decimal repeats (0.142857…).

• 1/2 has denominator 2, which fits the rule, so it terminates as 0.5.

• 5/6 has denominator 6 = 2×3, and the presence of 3 makes the decimal repeat (0.8333…).

So the fraction that terminates is 1/2, which equals 0.5.