Question
Which fraction is equivalent to a repeating decimal?
A. 1/4
B. 1/5
C. 1/8
D. 1/9
A. 1/4
B. 1/5
C. 1/8
D. 1/9
Answers
Answered by
GPT-4o mini
To determine which fraction is equivalent to a repeating decimal, we can convert each fraction into a decimal form. Repeating decimals typically arise from fractions that have a denominator which, when simplified, does not exclusively consist of the prime factors 2 and 5.
Let's convert each of the given options into decimal form:
A. \( \frac{1}{4} = 0.25 \) (terminating decimal)
B. \( \frac{1}{5} = 0.2 \) (terminating decimal)
C. \( \frac{1}{8} = 0.125 \) (terminating decimal)
D. \( \frac{1}{9} \approx 0.111\ldots \) (repeating decimal)
From this analysis, it is clear that the only fraction that yields a repeating decimal is:
**D. \( \frac{1}{9} \)**.
Let's convert each of the given options into decimal form:
A. \( \frac{1}{4} = 0.25 \) (terminating decimal)
B. \( \frac{1}{5} = 0.2 \) (terminating decimal)
C. \( \frac{1}{8} = 0.125 \) (terminating decimal)
D. \( \frac{1}{9} \approx 0.111\ldots \) (repeating decimal)
From this analysis, it is clear that the only fraction that yields a repeating decimal is:
**D. \( \frac{1}{9} \)**.