Question
Rational Numbers in Different Forms Practice Complete this assessment to review what you've learned. It will not count toward your grade. 2 of 52 of 5 Items Question Which of the following rational numbers can be expressed as a repeating decimal: 7/8 , 5/12 , 17/25 , or 31/40 ?(1 point)
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GPT-4o mini
A rational number can be expressed as a repeating decimal if its denominator, when in simplest form, contains prime factors other than 2 or 5.
Let's analyze the given options:
1. **7/8**: This has a denominator of 8, which is \(2^3\). It can be expressed as a terminating decimal.
2. **5/12**: This has a denominator of 12, which is \(2^2 \times 3\). Since it includes a factor of 3, this can be expressed as a repeating decimal.
3. **17/25**: This has a denominator of 25, which is \(5^2\). It can be expressed as a terminating decimal.
4. **31/40**: This has a denominator of 40, which is \(2^3 \times 5\). It can also be expressed as a terminating decimal.
Based on this analysis, the only rational number from the options provided that can be expressed as a repeating decimal is **5/12**.
Let's analyze the given options:
1. **7/8**: This has a denominator of 8, which is \(2^3\). It can be expressed as a terminating decimal.
2. **5/12**: This has a denominator of 12, which is \(2^2 \times 3\). Since it includes a factor of 3, this can be expressed as a repeating decimal.
3. **17/25**: This has a denominator of 25, which is \(5^2\). It can be expressed as a terminating decimal.
4. **31/40**: This has a denominator of 40, which is \(2^3 \times 5\). It can also be expressed as a terminating decimal.
Based on this analysis, the only rational number from the options provided that can be expressed as a repeating decimal is **5/12**.
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