Question

why is $-3\frac{1}{8}$ a rational number? \
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it is rational because all negative numbers are rational \
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it is rational because all integers are rational \
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it is rational because it can be expressed as a repeating decimal \
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it is rational because it can be expressed as a terminating decimal

Explanation:

1. Analyze the first option: Not all negative numbers are rational (e.g., \(-\sqrt{2}\) is irrational), so this is incorrect.
2. Analyze the second option: \(-3\frac{1}{8}\) is a mixed number, not an integer (though integers are rational, this reasoning doesn't apply here as it's a fraction), so this is incorrect.
3. Analyze the third option: \(-3\frac{1}{8}=-\frac{25}{8}=-3.125\), which is a terminating decimal, not a repeating decimal, so this is incorrect.
4. Analyze the fourth option: A rational number is a number that can be expressed as a fraction of two integers (\(\frac{p}{q}, q

eq0\)) or as a terminating or repeating decimal. \(-3\frac{1}{8}=-\frac{25}{8}=-3.125\), which is a terminating decimal, so it is rational because it can be expressed as a terminating decimal.

Answer:

It is rational because it can be expressed as a terminating decimal (the fourth option).