The decimal representation of 18/7 is a non-terminating repeating decimal.

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Multiple Choice

The decimal representation of 18/7 is a non-terminating repeating decimal.

Explanation:
The decimal form of a fraction terminates only when the denominator, in simplest form, has no prime factors other than 2 or 5. Here the denominator is 7, which is not 2 or 5, so the decimal cannot terminate. Instead it repeats forever. In fact, 18/7 equals 2.571428571428..., with the block 571428 repeating. So it’s a non-terminating repeating decimal. It’s not irrational because it’s a ratio of integers, and it’s not a whole number because there’s a nonzero fractional part.

The decimal form of a fraction terminates only when the denominator, in simplest form, has no prime factors other than 2 or 5. Here the denominator is 7, which is not 2 or 5, so the decimal cannot terminate. Instead it repeats forever. In fact, 18/7 equals 2.571428571428..., with the block 571428 repeating. So it’s a non-terminating repeating decimal. It’s not irrational because it’s a ratio of integers, and it’s not a whole number because there’s a nonzero fractional part.

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