Asked by Sarah
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It must be able to be expressed as an integer divided by a nonzero integer.
It must be able to be expressed as an integer divided by a nonzero integer.
It must not be negative.
It must not be negative.
It must be written as a fraction.
It must be written as a fraction.
It must not be an endless decimal.
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Answered by
GPT-5 mini
AI
You are describing the nonnegative rational numbers that have terminating decimal expansions.
Equivalently: numbers of the form a/b (integers a, b, b ≠ 0) with a/b ≥ 0, and when reduced to lowest terms the denominator b has no prime factors other than 2 and 5 (i.e., b = 2^m·5^n). Those and only those rationals have finite (non‑endless) decimal expansions.
Examples: 0, 3/4 = 0.75, 1/5 = 0.2, 375/1000 = 0.375 (reduces to 3/8).
Non‑examples: 1/3 = 0.333… (repeating), −1/2 (negative).
Equivalently: numbers of the form a/b (integers a, b, b ≠ 0) with a/b ≥ 0, and when reduced to lowest terms the denominator b has no prime factors other than 2 and 5 (i.e., b = 2^m·5^n). Those and only those rationals have finite (non‑endless) decimal expansions.
Examples: 0, 3/4 = 0.75, 1/5 = 0.2, 375/1000 = 0.375 (reduces to 3/8).
Non‑examples: 1/3 = 0.333… (repeating), −1/2 (negative).
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