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Any TERMINATING decimal can be written as a fraction with a denominator that is a power of 10 - which has the prime factors 2 and 5. Therefore, any fraction (in simplest terms) must have a denominator which is only made up of the prime factors 2 and 5. Any other factor, and the fraction will not be terminating.As to why it repeats, that's because in the division, there are only so many options. For example, if you divide by 7, the remainder, in each step of the division, can only be a number between 1 and 6. Eventually, the pattern will repeat.

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9y ago
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8y ago

You will get a repeating decimal (or decimals) if the divisor, in the simplified form of the division, contains any prime factor other than 2 or 5.

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Q: Why do I get a repeating decimal when I divide?
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