Question

Write the decimal expansion of 13/80
without actual division

Answer 1

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If the prime factorization of the denominator of a fraction has only factors of 2 and factors of 5, the decimal expansion terminates.80=2×2×2×2×5Thus, only factors of 2 and 5 hence terminates
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Answer 2

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If the prime factorization of the denominator of a fraction has only factors of 2 and factors of 5,

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