how will you prove that 17/8 is terminating whereas 17/6 is non terminating without doing long division method
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the denominator 8 in 17/8 can be written as 2^3.
As the denominator is of the 2^m( it can also be of the form 5^n or 2^m×5^n) it has a terminating decimal expansion.
Whereas in 17/6 the denominator 6 can be expressed as 2×3 which is not of the form 2^m or 5^n or 2^m×5^n, it has a non terminating decimal expansion.
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