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Without actually performing the long division state whether the given number will have a terminating or non terminating repeating decimal expansion for: 131 / 2 raise to 5 * 5 raise to 7 * 7 raise to 5.

Answers (1)

D Deependra Verma

Theorem: Let $x=fracpq$ ? be a rational number, s.t. prime factorisation of denominator q is in the form of $2^a*5^b$ , where a, b are non-negative integers. Then, x has a decimal expansion which surely terminate.

$frac1312^5*5^7*7^5.$

Here, the denominator of given rational number is not in the form of $2^a*5^b$ so, $frac1312^5*5^7*^5$ is not terminating.

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