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)

Theorem: Let$x=\frac{p}{q}$? 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.

$\frac{131}{2^5*5^7*7^5}.$

Here, the denominator of given rational number is not in the  form of $2^a*5^b$ so, $\frac{131}{2^5*5^7*^5}$ is  not terminating.

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