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Write the Condition to Be Satisfied by Q So that a Rational Number P Q Has a Terminating Decimal Expansions. - Mathematics

Numerical

Write the condition to be satisfied by q so that a rational number\[\frac{p}{q}\]has a terminating decimal expansions.

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Solution

We need to find the condition to be satisfied by q so that a rational number `p/q` has a terminating decimal expression.

For the terminating decimal expression, we should have a multiple of 10 in the denominator.

Hence, the prime factorization of q must be of the form `2^mxx5^n`, where m and n are non-negative integers.

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APPEARS IN

RD Sharma Class 10 Maths
Chapter 1 Real Numbers
Q 8 | Page 58
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