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Has the Rational Number 441 2 2 × 5 7 × 7 2 a Terminating Or a Nonterminating Decimal Representation? - Mathematics

Numerical

Has the rational number \[\frac{441}{2^2 \times 5^7 \times 7^2}\]a terminating or a nonterminating decimal representation?

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Solution

We have, 

`441/(2^2xx5^7xx7^2)`

Theorem states: 

Let  `x=p/q` be a rational number, such that the prime factorization of q is not of the form  `2^nxx5^m` , where mand n are non-negative integers.

Then, x has a decimal expression which is non-terminating repeating.

This is clear that the prime factorization of the denominator is not of the form `2^nxx5^m` .

Hence, it has terminating decimal expansion.

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 1 Real Numbers
Q 12 | Page 58
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