# 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?

#### 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.

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#### APPEARS IN

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