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Question
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 non-terminating decimal representation.
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