Question

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

Answer 1

If the factors of denominator of the given rational number is of form 2^m 5ⁿ ,where n and m are non negative integers, then the decimal expansion of the rational number is terminating otherwise non terminating recurring.It terminates after k places of decimals where k is the larger of m and n.

SOLUTION :

Given : 441/2² × 5^7 × 7²

Here, the factors of the denominator are  2² × 5^7 × 7²  which is not in  the form 2^m 5ⁿ . So , 441/2² × 5^7 × 7² has a non terminating  repeating decimal expansion.

Hence, 441/2² × 5^7 × 7² has non terminating  decimal expansion.

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Answer 2

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