Has the rational number 44122 - 57 - 72 a terminating or a nonterminating decimal representation-

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Byju's Answer

Standard X

Mathematics

Irrational Numbers

Has the ratio...

Question

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,

Theorem states:

Let be a rational number, such that the prime factorization of q is not of the form , where m and 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.

Hence, it has non-terminating decimal expansion.

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Similar questions

Q. Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
(i)

\frac{23}{8}

(ii)

\frac{125}{441}

(iii)

\frac{35}{50}

(iv)

\frac{77}{210}

(v)

\frac{129}{2^{2} \times 5^{7} \times 7^{17}}

(vi)

\frac{987}{10500}

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{6}{15}$

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{129}{2^{2} {.5}^{7} {.7}^{5}}$

\sqrt{2}

is
(a) a rational number
(b) an irrational number
(c) a terminating decimal
(d) a nonterminating repeating decimal

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Has the rational number 44122×57×72a terminating or a nonterminating decimal representation?

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