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Check If a Given Rational No. Is Terminating or Not

Let x = p / q...

Question

Let $x = \frac{p}{q}$ be a rational number, such that the prime factorisation of q is not of the form $2^{m} 5^{n}$ , where n, m are non-negative integers. Then, x has a decimal expansion which is:

Non-terminating repeating (recurring)

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Terminating non-repeating (non-recurring)

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Real Integer

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None of these

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Solution

The correct option is A Non-terminating repeating (recurring)
A decimal is terminating only when the denominators can be prime factored in the form of $2^{m} 5^{n}$ . If the denominator has any other prime factor then the decimal becomes non-terminating and repeating.

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Similar questions

Let $x = \frac{p}{q}$ be a rational number, such that the prime factorization of q is not of the form $2^{n} 5^{m}$ , where n, m are non-negative integers. Then, x has a decimal expansion which is ____________.

Q. Assertion (A):

\frac{29}{9261}

will have a non-terminating, non-repeating decimal expansion.
Reason (R): Let

a = \frac{p}{q}

be a rational number such that

p

and

q

are co-prime and the prime factorisation of

q

is of the form

2^{n} \times 5^{m}

, where

n

and

m

are non-negative integers. Then

a

has a decimal expansion, which is non-terminating.

Let $x = \frac{p}{q}$ be a rational number, such that the prime factorisation of $q$ is not of the form $2^{m} 5^{n}$ , where $n, m$ are non-negative integers. Then, $x$ has a decimal expansion which is

Q. If

x = \frac{p}{q}

be a rational number such that the prime factorization of

q

is not of the form

2^{n} 5^{m}

, where

n, m

are non-negative integers. Then

x

has a decimal expansion which is terminating.

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Let x=pq be a rational number, such that the prime factorisation of q is not of the form 2m5n, where n, m are non-negative integers. Then, x has a decimal expansion which is:

The correct option is A Non-terminating repeating (recurring) A decimal is terminating only when the denominators can be prime factored in the form of 2m5n. If the denominator has any other prime factor then the decimal becomes non-terminating and repeating.

Let $x = \frac{p}{q}$ be a rational number, such that the prime factorisation of q is not of the form $2^{m} 5^{n}$ , where n, m are non-negative integers. Then, x has a decimal expansion which is:

The correct option is A Non-terminating repeating (recurring)
A decimal is terminating only when the denominators can be prime factored in the form of $2^{m} 5^{n}$ . If the denominator has any other prime factor then the decimal becomes non-terminating and repeating.