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 and repeating (recurring)

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Terminating and non-repeating (non-recurring)

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None of these

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Real Integer

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Solution

The correct option is A
Non-terminating and repeating (recurring)

A decimal is terminating only when the denominator 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

Q. 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:

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. Let

x = \frac{p}{q}

be a rational number, such that the prime factorization of

q

is of the form

2^{n} 5^{m}

, where

n, m

are non-negative integers. Then

x

has a decimal expansion which terminates.

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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 and repeating (recurring) A decimal is terminating only when the denominator 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 and repeating (recurring)

A decimal is terminating only when the denominator 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.