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.

True

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False

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Neither

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Either

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Solution

The correct option is B False
If q is not of the form $2^{n} * 5^{m}$ then definitely q can take any of the values 3,6,9,12,15,...etc.
As we know 4/3,20/6 all are non-terminating, thus required decimal expansion is non terminating.

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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 ____________.

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. 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:

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If x=pq be a rational number such that the prime factorization of q is not of the form 2n5m, where n,m are non-negative integers. Then x has a decimal expansion which is terminating.

The correct option is B FalseIf q is not of the form 2n∗5m then definitely q can take any of the values 3,6,9,12,15,...etc.As we know 4/3,20/6 all are non-terminating, thus required decimal expansion is non terminating.

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.

The correct option is B False
If q is not of the form $2^{n} * 5^{m}$ then definitely q can take any of the values 3,6,9,12,15,...etc.
As we know 4/3,20/6 all are non-terminating, thus required decimal expansion is non terminating.