Decide whether 52.123456789 is a rational number or not. If rational (in the form $\frac{p}{q}$ ), what can you say about the prime factors of q?

Rational Number, Prime factors of q will have either 2 or 5 or both

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Not rational number

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Rational Number, Prime factor of q will have a factor other than 2 or 5.

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Rational Number, Prime factor of q will be only 2.

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Solution

The correct option is A
Rational Number, Prime factors of q will have either 2 or 5 or both

It is rational because decimal expansion is terminating. Therefore, it can be expressed in $\frac{p}{q}$ form where factors of q are of the form $2^{n} {.5}^{m}$ and n and m are non-negative integers.

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Similar questions

Decide whether 52.123456789 is a rational number or not. If rational (in the form $\frac{p}{q}$ ), what can you say about the prime factors of q?

Decide whether the real number with decimal expansion as $125. ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 987654321$ is rational or not. If rational, and of the form $\frac{p}{q}$ , what can you say about the prime factors of $q$ ?

Following real number has decimal expansion as given below. Decide whether rational, or not. If rational, and of the form $\frac{p}{q}$ , what can you say about the prime factors of q? 43.123456789

Q. The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational or not. If they are rational, and of them

\frac{p}{q}

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q

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Decide whether 52.123456789 is a rational number or not. If rational (in the form pq), what can you say about the prime factors of q?

The correct option is A Rational Number, Prime factors of q will have either 2 or 5 or both It is rational because decimal expansion is terminating. Therefore, it can be expressed in pq form where factors of q are of the form 2n.5m and n and m are non-negative integers.

Decide whether 52.123456789 is a rational number or not. If rational (in the form $\frac{p}{q}$ ), what can you say about the prime factors of q?

The correct option is A
Rational Number, Prime factors of q will have either 2 or 5 or both

It is rational because decimal expansion is terminating. Therefore, it can be expressed in $\frac{p}{q}$ form where factors of q are of the form $2^{n} {.5}^{m}$ and n and m are non-negative integers.