Question 3 i Is 43-123456789 rational or not- If it is rational- and of the form p-q- what can you say about the prime factors of q-

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Standard X

Mathematics

Rational Numbers

Question 3 i ...

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Question 3 (i)
Is 43.123456789 rational or not. If it is rational, and of the form $\frac{p}{q}$ , what can you say about the prime factors of q?

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Solution

The number 43.123456789 has a terminating decimal expansion. Thus, it is a rational number of the form $\frac{p}{q}$ .
And, q is of the form $2^{m} \times 5^{n}$ where m and n are non-negative integers.

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Q. Is 43.123456789 rational or not. If it is rational, and of the form

\frac{p}{q}

, what can you say about the prime factors of q?

Question 3 (ii)
Is 0.120120012000120000... rational or not. If it is rational, and of the form $\frac{p}{q}$ , what can you say about the prime factors of q?

Question 3 (ii)
Is 0.120120012000120000... rational or not. If it is rational, and of the form $\frac{p}{q}$ , what can you say about the prime factors of q?

Q. Question 3 (i)
The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form

\frac{p}{q}

, what can you say about the prime factors of q?
43.123456789

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

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Rational Numbers

Standard X Mathematics

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Question 3 (i) Is 43.123456789 rational or not. If it is rational, and of the form pq, what can you say about the prime factors of q?

The number 43.123456789 has a terminating decimal expansion. Thus, it is a rational number of the form pq. And, q is of the form 2m× 5n where m and n are non-negative integers.

Question 3 (i)
Is 43.123456789 rational or not. If it is rational, and of the form $\frac{p}{q}$ , what can you say about the prime factors of q?

The number 43.123456789 has a terminating decimal expansion. Thus, it is a rational number of the form $\frac{p}{q}$ .
And, q is of the form $2^{m} \times 5^{n}$ where m and n are non-negative integers.