Question 3 ii Is 0-120120012000120000 - rational or not- If it is rational- and of the form p - g- what can you say about the prime factors of q-

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Standard X

Mathematics

Terminating and Non-Terminating Decimals

Question 3 ii...

Question

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?

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Solution

The decimal expansion is neither terminating nor recurring.
Therefore, the given number is an irrational number. And, q is not of the form $2^{m} \times 5^{n}$ where m and n are non-negative integers.

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Terminating and Non-Terminating Decimals

Standard X Mathematics

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

The decimal expansion is neither terminating nor recurring. Therefore, the given number is an irrational number. And, q is not of the form 2m× 5n where m and n are non-negative integers.

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?

The decimal expansion is neither terminating nor recurring.
Therefore, the given number is an irrational number. And, q is not of the form $2^{m} \times 5^{n}$ where m and n are non-negative integers.