Question 3 iii Is 43-123446789 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 ii...

Question

Question 3 (iii)
Is $43. ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 123446789$ 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

It is rational because decimal expansion is recurring.
Therefore, it can be expressed in the form of $\frac{p}{q}$ and the factorisation of q is not of the form $2^{m} \times 5^{n}$ where m and n are non-negative integers.

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Question 3 (iii) Is 43.¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯123446789 rational or not. If it is rational, and of the form pq, what can you say about the prime factors of q?

It is rational because decimal expansion is recurring. Therefore, it can be expressed in the form of pq and the factorisation of q is not of the form 2m×5n where m and n are non-negative integers.

Question 3 (iii)
Is $43. ¯ ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ ¯ 123446789$ rational or not. If it is rational, and of the form $\frac{p}{q}$ , what can you say about the prime factors of q?

It is rational because decimal expansion is recurring.
Therefore, it can be expressed in the form of $\frac{p}{q}$ and the factorisation of q is not of the form $2^{m} \times 5^{n}$ where m and n are non-negative integers.