Q.1. Write the following in decimal form and say what kind of decimal expansion each has:

(i) $\frac{36}{100}$

(ii) $\frac{1}{11}$

(iii) $4\frac{1}{8}$

(iv) $\frac{3}{13}$

(v) $\frac{2}{11}$

(vi) $\frac{329}{400}$

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Q.2. You know that $\frac{1}{7}=0.\overline{142857}$. Can you predict what the decimal expansions of $\frac{2}{7},\,\frac{3}{7},\frac{4}{7},\,\frac{5}{7},\,\,\frac{6}{7}\,$are, without actually doing the long division? If so, how?

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Q.3. Express the following in the form $\frac{p}{q}$, where p and q are integers and q ≠ 0.

(i) $0.\overline{6}$

(ii) $0.4\overline{7}$

(iii) $0.\overline{001}$

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Q.4. Express 0.99999 …. in the form $\frac{p}{q}$ . Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

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Q.5. What can the maximum number of digits be in the repeating block of digits in the decimal expansion of $\frac{1}{17}$? Perform the division to check your answer.

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Q.6. Look at several examples of rational numbers in the form $\frac{p}{q}(q\ne 0)$, where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

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Q.7. Write three numbers whose decimal expansions are non-terminating non-recurring.

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Three numbers whose decimal representations are non-terminating and non-repeating are

0.10100100010000…., 0.20200200020000…, 0.30300300030000…. so on.

Q.8. Find three different irrational numbers between the rational numbers $\frac{5}{7}$ and $\frac{9}{11}$.

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Q.9. Classify the following numbers as rational or irrational:

(i) $\sqrt{23}$

(ii) $\sqrt{225}$

(iii) 0.3796

(iv) 7.478478…

(v) 1.101001000100001…

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NCERT Solutions For Class 9 Maths Chapter 1 Number Systems (All Exercises)