## EXERCISE 1.3 1

MATHEMATICS · Subjective · CBSE · Mathematics · Number Systems · Number Systems

Problem

## EXERCISE 1.3 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}

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? [Hint : Study the remainders while finding the value of

\frac{1}{7}

carefully.] 3. Express the following in the form

\frac{p}{q}

, where

p

and

q

are integers and

q \neq 0

. (i)

0 . \overline{6}

(ii)

0.4 \overline{7}

(iii)

0 . \overline{001}

4. Express

0.99999 \ldots

in the form

\frac{p}{q}

. Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense. 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. 6. Look at several examples of rational numbers in the form

\frac{p}{q}(q \neq 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? 7. Write three numbers whose decimal expansions are non-terminating non-recurring. 8. Find three different irrational numbers between the rational numbers

\frac{5}{7}

and

\frac{9}{11}

. 9. Classify the following numbers as rational or irrational : (i)

\sqrt{23}

(ii)

\sqrt{225}

(iii) 0.3796 (iv)

7.478478 \ldots

(v)

1.101001000100001 \ldots

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