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## Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 2 Real Numbers Ex 2.2

Therefore, one Decimal is equal to four hundred and thirty five decimal point six Square Feet (sq ft) in Online.

Question 1.

Express the following rational numbers into decimal and state the kind of decimal expression.

(i) \(\frac{2}{7}\)

(ii) -5\(\frac{3}{11}\)

(iii) \(\frac{22}{3}\)

(iv) \(\frac{327}{200}\)

Solution:

(i) \(\frac{2}{7}\) = 0.2857142….

= 0.\(\overline {285714}\)

Non-terminating and recurring decimal expansion.

(ii) -5\(\frac{3}{11}\) = -5 + 0.272 = -5.272……..

= -5.\(\overline {27}\)

Non-terminating and recurring decimal expansion.

(iii) \(\frac{22}{3}\) = 7.333……..

= 7.\(\overline {3}\)

Non-terminating and recurring decimal expansion.

(iv) \(\frac{327}{200}\) = \(\frac{327}{2×100}\)

= \(\frac{3.27}{2}\)

= 1.635

Terminating decimal expansion.

How to convert 1/32 to decimal form? … In the fraction 1/32, 1 is the numerator and 32 is the denominator, the fraction bar means “divided by”.

Question 2.

Express \(\frac{1}{13}\) in decimal form. Find the length of the period of decimals.

Solution:

\(\frac{1}{13}\) = 0.07692307

= 0.\(\overline {076923}\)

Length of the period of decimal is 6.

9/20 as a decimal is 0.45

Question 3.

Express the rational number \(\frac{1}{33}\) in recurring decimal form by using the recurring decimal expansion of \(\frac{1}{11}\). Hence write \(\frac{71}{33}\) in recurring decimal form.

Solution:

\(\frac{1}{11}\) = 0.0909……… = 0.\(\overline {09}\)

∴ \(\frac{1}{33}\) = \(\frac{1}{3}\) × \(\frac{1}{11}\)

= \(\frac{1}{3}\) × 0.0909 ……..

= 0.0303 …… = 0.\(\overline {03}\)

\(\frac{71}{33}\) = 2\(\frac{5}{33}\) = 2 + \(\frac{5}{33}\) = 2 + 5 × \(\frac{1}{33}\)

= 2 + 5 × 0.\(\overline {03}\)

2 + (5 × 0.030303 ……..)

2 + 0.151515 ………

2+ 0.\(\overline {15}\)

2.\(\overline {15}\)

That’s literally all there is to it! 1/2 as a decimal is 0.5.

Question 4.

Express the following decimal expression into rational numbers.

(i) 0.24

Solution:

Let x = 0.242424 ………. →(1)

100 x = 24.2424 ……… →(2)

(2) – (1) ⇒ 100 x – x = 24.2424 ……….. (-)

0.2424 ……..

99 x = 24.0000

x = \(\frac{24}{99}\)

(or)

\(\frac{8}{33}\)

(ii) 2.327

Solution:

Let x = 2.327327327 ………. →(1)

1000 x = 2327.327327 ……… →(2)

(2) – (1) ⇒ 1000 x – x = 2327.327327 ……….. (-)

2.327327 ……..

999 x = 2325.000

x = \(\frac{2325}{999}\)

(or)

\(\frac{775}{333}\)

3/5 as a decimal is 0.6

(iii) – 5.132

Solution:

– 5.132 = -5 + \(\frac{1}{10}\) + \(\frac{3}{100}\) + \(\frac{2}{1000}\)

= \(\frac{-5000 + 100 +30 + 2}{1000}\) = \(\frac{-4868}{1000}\)

(or)

\(\frac{-1217}{250}\)

(iv) 3.17

Solution:

Let x = 3.1777 ………. →(1)

10 x = 31.777 ……… →(2)

100 x = 317.77 …….. →(3)

(3) – (2) ⇒ 100 x – 10 x = 317.77 ……….. (-)

31.777 ……..

90 x = 286.000

x = \(\frac{286}{90}\)

(or)

\(\frac{143}{45}\)

(v) 17.215

Solution:

Let x = 17.2151515 ………. →(1)

10 x = 172.151515 ……… →(2)

100 x = 17215.1515 …….. →(3)

(3) – (2) ⇒ 1000 x – 10 x = 17215.1515 ……….. (-)

17215.1515 ……..

990 x = 17043

x = \(\frac{17043}{990}\)

(or)

\(\frac{5681}{330}\)

(vi) -21.2137

Solution:

Let x = -21.213777 ………. →(1)

1000 x = -21213.777 ……… →(2)

100 x = -212137.77 …….. →(3)

(3) – (2) ⇒ 10000 x – 1000 x = -21213.777 ……….. (-)

-21213.777 ……..

9000 x = -190924

x = \(\frac{-190924}{9000}\)

(or)

\(\frac{-47731}{2250}\)

That’s literally all there is to it! 11/16 as a decimal is 0.6875.

Question 5.

Without actual division, find which of the following rational numbers have terminating decimal expression.

(i) \(\frac{7}{128}\)

Solution:

\(\frac{7}{128}\) = \(\frac{7}{2^{7}}\)

∴ \(\frac{7}{128}\) has terminating decimal expression.

(ii) \(\frac{21}{15}\)

Solution:

\(\frac{21}{15}\) = \(\frac{7}{5}\) = \(\frac{7}{5^1}\)

\(\frac{21}{15}\) has terminating decimal expression.

(iii) 4\(\frac{9}{35}\)

Solution:

4\(\frac{9}{35}\) = \(\frac{149}{35}\)

4\(\frac{149}{5×7}\) (It is not in the form of \(\frac{P}{2^{m} × 5^{n}}\)

∴ 4\(\frac{9}{35}\) has non-terminating recurring decimal expression.

(iv) \(\frac{219}{2200}\)

Solution:

\(\frac{219}{2200}\) = \(\frac{219}{2^{3} × 5^{2} × 11}\) (It is not in the form of \(\frac{P}{2^{m} × 5^{n}}\)

∴ \(\frac{219}{2200}\) has non-terminating recurring decimal expression.