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## Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 2 Real Numbers Additional Questions

I. Multiple choice question

Question 1.
The decimal form of –$$\frac{3}{4}$$ is ………
(a) – 0.75
(b) – 0.50
(c) – 0.25
(d) – 0.125
Solution:
(a) – 0.75

Question 2.
If a number has a non-terminating and non-recurring decimal expansion, then it is……….
(a) a rational number
(b) a natural number
(c) an irrational number
(d) an integer
Solution:
(c) an irrational number

Question 3.
Which one of the following has terminating decimal expansion?
(a) $$\frac{7}{9}$$
(b) $$\frac{8}{15}$$
(c) $$\frac{1}{12}$$
(d) $$\frac{5}{32}$$
Solution:
(d) $$\frac{5}{32}$$

Question 4.
Which of the following are irrational numbers?
(i) $$\sqrt{2+\sqrt3}$$
(ii) $$\sqrt{4+\sqrt25}$$
(iii) $$\sqrt[3]{5+\sqrt7}$$
(iv) $$\sqrt{8-\sqrt[3]8}$$
(a) (ii), (iii) and (iv)
(b) (i), (iii) and (iv)
(c) (i), (ii) and (iii)
(d) (i), (iii) and (iv)
Solution:
(d) (i), (iii) and (iv)

Question 5.
Irrational number has a
(a) terminating decimal
(b) no decimal part
(c) non-terminating and recurring decimal
(d) non-terminating and non-recurring decimal
Solution:
(d) non-terminating and non-recurring decimal

Question 6.
If $$\frac{1}{7}$$ = 0.142857, then the value of $$\frac{3}{7}$$ is……..
(a) 0.285741
(b) 0.428571
(c) 0.285714
(d) 0.574128
Solution:
(b) 0.428571

Question 7.
Which of the following are not rational numbers?
(a) 7√5
(b) $$\frac{7}{\sqrt{5}}$$
(c) $$\sqrt{36}$$ – 9
(d) π + 2
Solution:
(c) $$\sqrt{36}$$ – 9

Question 8.
The product of 2√5 and 6√5 is……….
(a) 12√5
(b) 60
(c) 40
(d) 8√5
Solution:
(b) 60

Question 9.
The rational number lying between $$\frac{1}{5}$$ and $$\frac{1}{2}$$
(a) $$\frac{7}{20}$$
(b) $$\frac{2}{10}$$
(c) $$\frac{2}{7}$$
(d) $$\frac{3}{10}$$
Solution:
(a) $$\frac{7}{20}$$

Question 10.
The value of 0.03 + 0.03 is ……….
(a) 0.$$\overline { 09 }$$
(b) 0.$$\overline { 0303 }$$
(c) 0.$$\overline { 06 }$$
(d) 0
Solution:
(c) 0.06

Question 11.
The sum of $$\sqrt{343}$$ + $$\sqrt{567}$$ is
(a) 18√3
(b) 16√7
(c) 15√3
(d) 14√7
Solution:
(b) 16√7

Question 12.
If $$\sqrt{363}$$ = x√3 then x = ………
(a) 8
(b) 9
(c) 10
(d) 11
Solution:
(d) 11

Question 13.
The rationalising factor of $$\frac{1}{\sqrt{7}}$$ is ……….
(i) 7
(b) √7
(c) $$\frac{1}{7}$$
(d) $$\frac{1}{\sqrt{7}}$$
Solution:
(b) √7

Question 14.
The value of $$(\frac{1}{3^5})^4$$ is ……..
(a) 320
(b) 3-20
(c) $$\frac{1}{3^{-20}}$$
(d) $$\frac{1}{3^{9}}$$
Solution:
(b) 3-20

Question 15.
What is 3.976 × 10-4 written in decimal form?
(a) 0.003976
(b) 0.0003976
(c) 39760
(d) 0.03976
Solution:
(b) 0.0003976

Question 1.
Find any seven rational numbers between $$\frac{5}{8}$$ and –$$\frac{5}{6}$$
Solution:
Let us convert the given rational numbers having the same denominators.
L.C.M of 8 and 6 is 24.

Now the rational numbers between

We can take any seven of them.

Question 2.
Find any three rational numbers between $$\frac{1}{2}$$ and $$\frac{1}{5}$$
Solution:

Thus the three rational numbers are $$\frac{7}{20}$$, $$\frac{17}{40}$$ and $$\frac{37}{80}$$

Question 3.
Represent $$-\frac{2}{11}$$, $$-\frac{5}{11}$$ and $$-\frac{9}{11}$$ on the number lines.
Solution:

To Represent $$-\frac{2}{11}$$, $$-\frac{5}{11}$$ and $$-\frac{9}{11}$$ on the number line we make 11 markings each being equal distence $$\frac{1}{11}$$ on the left of 0.
The point A represent $$(-\frac{2}{11})$$, the point B represents $$(-\frac{5}{11})$$ and the point C represents $$(-\frac{9}{11})$$

Question 4.
Express the following in the form $$\frac{p}{q}$$, where p and q are integers and q ≠ 0.
(i) 0.$$\overline { 47 }$$
Solution:
Let x = 0.474747…….. →(1)
100 x = 47.4747…….. →(2)
(2) – (1) ⇒ 100x – x = 47.4747……..
(-) 0.4747……..
99 x = 47.0000
x = $$\frac{47}{99}$$
∴ 0.$$\overline { 47 }$$ = $$\frac{47}{99}$$

(ii) 0.$$\overline { 57 }$$
Solution:
Let x = 0.57777…….. →(1)
10 x = 5.77777…….. →(2)
100 x = 57.7777…….. →(3)
(3) – (2) ⇒ 100 x – 10 x = 57.7777……..
(-) 5.7777……..
99 x = 52.0000
x = $$\frac{52}{90}$$ = $$\frac{26}{45}$$
∴ 0.$$\overline { 57 }$$ = $$\frac{26}{45}$$

(iii) 0.$$\overline { 245 }$$
Solution:
Let x = 0.2454545…….. →(1)
10 x = 2.454545…….. →(2)
1000 x = 245.4545…….. →(3)
(3) – (2) ⇒ 1000 x – 10 x = 245.4545
(-) 2.4545………
990 x = 243.00000
x = $$\frac{243}{990}$$ (or) $$\frac{27}{110}$$
∴ 0.$$\overline { 245 }$$ = $$\frac{27}{110}$$

Question 5.
Without actual division classify the decimal expansion of the following numbers as terminating or non-terminating and recurring.
(i) $$\frac{7}{16}$$
(ii) $$\frac{13}{150}$$
(ii) –$$\frac{11}{75}$$
(iv) $$\frac{17}{200}$$
Solution:
(i) $$\frac{7}{16}$$ = $$\frac{7}{2^4}$$ = $$\frac{7}{2^{4} \times 5^{0}}$$
∴ $$\frac{7}{16}$$ has a terminating decimal expansion.

(ii) $$\frac{13}{150}=\frac{13}{2 \times 3 \times 5^{2}}$$
Since it is not in the form of $$\frac{P}{2^{m} \times 5^{n}}$$
∴ $$\frac{13}{150}$$ as non-terminating and recurring decimal expansion.

(iii) $$-\frac{11}{75}=-\frac{11}{3 \times 5^{2}}$$
Since it is not in the form of $$\frac{P}{2^{m} \times 5^{n}}$$
∴ –$$\frac{11}{75}$$ as non-terminating and recurring decimal expansion.

(iv) $$\frac{17}{200}=\frac{17}{2^{3} \times 5^{2}}$$
∴ $$\frac{17}{200}$$ has a terminating decimal expansion.

Question 6.
Find the value of $$\sqrt{27}$$ + $$\sqrt{75}$$ – $$\sqrt{108}$$ + $$\sqrt{48}$$
Solution:

= 3√3 + 5√3 – 6√3 + 4√3
= 12√3 – 6√3
= 6√3
= 6 × 1.732
= 10.392

Question 7.
Evaluate $$\frac{\sqrt{2}+1}{\sqrt{2-1}}$$
Solution:

= 2√2 + 3
= 2 × 1.414 + 3
= 2.828 + 3
= 5.828

Question 8.

Solution:

= 69984 × 1021-21-20+9
= 69984 × 10-32
= 6.9984 × 104 × 10-32
= 6.9984 × 10-32+4
= 6.9984 × 10-28

Question 9.
Write
(a) 9.87 × 109
(b) 4.134 × 10-4 and
(c) 1.432 × 10-9 in decimal form.
Solution:
(a) 9.87 × 109 = 9870000000
(b) 4.134 × 10-4 = 0.0004134
(c) 1.432 × 10-9 = 0.000000001432