MATH CLASS 9 Exercise 2.1 (Solutions)

Exercise 2.1 (Solutions)

            

Question 1

Identify which of the following are rational and irrational numbers:

(i) 3√ (ii) 16 (iii) π (iv) 152 (v) 7.25 (vi)29−−√

Solution

• Rational: 16, 152, 7.25
• Irrational: 3√, π, 29−−√

Question 2

Convert the following fraction into decimal fraction.

(i) 1725 (ii) 194 (iii)578

(iv) 20518 (v) 58 (vi) 2538

Soluation

• (i) o.68
• (ii) 4.75
• (iii) 7.125
• (iv) 11.3889
• (v) 0.625
• (vi) .65789

Question 3

Which of the statements are true and which of the false?

• (i) 23 is an irrational number.
• (ii) π is an irrational number.
• (iii) 19 is a terminating fraction.
• (iv) 34 is a terminating fraction.
• (v) 45 is a recurring fraction.

Soluaton

• (i) 23 is an irrational number. False
• (ii) π is an irrational number. True
• (iii) 19 is a terminating fraction. False
• (iv) 34 is a terminating fraction. True
• (v) 45 is a recurring fraction. False

Question 4

Represent the following numbers on the number line.

(i) 23 (ii) −45 (iii) 34

(iv) −258 (v) 234 (vi) 5√

Soluation

(i)

1. To represent the rational number 23 , divide unit length between 0 and 1 into 3 equal parts.
2. (ii) Take 2 parts on right of 0
3. (iii) Point M represents 23 on the number line in the following figure.

(ii)

1. To represent the rational number −45 , divide unit length between 0 and -1 into 5 equal parts.
2. Take 4 parts on right of 0
3. Point M represents −45 on the number line in the following figure.

(iii)

1. Rational number 34 lies between 1 and 2 on the number line.
2. The distance between 1 and 2 is divided into 4 equal parts , from L we take 3 parts.
3. Point M represent 34 on the number line.

(iv)

1. Rational number −258 lies between 2 and -3 on the number line.
2. The distance between 2 and -3 is divided into 8 equal parts , from 2 we take 5 parts.

(v)

1. Rational number 234 lies between 2 and 3 on the number line.
2. The distance between 2 and 3 is divided into 4 equal parts , from 2 we take 3 parts.

(vi)

1. (i) Construct a ΔOAB which mOA¯¯¯¯¯=2 unit and ⊥BA=1
2. (ii) Take O as centre and draw an arc of radius OB¯¯¯¯¯. It cuts the number line at M. mOM¯¯¯¯¯¯=5√

(mOB)2=(mOA)2+(mAB)2(PythagoreanTheorem)

(mOB¯¯¯¯¯)2=4+1=5

therefore

mOB¯¯¯¯¯=5√

thus

mOB¯¯¯¯¯=mOM¯¯¯¯¯¯=5√

Question 5

Give a rational number between 34 and 59.

Soluation

The mean of the numbers is between given numbers. Therefore 3/4+5/92=4772 is a number between required numbers.

Question 6

Express the following recurring decimals as the rational number pq, where p , q are integers and q≠0.

(i) 0.5¯ (ii) 0.13¯¯¯ (iii) 0.67¯¯¯

Soluation

(i) Let x=0.5¯. That is

x=0.5555....(1)

Only one digit 5 is being repeated, multiply 10 on both sides

10x=(0.5555.....)×10

10x=5.5555.....(2)

Subtract (1) from (2), we get

9x=5

∴x=59

0.5¯=59

(ii) Let x=0.13¯¯¯. That is

x=0.13131313....(1)

Only one digit 13 is being repeated, multiply 100 on both sides

100x=(0.13131313.....)×100

100x=13.13131313.....(2)

Subtract (1) from (2)

99x=13

∴x=1399

0.13¯¯¯=1399

(iii) Let x=0.67¯¯¯. That is

x=0.67676767....(1)

Only one digit 67 is being repeated, multiply 100 on both sides

100x=(0.67676767.....)×100

100x=67.67676767.....(2)

Subtract (1) from (2)

99x=67

∴x=6799

0.67¯¯¯=6799