Rational and Irrational Numbers Class 9 OP Malhotra Exe-1A ICSE Maths Solutions Ch-1. We Provide Step by Step Solutions / Answer of Rational and Irrational Numbers OP Malhotra Maths . Visit official Website CISCE for detail information about ICSE Board Class-9 Mathematics.
Rational and Irrational Numbers Class 9 OP Malhotra Exe-1A ICSE Maths Solutions Ch-1
| Board | ICSE |
| Publications | S Chand |
| Subject | Maths |
| Class | 9th |
| Chapter-1 | Rational and Irrational Numbers |
| Writer | OP Malhotra |
| Exe-1A | Rational Numbers |
| Edition | 2025-2026 |
Exercise-1A Rational and Irrational Numbers
Numbers Class 9 OP Malhotra ICSE Maths Solutions Ch-1
Que-1: (i) Find a rational number between 1/2 and 3/4.
(ii) Find two rational numbers between 0.1 and 0.2.
(iii) How many rational numbers can you find between two given rational numbers?
Sol: (i) One rational number between 1/2 and 3/4
= (1/2) [(1/2) + (3/4)]
= (1/2)[(2+3)/4]
= (1/2) × (5/4) = 5/8
(ii) Two rational numbers between 0.1 and 0.2 1
First number = (1/2) [0.1 + 0.2]
= (1/2) x 0.3 = 0.15 or 15/100 = 3/20
and second number = (1/2)[(3/20) + (2/10)]
= (1/2)[(3+4)/20]
= (1/2) × (7/20) = 7/40
∴ Two numbers are 3/10 and 7/40
(iii) We can find infinite numbers of rational numbers between two given rational numbers.
Que-2: Find two rational numbers between
(i) 4/5 and 7/13
(ii) 3/4 and 1*(1/5)
Sol: (i) One rational number between 4/5 and 7/13
= (1/2)[(4/5) + (7/13)] (1/2){a + b}
= (1/2) {(52+35)65} = 87/130
and second rational number
= (1/2) [(87/130) + (7/13)]
= (1/2) [(87+70)/130]
= (1/2) [157/130]
= 157/260
(ii) One rational number between 3/4 and 1*(1/5) or 3/4 and 6/5
= (1/2)[(3/4)+(6/5)]
= (1/2)[(15+24)/20]
= (1/2) [39/20]
= 3940
and second rational number
= (1/2) [(39/40) + (6/5)]
= (1/2) [(39+48)40]
= (1/2) × (87/40)
= 87/80
Que-3: Find three rational numbers between 0 and 0.2.
Sol: First rational number between 0 and 0.2 = 1/2 [0 + 0.2] = 0.1
Second rational number = 1/2 [0 + 0.1]
= 1/2 [0.1] = 0.05
and third rational number
= 1/2 [0.1 + 0.2] = 1/2 [0.3]
= 0.15
Hence three rational numbers are 0.05, 0.1 and 0.15
Que-4: Find three rational numbers between 3 and 4.
Sol: First rational number between 3 and 4
= 1/2 [3 + 4] = (1/2) x 7 = 7/2
Second rational number between 3 and 7/2
= 1/2[3+(7/2)]
= (1/2)×{(6+7)/2} = 13/4
and third number between 7/2 and 4
= 1/2[(7/2)+4]
= (1/2)[(7+8)/2]
= (1/2) × (15/2) = 15/4
Hence three rational number are
13/4, 7/2 and 15/4
Que-5: Find the rational number that is one seventh of the way from 1*(3/4) to 4*(3/8)
Sol: 1*(3/4) to 4*(3/8) = 7/4 to 35/8
= 14/8 to 35/8
Between 14 and 35, there are 21 terms i.e.
15/8, 16/8, 17/8, 18/8….., 34/8
∴ (1/7)th of 21 terms = 21 x (1/7) = 3rd
∴ 7th term = 17/8 i.e. 2*(1/8).
Que-6: Find four rational numbers between – 1 and -1/2.
Sol: We express -1 and -1/2 with a common denominator :
-1 = -2/2 = -4/4 = -8/8
-1/2 = -2/4 = -4/8
We need four rational number between -8/8 and -4/8.
Some possible choices are :
-7/8, -6/8, -5/8 and -9/16
Thus, four rational number between -1 and -1/2 are :
-7/8, -6/8, -5/8 and -9/16.
Que-7: Express 12/125 as decimal fraction.
Sol: 12/125 = 0.096
Que-8: Find a vulgar fraction equivalent to 0.0
Sol: 0.03 = 0.033333
Let x = 0.033333 ….
10x = 3.3333 …. (i)
100x = 3.3333 …. (ii)
Subtracting (i) from (ii)
99x = 3.00 ….
x = 3/90 = 1/30
∴ Required vulgar fraction = 1/10
Que-9: Express the following rational numbers in the form p/q, p, q are integers, q ≠ 0.
(i) 6.(46)¯¯
(ii) 0.1(36)¯¯
(iii) 3.(146)¯¯
(iv) – 5.(12)¯¯
Sol: (i) 6.(46)¯¯ = 6.464646 ….
Let x = 6.46464646 …. (i)
100x = 646.46464646 ….(ii)
Subtracting (i) from (ii)
99x = 646 – 6 = 640
x = 640/99
∴ Fraction = 640/99
(ii) 0.1(36)¯¯ = 0.1363636…
Let x = 0.1363636….
10x = 1.363636… (i)
and 1000x = 136.363636 ….(ii)
Subtracting (i) from (ii)
990x = 135
x = 135/990 = 27/198 = 3/22
∴ Fraction = 3/22
(iii) 3.(146)¯¯
Let x = 3.(146)¯¯ = 3.146146146… (i)
1000x = 3146.146146146…. (ii)
Subtracting (i) from (ii)
999x = 3143
x = 3143/999
Hence fraction = 3143/999
(iv) – 5.(12)¯¯
Let x = – 5.(12)¯¯ = – 5.121212 … (i)
100x = – 512.121212 ….(ii)
Subtracting (i) from (ii)
99x = 507
⇒ x = −507/99 = −169/33
∴ Fraction = −169/33.
Que-10: Write the terminating decimal numeral for the given rational number :
(i) 7/4
(ii) 29/50
(iii) 17/32
Sol: (i) 7/4 = 1.75
(ii) 29/50 = 0.58
(iii) 17/32 = 0.53125
Que-11: Write the repeating decimal for each of the following and use a bar to show the repetend.
(i) 1/9
(ii) −4/3
(iii) 1/6
Sol: (i) 1/9 = 0.1111……
= 0.(1)¯¯
(ii) -4/3 = 1.333…..
= 1.(3)¯¯
(iii) 1/6 = 0.16666……
= 0.1(6)¯¯
— : End of Rational and Irrational Numbers Class 9 OP Malhotra Exe-1A ICSE Maths Step by step Solutions :–
Return to :– OP Malhotra S Chand Solutions for ICSE Class-9 Maths
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