# Brilliant’s Composite Mathematics Class 7 Solutions Chapter 3

## Brilliant’s Composite Mathematics Class 7 Solutions Chapter 3 Decimal Representation of Rational Numbers

Welcome to NCTB Solutions. Here with this post we are going to help 7th class students for the Solutions of Brilliant’s Composite Mathematics Class 7 Math Book, Chapter 3, Decimal Representation of Rational Numbers. Here students can easily find step by step solutions of all the problems for Decimal Representation of Rational Numbers, Exercise 3.1, 3.2 and 3.3 Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily.

Decimal Representation of Rational Numbers Exercise 3.1 Solution

Question no – (1)

Solution :

Given, 3/4

= Terminating

Question no – (2)

Solution :

Given, -7/13

= Not terminating

Question no – (3)

Solution :

Given, 5/28

= Not terminating

Question no – (4)

Solution :

Given, 33/45

= Not terminating

Question no – (5)

Solution :

Given, -7/15

= Not terminating

Question no – (6)

Solution :

Given, 13/25

= Terminating

Question no – (7)

Solution :

Given, -13/28

= non-terminating

Question no – (8)

Solution :

Given, 15/32

= Terminating

Question no – (9)

Solution :

Given, 4/15

= Non-terminating

Question no – (10)

Solution :

Given, 45/132

= Non-terminating

Question no – (11)

Solution :

Given, -23/60

= Non-terminating

Question no – (12)

Solution :

Given, 17/125

= Terminating

Question no – (13)

Solution :

Given, -5/27

= -0.185

Question no – (14)

Solution :

Given, 13/25

= 0.52

Question no – (15)

Solution :

Given, 9/16

= 0.5625

Question no – (16)

Solution :

Given, -41/45

= -0.9111

Question no – (17)

Solution :

Given, 16/33

= 0.48

Question no – (20)

Solution :

(a) 3/4 can be written as a terminating decimal → True

(b) -2/5 can be not be written as a terminating → False

(c) 5/4 can be written as a terminating decimal → True

(d) -13/45 can not be written as a terminating decimal → True

(e) 2/5 + 3/7 + 4/9 can be written as a terminating decimal → True

(f) Number 5.324 is the same as 5.32432432 → False

(g) Decimal representation of 14/19 is a non- terminating repeating decimal → True

Decimal Representation of Rational Numbers Exercise 3.2 Solution

Question no – (1)

Solution :

Given, .475

= 475/1000

= 5 × 5 × 19/5 × 5 × 40

= 19/40

Question no – (2)

Solution :

Given, 3.72

= 372/100

= 93 × 2 × 2/5 × 5 × 2 × 2

= 93/25

Question no –  (3)

Solution :

Given, 15.7208

= 157208/1000

= 19651 × 4 × 2/5 × 5 × 5 × 4 × 5 × 4

= 19651/1250

Question no – (4)

Solution :

Given, 17.855

= 17855/1000

= 3571 × 5/5 × 5 × 5 × 8

= 3571/200

Question no – (5)

Solution :

Given, 132.884

= 132884/1000

= 33221 × 4/ × 5 × 5 × 5 × 8

= 33221/250

Question no – (6)

Solution :

Given, 10.1001

= 101001/10000

= 101001 × 1/5 × 5 × 5 × 5 × 4 × 5 × 4

= 101001/10000

Question no – (7)

Solution :

Given, 3.24

Let, x = n = 3.24

100n = 342.24

n = 3.24
——————————————
99n = 321

n = 321/99 = 107/33

Question no – (8)

Solution :

Given, .7575

Let, n = 575

100n = 575. 575

n = 575
——————————————
= 999 n = 575

n = 575/999

Question no – (9)

Solution :

Given, 102.255

Let, 100n = 10225.55

= 10n = 1025.55
——————————————
90n = 9203

or, n = 9203/90

Question no – (10)

Solution :

Given, 3.4 + 14.2

3.4 = 3.4444

+ 14.2 = 14.2222
——————————————
= 3.4+14.2 = 17.666666

Let, 10n = 1766.6

= n = 17.6

Question no – (14)

Solution :

(a) 2.818181 is not a rational number → False

(b) 5.10203040 is a rational number → False

(c) 13.65234234234 is a rational number → True

(d)  .234423442344 is a rational number → True

Decimal Representation of Rational Numbers Exercise 3.3 Solution

Question no – (1)

Solution :

Given numbers are 4/5, 5/2

= 4/5 = 0.5

= 2/5 = 0.4

Five rational number 0,41, 0.42, 0.43, 0.44, 0.45, 0.5

Question no – (2)

Solution :

Given, 5400000

= 5.4 × 106

Question no – (3)

Solution :

Given, .0007652

= 7.652 × 10-4

Question no – (4)

Solution :

Given, 3.2 × 106 × 1.2 × 10-2

= 3.84 × 104

Question no – (5)

Solution :

Given, .000002

= 2 × 10-6

Question no – (6)

Solution :

Given, 1.5 × 107/3.6 × 10

= 125/3 × 10

Question no – (7)

Solution :

Given, x × y, where x = 5.5 × 104; y = 3.2×10

= 1.76 × 108

Question no – (8)

Solution :

Given, 6.024 × 105

= 602400

Question no – (9)

Solution :

Given, 9.2 × 106

= 9200000

Question no – (10)

Solution :

Given, 1.07 × 10-7

= .000000107

Question no – (11)

Solution :

Given, 1.5 × 10-4

= .00015

Question no – (12)

Solution :

The total number of blood cells = 550000 × 5000000

= 27.5 × 1012

Question no  – (13)

Solution :

= V = 33000 cm/sec

= 3.3 × 104 cm/sec

Question no -(14)

Solution :

Scientific notation,

= 9460500000000 × 9.4605 × 1015

= 8.950106025   …(Simplified)

Next Chapter Solution :

Updated: June 9, 2023 — 4:20 pm