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**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 × 10^{4}

**Question no – (5)**

**Solution : **

Given, .000002

= 2 × 10^{-6}

**Question no – (6)**

**Solution : **

Given, 1.5 × 10^{7}/3.6 × 10^{4 }

= 125/3 × 10

**Question no – (7)**

**Solution : **

Given, x × y, where x = 5.5 × 10^{4}; y = 3.2×10^{3 }

= 1.76 × 10^{8}

**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 × 10^{12 }

**Question no – (13) **

**Solution : **

= V = 33000 cm/sec

= 3.3 × 10^{4} cm/sec

**Question no -(14) **

**Solution : **

Scientific notation,

= 9460500000000 × 9.4605 × 10^{15}

= 8.950106025 **…(Simplified)**

**Next Chapter Solution : **

👉 Chapter 4 👈