A Story of Numbers l Exercise 3.5 l Class 8 l NCERT Solutions – Ganita Prakash

NCERT Solutions for Class 8 Maths – Ganita Prakash

Chapter 3: A Story of Numbers

Exercise 3.5

1. Write the following numbers in base-5 system:

Method: Divide the number repeatedly by 5 and write remainders.

(i) 15

15 ÷ 5 = 3 remainder 0
3 ÷ 5 = 0 remainder 3
So, 15 = 30₅

(ii) 50

50 ÷ 5 = 10 remainder 0
10 ÷ 5 = 2 remainder 0
2 ÷ 5 = 0 remainder 2
So, 50 = 200₅

(iii) 137

137 ÷ 5 = 27 remainder 2
27 ÷ 5 = 5 remainder 2
5 ÷ 5 = 1 remainder 0
1 ÷ 5 = 0 remainder 1
So, 137 = 1022₅

(iv) 293

293 ÷ 5 = 58 remainder 3
58 ÷ 5 = 11 remainder 3
11 ÷ 5 = 2 remainder 1
2 ÷ 5 = 0 remainder 2
So, 293 = 2133₅

(v) 651

651 ÷ 5 = 130 remainder 1
130 ÷ 5 = 26 remainder 0
26 ÷ 5 = 5 remainder 1
5 ÷ 5 = 1 remainder 0
1 ÷ 5 = 0 remainder 1
So, 651 = 10101₅

2. Is there a number that cannot be represented in base-5 system?

No. Every number can be represented in base-5 system.

Reason: Any number system with base n can represent all numbers using digits from 0 to (n−1).

So, base-5 uses digits 0,1,2,3,4 and can represent all numbers.

3. Landmark numbers of base-7 system:

Landmark numbers are powers of 7:

• 7⁰ = 1
• 7¹ = 7
• 7² = 49
• 7³ = 343
• 7⁴ = 2401

General Rule:

Landmark numbers of base-n system are:

n⁰, n¹, n², n³, …