A Story of Numbers l Exercise 3.8 l Class 8 l NCERT Solutions – Ganita Prakash

NCERT Solutions for Class 8 Maths – Ganita Prakash

Chapter: A Story of Numbers

Exercise 3.8

1. Represent the following numbers in the Mesopotamian (Babylonian) system:

Note:

• Mesopotamian system is a base-60 system.
• It uses two symbols:
  • 𒐕 (vertical wedge) = 1
  • 𒐖 (corner wedge) = 10
• Numbers are written in groups of 60 (like place value system).

(i) 63

63 = 1 × 60 + 3

Representation:

(1 sixty)    (3 ones → 𒐕𒐕𒐕)

(ii) 132

132 = 2 × 60 + 12

12 = 10 + 2 → 𒐖𒐕𒐕

Representation:

(2 sixties)    (𒐖𒐕𒐕)

(iii) 200

200 = 3 × 60 + 20

20 = 2 × 10 → 𒐖𒐖

Representation:

(3 sixties)    (𒐖𒐖)

(iv) 60

60 = 1 × 60 + 0

Representation:

(1 sixty)    (0)

(v) 3605

3605 ÷ 60 = 60 remainder 5
60 ÷ 60 = 1 remainder 0

So, 3605 = 1 × 60² + 0 × 60 + 5

Representation:

(1 in 60² place)    (0 in 60 place)    (𒐕𒐕𒐕𒐕𒐕)

Conclusion:

Mesopotamian numbers are written in base-60 using groups, where each group represents a place value (like units, 60s, 60², etc.).