Look at the representation of 60. What will be the representation for 3,600?
Given: The Mesopotamian system is a place value system with base 60.
Positions:
- Rightmost = 1s position (60⁰)
- Next = 60s position (60¹)
- Next = 3600s position (60²)
Pattern:
- 1 is in the 1s position
- 60 is in the 60s position
- 3600 is in the 3600s position
Calculation: 3,600 = 60²
Answer: The representation for 3,600 would be a single ⌈ symbol placed in the 3600s position (the third position from the right), with blank spaces or placeholders in the 60s and 1s positions.
Reasoning: Since 3,600 = 60², it occupies the position for 3600s, just as 60 occupies the position for 60s. This illustrates the elegance of place value systems.
Explanation
The chapter explains that the Mesopotamian system is a place value system with base 60. The positions represent powers of 60: rightmost = 1s (60⁰), next = 60s (60¹), next = 3600s (60²). Just as 60 is represented by a single symbol in the 60s position, 3600 is represented by a single symbol in the 3600s position. This illustrates the elegance of place value systems.
Solution Steps
Identify the Mesopotamian number system as a base-60 place value system.
Recognize the positions: 1s (60⁰), 60s (60¹), 3600s (60²).
Calculate: 3,600 = 60².
Place a single ⌈ symbol in the 3600s position (third position from the right).
Leave the 60s and 1s positions blank or with placeholders.