Look at the representation of 60. What will be the representation for 3,600?

Question

Homi · Accepted Answer

Understand the Question

The Mesopotamian numeral system is a sexagesimal (base-60) positional number system.
In this system, position determines the place value:
- Units place: $60^0 = 1$
- Sixties place: $60^1 = 60$
- Thirty-six hundreds place: $60^2 = 3600$
Because each power of $60$ occupies a new place value, a single unit in the $60^0$ , $60^1$ , or $60^2$ place is written with the same single unit symbol (a downward wedge $\nabla$ ).

Step 1 · Analyze the Mesopotamian Positional System

Diagram 1

In the Mesopotamian number system, the basic symbols are: $\nabla = 1$ $< = 10$

Combined within a single position: $<< \nabla\nabla = 10 + 2 = 12$

Because it is a base-60 system, place values are powers of $60$ :

First position: $60^0 = 1$
Second position: $60^1 = 60$
Third position: $60^2 = 3600$

For example: $10 \times 60^1 + 2 \times 60^0 = 600 + 2 = 602$ $10 \times 60^2 + 0 \times 60^1 + 2 \times 60^0 = 36000 + 0 + 2 = 36002$

Step 2 · Determine Representation for 3,600

Since $3600 = 1 \times 60^2$ , it corresponds to $1$ unit placed in the $60^2$ position.

Just as $1$ ( $1 \times 60^0$ ) and $60$ ( $1 \times 60^1$ ) are represented by a single downward wedge ( $\nabla$ ), the number $3600$ ( $1 \times 60^2$ ) is also represented by a single downward wedge $\nabla$ .

Answer

$\nabla$ (a single downward wedge)

Common Mistakes

Expecting a New Symbol: Assuming higher numbers like $3,600$ require a completely new symbol rather than the unit wedge $\nabla$ positioned in the $60^2$ place.
Base Confusion: Treating the system as base-10 rather than base-60, where place values increment by factors of $60$ ( $1, 60, 3600, \dots$ ).

Question 22

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