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

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Homi · Accepted Answer

The Mesopotamian number system uses symbols whose value depends on their position.

Step 1 — Understanding the basic symbols

Let us examine the symbols used in the Mesopotamian representation. The table shows a single downward wedge represents 1.

$\nabla = 1$

The table also shows a left-pointing chevron represents 10.

$< = 10$

These symbols combine for numbers from 1 to 59 in one place. For example, 12 uses one '10' symbol and two '1' symbols.

$<< \nabla\nabla = 10 + 2 = 12$

Step 2 — Analyzing the positional system

Now, let us look at the representations for 1, 60, and 3600. The table shows that 1 is represented by $\nabla$ . The number 60 is also represented by $\nabla$ . The number 3600 is also represented by $\nabla$ . This indicates the Mesopotamian system is a base-60 positional system. In this system, a symbol's value changes with its position. The rightmost position represents units ( $60^0 = 1$ ). The next position to the left represents multiples of 60 ( $60^1 = 60$ ). The next position to the left represents multiples of 3600 ( $60^2 = 3600$ ). For example, 602 is represented as $<< \nabla\nabla$ . This means 10 units in the 60s place and 2 units in the 1s place.

$10 \times 60^1 + 2 \times 60^0 = 600 + 2 = 602$

Similarly, 36002 is represented as $<< \nabla\nabla$ . This means 10 units in the 3600s place, 0 in the 60s, and 2 in the 1s place.

$10 \times 60^2 + 0 \times 60^1 + 2 \times 60^0 = 36000 + 0 + 2 = 36002$

Step 3 — Determining the representation for 3600

The question asks for the representation of 3600. From our analysis, 3600 is $60^2$ . In a base-60 system, a single unit in the $60^2$ place uses the unit symbol. The table directly confirms this. We look at the column for the number 3600. In the Mesopotamian row, the symbol is a single downward wedge. This symbol is also used for 1 and 60.

$\boxed{\text{The Mesopotamian representation for 3600 is } \nabla}$

Diagram 1

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