Q1.
Represent the following numbers in the Mesopotamian system — (i) 63 (ii) 132 (iii) 200 (iv) 60 (v) 3605
Answer
Write Y for the 1-wedge and < for the 10-wedge. Reading right to left, the slots stand for 1s, 60s, 3600s.
| Grouped as | 3600s | 60s | 1s | |
|---|---|---|---|---|
| (i) 63 | 1 × 60 + 3 | — | Y | YYY |
| (ii) 132 | 2 × 60 + 12 | — | YY | < YY |
| (iii) 200 | 3 × 60 + 20 | — | YYY | << |
| (iv) 60 | 1 × 60 + 0 | — | Y | (blank) |
| (v) 3605 | 1 × 3600 + 0 × 60 + 5 | Y | (blank) | YYYYY |
Checks: 60 + 3 = 63 ✓ 120 + 12 = 132 ✓ 180 + 20 = 200 ✓ 3600 + 0 + 5 = 3605 ✓
Why it happens: parts (iv) and (v) are the ones that expose the flaw. In (iv) the single wedge stands in the 60s slot with an empty ones slot — but the emptiness is invisible, so the numeral looks exactly like the numeral for 1. In (v) two consecutive slots are empty, and no amount of careful spacing tells a reader whether one blank was intended or two. This is what the later Mesopotamians fixed with a placeholder symbol, and what our 0 fixes completely.
Tip: to convert any number, divide repeatedly by 60. For 3605: 3605 ÷ 60 = 60 remainder 5, and 60 ÷ 60 = 1 remainder 0. Reading the remainders upwards gives the slots 1, 0, 5 — that is 1 × 3600 + 0 × 60 + 5.