Q1.
Represent the following numbers in the Egyptian system: 10458, 1023, 2660, 784, 1111, 70707.
Answer
The Egyptian symbols run through the powers of 10:
| = 1 ∩ = 10 coil = 102 lotus = 103 finger = 104 tadpole = 105 kneeling man = 106 sun = 107
Group each number into powers of 10 and draw that many of each symbol.
| Number | Grouped as | Symbols needed |
|---|---|---|
| 10458 | 10000 + 400 + 50 + 8 | 1 finger, 4 coils, 5 arches, 8 strokes |
| 1023 | 1000 + 20 + 3 | 1 lotus, 2 arches, 3 strokes |
| 2660 | 2000 + 600 + 60 | 2 lotus, 6 coils, 6 arches |
| 784 | 700 + 80 + 4 | 7 coils, 8 arches, 4 strokes |
| 1111 | 1000 + 100 + 10 + 1 | 1 lotus, 1 coil, 1 arch, 1 stroke |
| 70707 | 70000 + 700 + 7 | 7 fingers, 7 coils, 7 strokes |
Why it happens: compare the last two lines with the Hindu numerals 1111 and 70707. The Egyptians wrote as many copies as the digit says, in any order, and had no way to show a zero — but they did not need one, because a missing power of 10 simply means that symbol is absent. In 1023, no coil is drawn; in 70707, no lotus and no arch. The digit 0 becomes necessary only when the symbols are dropped and the position has to do the work.
Tip: the number of symbols you draw is the sum of the digits. 70707 needs 7 + 0 + 7 + 0 + 7 = 21 symbols, while the Hindu numeral needs 5. That is the price the Egyptian system pays.