NCERT Solutions for Class 8 Maths Ganita Prakash Chapter 3 — Figure it Out (Page 62)#
The Egyptian landmark numbers are the powers of 10, each with its own hieroglyph:
| Value | 1 | 10 | 100 | 1000 | 10,000 | 100,000 | 1,000,000 |
|---|---|---|---|---|---|---|---|
| Symbol | stroke | heel bone (∩) | coil of rope | lotus flower | finger | tadpole | kneeling man |
A number is written by repeating each symbol as many times as that power of 10 occurs in it. Below, each answer lists how many of each symbol to draw.
1. Represent the following numbers in the Egyptian system: 10458, 1023, 2660, 784, 1111, 70707. #
Solution
We split each number into powers of 10, then draw that many of each symbol:
| Number | Split into landmark numbers | Symbols to draw |
|---|---|---|
| 10458 | $10000 + 400 + 50 + 8$ | 1 finger, 4 coils, 5 heel bones, 8 strokes |
| 1023 | $1000 + 20 + 3$ | 1 lotus, 2 heel bones, 3 strokes |
| 2660 | $2000 + 600 + 60$ | 2 lotuses, 6 coils, 6 heel bones |
| 784 | $700 + 80 + 4$ | 7 coils, 8 heel bones, 4 strokes |
| 1111 | $1000 + 100 + 10 + 1$ | 1 lotus, 1 coil, 1 heel bone, 1 stroke |
| 70707 | $70000 + 700 + 7$ | 7 fingers, 7 coils, 7 strokes |
A 0 digit (as in 1023 or 70707) simply means that symbol is not drawn at all.
2. What numbers do these numerals stand for? #
(i) 2 coils, 7 heel bones (3 + 3 + 1) and 6 strokes
The numeral has 2 coils (100 each), 7 heel bones (10 each) and 6 strokes (1 each):
Number $= 2 \times 100 + 7 \times 10 + 6 \times 1$
Number $= 200 + 70 + 6$
Number $= 276$
∴ The numeral stands for 276.
(ii) 4 lotuses, 3 coils, 2 heel bones and 2 strokes
The numeral has 4 lotus flowers (1000 each), 3 coils (100 each), 2 heel bones (10 each) and 2 strokes:
Number $= 4 \times 1000 + 3 \times 100 + 2 \times 10 + 2 \times 1$
Number $= 4000 + 300 + 20 + 2$
Number $= 4322$
∴ The numeral stands for 4322.