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NCERT Solutions Ganita Prakash (Part 1) Chapter 3 .3 Advantages of a Base-n System — In-text Questions

Book page 683 Updated on2026-09-05

Q1.
Now find the following products — (i) (coil coil coil coil coil coil ∩∩ ||) × ∩ (ii) (lotus ∩) × ∩
Answer

(i) Read the numeral in the bracket first: 6 coils, 2 arches, 2 strokes.

= 600 + 20 + 2 = 622
622 × 10 = 6220

Symbol by symbol, each one steps up:

WasBecomesValue
6 coils (600)6 lotus6000
2 arches (20)2 coils200
2 strokes (2)2 arches20
Product = 6 lotus, 2 coils, 2 arches = 6000 + 200 + 20 = 6220 ✓

(ii) lotus ∩ = 1000 + 10 = 1010

1010 × 10 = 10100
lotus → finger (1000 → 10,000)
∩ → coil (10 → 100)
Product = 1 finger, 1 coil = 10000 + 100 = 10100 ✓
Why it happens: in part (ii) notice that the numeral 1010 has an empty hundreds place and an empty ones place, and after multiplying, the product 10100 has empty thousands, tens and ones places. In Egyptian writing those gaps cost nothing — the symbol is simply not drawn. It is only when the symbols are dropped in favour of positions that these gaps must be filled with the digit 0.
Q2.
What would be a simple rule to multiply a number with ∩?
Answer

Replace every symbol by the next symbol in the list, keeping the count of each symbol exactly as it was.

stroke → arch → coil → lotus → finger → tadpole → kneeling man → sun

In Hindu numerals the very same rule reads: write a 0 at the end.

4 coils + 3 arches + 7 strokes = 437
↓ each symbol steps up
4 lotus + 3 coils + 7 arches = 4370 = 437 × 10 ✓
Why it happens: by the distributive law the number splits into its landmark parts, and by the law of exponents each landmark multiplied by 10 becomes the next landmark. Nothing merges and nothing is created, so the counts survive untouched — which is why the numeral looks the same, just shifted one place along.
Tip: the rule has one limit. The Egyptian list stops at the sun, 107. Multiply a numeral containing suns by 10 and there is no next symbol to step up to. In our system there is no such wall, because the next position is always available.
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