NCERT Solutions Ganita Prakash (Part 1) Chapter 1 –121.4 Exact and Approximate Values — Estimating Sums and Differences

Book page 11 Updated on2026-09-05

Q1.

4,63,128 + 4,19,682. Roxie: “The sum is near 8,00,000 and is more than 8,00,000.” Estu: “The sum is near 9,00,000 and is less than 9,00,000.” (a) Are these estimates correct? Whose estimate is closer to the sum? (b) Will the sum be greater than 8,50,000 or less than 8,50,000? Why do you think so? (c) Will the sum be greater than 8,83,128 or less than 8,83,128? Why do you think so? (d) Exact value of 4,63,128 + 4,19,682 = ___________

Answer

(a) Both estimates are correct, but Estu's is closer.

Exact sum = 4,63,128 + 4,19,682 = 8,82,810
Distance from 8,00,000 = 82,810 (Roxie)
Distance from 9,00,000 = 17,190 (Estu)
17,190 < 82,810 → Estu is closer

(b) The sum is greater than 8,50,000.

4,63,128 > 4,50,000 and 4,19,682 > 4,00,000
So the sum > 4,50,000 + 4,00,000 = 8,50,000 ✓

(c) The sum is less than 8,83,128.

8,83,128 = 4,63,128 + 4,20,000
But the second number is 4,19,682, which is 318 less than 4,20,000
So the sum = 8,83,128 − 318 = 8,82,810 < 8,83,128

(d) Exact value = 8,82,810.

Why it happens: You can answer (b) and (c) without adding at all. Replacing each number by a nearby round number tells you which side of a landmark the sum falls on — that is the whole point of estimation.

Q2.

14,63,128 – 4,90,020. Roxie: “The difference is near 10,00,000 and is less than 10,00,000.” Estu: “The difference is near 9,00,000 and is more than 9,00,000.” (a) Are these estimates correct? Whose estimate is closer to the difference? (b) Will the difference be greater than 9,50,000 or less than 9,50,000? Why do you think so? (c) Will the difference be greater than 9,63,128 or less than 9,63,128? Why do you think so? (d) Exact value of 14,63,128 – 4,90,020 = __________

Answer

(a) Both are correct, but Roxie's estimate is closer.

Exact difference = 14,63,128 − 4,90,020 = 9,73,108
Distance from 10,00,000 = 26,892 (Roxie)
Distance from 9,00,000 = 73,108 (Estu)
26,892 < 73,108 → Roxie is closer

(b) The difference is greater than 9,50,000.

14,63,128 − 5,00,000 = 9,63,128
We are actually subtracting 4,90,020, which is less than 5,00,000
Subtracting less leaves more, so difference > 9,63,128 > 9,50,000 ✓

(c) The difference is greater than 9,63,128.

9,63,128 = 14,63,128 − 5,00,000
5,00,000 − 4,90,020 = 9,980
So the difference = 9,63,128 + 9,980 = 9,73,108

(d) Exact value = 9,73,108.

Why it happens: In a subtraction, making the number you take away smaller makes the answer bigger. Rounding 4,90,020 up to 5,00,000 therefore gives a difference that is too small — a lower bound you can trust.

Check it yourself: Add back: 9,73,108 + 4,90,020 = 14,63,128 ✓

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