Page 24 - Start Up Mathematics_6

25,370 on rounding off remains the same, i.e., 25,370.

Therefore, estimated difference of 3,25,215 and 25,370 3,25,220
= 3,25,220 – 25,370 – 25,370
2,99,850
= 2,99,850
(c) 4,89,348 – 48,365
On rounding off to the nearest hundreds:
4,89,348 is rounded off to 4,89,300.
48,365 is rounded off to 48,400.
Therefore, estimated difference of 4,89,348 and 48,365 4,89,300

= 4,89,300 – 48,400 – 48,400
4,40,900
= 4,40,900
On rounding off to the nearest tens:
4,89,348 is rounded off to 4,89,350.
48,365 is rounded off to 48,370.

Therefore, estimated difference of 4,89,348 and 48,365 4,89,350
= 4,89,350 – 48,370 – 48,370
= 4,40,980 4,40,980

Estimation in Product

Let’s estimate the product 74 × 189.
If we approximate both to their nearest tens, we get 70 × 190 = 13,300. This is a reasonable
estimate, but is not quick enough. If we approximate both to the nearest hundreds, we get 100 ×
200 = 20,000. This is quick but not a good estimate.
To get a better estimate, we try rounding off 74 to the nearest tens, i.e., 70, and also 189 to the
nearest hundreds, i.e., 200. We get 70 × 200 = 14,000 which is both quick and a good estimate.
The general rule that we follow is, therefore, round off each factor to its greatest place and then
multiply the rounded off factors.
Example 24: Estimate the following products using general rule:

(a) 9,250 × 29 (b) 5,281 × 3,849 (c) 1,291 × 592 (NCERT)
Solution: (a) 9,250 × 29
Rounding off each factor to its greatest place:

9,250 rounded off to the nearest thousands is 9,000.
29 rounded off to the nearest tens is 30.
9,000
Therefore, estimated product of 9,250 and 29 × 30
= 9,000 × 30 2,70,000

= 2,70,000
(b) 5,281 × 3,849

Rounding off each factor to the nearest thousands:
5,281 is rounded off to 5,000.
3,849 is rounded off to 4,000.

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