Page 27 - ICSE Math 6

25,370 on rounding off remains the same, i.e., 25,370. 3,25,220
Therefore, the estimated difference of 3,25,215 and 25,370 – 25,370

= 3,25,220 – 25,370 = 2,99,850 2,99,850

Example 19: Estimate and compare with the actual sum or difference.
(a) 870 + 986 (b) 1,355 – 566
Solution: (a) 870 + 986
Let’s round off to the nearest hundreds. 900
870 is rounded off to 900. + 1,000

986 is rounded off to 1,000. 1,900
Therefore, the estimated sum = 900 + 1,000 = 1,900
However, the actual sum = 870 + 986 = 1,856 870

On rounding off 1,856 to the nearest hundreds, it becomes 1,900. + 986
Therefore, the estimation is reasonable. 1,856

(b) 1,355 – 566
Let’s round off to the nearest hundreds. 1,400
1,355 is rounded off to 1,400. – 600
566 is rounded off to 600. 800

Therefore, the estimated difference = 1,400 – 600 = 800
However, the actual difference = 1,355 – 566 = 789 1,355
On rounding off 789 to the nearest hundreds, it becomes 800. – 566
Therefore, the estimation is quite reasonable. 789

Estimation in product or quotient
Let’s estimate the product 74 × 189.
If we approximate both the factors to the nearest tens, we get 70 × 190 = 13,300. This is a reasonable
estimate, but is not quick enough. If we approximate both the factors 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. Similarly to estimate the quotient, round off the numbers to their greatest place
and then find the quotient of the rounded off numbers.

Example 20: Estimate the following products using the general rule.
(a) 9,250 × 29 (b) 5,281 × 3,849
Solution: (a) 9,250 × 29

Let’s round 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, the estimated product of 9,250 and 29 × 30
2,70,000
= 9,000 × 30 = 2,70,000

11