Page 89 - Ganit Kaushal

The following examples will clarify the concept of estimation of sum, difference and multiplication.

Ex 1. Estimate the following sums and compare the result with the actual sum.
(a) 720 + 682 (b) 1480 + 1975
Sol. (a) Rounding off to the nearest hundreds, 720 is rounded Note
off to 700 and 682 is rounded off to 700. Rounding off to the nearest tens,
So, estimated sum = 700 + 700 = 1400 1480 remains the same, and 1975 is
Actual sum = 720 + 682 = 1402 rounded off to 1980. So, estimated
sum = 1480 + 1980 = 3460. Clearly,
\ The estimated sum is less than the actual sum by 2. this is closer to the actual sum of
(b) Rounding off to the nearest thousands, 1480 is rounded 3455. It must be clear now that if
off to 1000, and 1975 is rounded off to 2000. we round off a number to a higher
So, estimated sum = 1000 + 2000 = 3000 place, the accuracy decreases, and if
we round off a number to a lower
Actual sum = 1480 + 1975 = 3455 place, the accuracy increases.
\ The estimated sum is 455 less than the actual sum.
Ex 2. Estimate the following difference and compare the result with the actual difference.
(a) 762 – 216 (b) 3967 – 1089
Sol. (a) Rounding off to the nearest hundreds, 762 is rounded off to 800 and 216 is rounded off to 200.

So, estimated difference = 800 – 200 = 600
Actual difference = 762 – 216 = 546
\ The estimated difference is greater than the actual difference by 54.
(b) Rounding off to the nearest thousands, 3967 is rounded off to 4000 and 1089 is rounded off to 1000.
So, estimated difference = 4000 – 1000 = 3000

Actual difference = 3967 – 1089 = 2878
\ The estimated difference is greater than the actual difference by 122.
Ex 3. Find the estimated product of (92 × 589) and compare the result with the actual product.
Sol. For estimating a product, we round off each factor of multiplication to the greatest place.
\ Rounding off to the nearest tens, 92 is rounded off to 90 and rounding off to the nearest hundreds,
589 is rounded off to 600.
The estimated product = 90 × 600 = 54,000
The actual product = 92 × 589 = 54,188

Difference = 54,188 – 54,000 = 188
\ The estimated product is less than the actual product by 188.

Estimation (by Logic)

Most times, we do estimation to justify or fulfil some purposes at hand. So, our estimation depends on
logic — whether it fulfils our purpose or not. As explained in example-1, Section 3.15, if we need 26 litres of
petrol to travel from one city to another city by car, we get our car filled with 30 litres of petrol, so that our
journey should be without any tension of bothering about the fuel in the car.
But, if you need 24 litres of petrol, would you get your car filled with only 20 litres of petrol?

We think most of you will answer, ‘No’. You would still get your car filled with 30 litres of petrol because the
purpose at hand is to have a peaceful journey without bothering about the fuel in your car.

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