Estimating Sum and Difference

The procedure of estimating sum and difference are in the following examples.

Example 1:

Estimate the sum 5290 + 17986 by estimating the numbers to their nearest (i) hundreds (ii) thousands.

Solution:

(i) Estimating the numbers 5290 and 17986 to their nearest hundreds, we get 5300 and 18000 respectively.

We have,

$Estimating Sum and Difference$

Therefore, estimated sum is 23300.

(ii) Estimating the numbers 5290 and 17986 to their nearest

hundreds, we get 5000 and 18000 respectively.

We have,

$Estimated Sum is 23000$

Therefore, estimated sum is 23000.

Example 2:

Estimate: 5673 – 436 by rounding off the numbers to their greatest places. Also,, find the reasonable estimate.

Solution:

We have, 5673 – 436 = 5237.

The greatest place in 5673 is thousands place and in 436 the greatest place is hundred place.

Estimating 5673 to nearest thousands, we get 6000

Estimating 436 to nearest hundreds, we get 400

Therefore estimated difference = 6000 – 400 = 5600

Clearly, it is not closer to the actual difference. So, it is not a reasonable estimate.

Let us round off 5673 and 436 to nearest hundreds.

5673 rounds off as 5700.

436 rounds off as 400

Therefore estimated difference = 5700 – 400 = 5300

Example 3:

Give a rough estimate and also a closer estimate of 489342 – 48365.

Solution:

We have,

489342 – 48365 = 440877

To find rough estimate, let us round off each number to nearest ten thousands.

489342 rounds off as 490000

48365 rounds off as 50000

Estimates difference = 490000 – 50000 = 440000

So, rough estimate = 440000

In order to obtain a closer estimate, let us round off each number to nearest thousands.

489342 rounds off as 489000

48365 rounds off as 48000

Estimated difference = 489000 – 48000 = 441000

Clearly, it is closer to the actual difference 440977Hence, closer estimate is 441000