Estimation of the Numbers

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The estimation of a number is a reasonable guess of the actual value. Estimation means approximating a quantity to the accuracy required. This is done by rounding off the numbers involved and getting a quick and rough answer. 

Rounding off a number to the nearest tens
The numbers 1, 2, 3 and 4 are nearer to 0. So, these numbers are rounded off to the lower ten. The numbers 6, 7, 8 and 9 are nearer to 10. So, these numbers are rounded off to the higher ten. The number 5 is equidistant from both 0 and 10, so it is rounded off to the higher ten. 
e.g.
(i) We round off 31 to the nearest ten as 30
(ii) We round off 57 to the nearest ten as 60
(iii) We round off 45 to the nearest ten as 50


Rounding off a number to the nearest hundreds
The numbers 201 to 249 are closer to 200. So, these numbers are rounded off to the nearest hundred i.e. 200. The numbers 251 to 299 are closer to 300. So, these numbers are rounded off to the higher hundred i.e. 300. The number 250 is rounded off to the higher hundred.
e.g.
(i)  We round off 578 to the nearest 100 as 600.
(ii)  We round off 310 to the nearest 100 as 300.

Rounding off a number to the nearest thousands
Similarly, 1001 to 1499 are rounded off to the lower thousand i.e.1000, and 1501 to 1999 to the higher thousand i.e. 2000. The number 1500 is equidistant from both 0 and 1000, and so it is rounded off to the higher thousand i.e.2000. 
e.g.
(i) We round off 2574 to the nearest thousand as 3000.
(ii) We round off 7105 to the nearest thousand as 7000.

Estimation of sum or difference:

When we estimate sum or difference, we should have an idea of the place to which the rounding is needed.
e.g.
(i)  Estimate 4689 + 19316
We can say that 19316 > 4689
We shall round off the numbers to the nearest thousands.
19316 is rounded off to 19000
4689 is rounded off to 5000

Estimated sum:
19000 + 5000 = 24000

(ii) Estimate 1398 – 526
We shall round off these numbers to the nearest hundreds. 
1398  is rounded off to 1400
526 is rounded off to 500

Estimated difference:
1400 – 500 = 900

Estimation of the product:

To estimate the product, round off each factor to its greatest place, then multiply the rounded off factors. 
e.g.
Estimate 92 x 578
The first number, 92, can be rounded off to the nearest ten as 90.
The second number, 578, can be rounded off to the nearest hundred as 600.
Hence, the estimated product =90 x 600 = 54,000.

Estimating the outcome of number operations is useful in checking the answer.

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