Estimation of the Numbers
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.

#### Summary

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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