Page 88 - Ganit Kaushal

Estimation to the Nearest Hundreds (By rounding off)

The numbers 1 to 49 are nearer to 0 than to 100. Therefore, we round off the numbers 1 to 49 to 0. The numbers
51 to 99 are nearer to 100 than to 0. Therefore, we round them off to 100. 50 is equidistant from 0 and 100,
but it is a common practice to round it off to 100.

• 513 is closer to 500 than to 600, therefore, it is rounded off to 500.
• 288 is closer to 300 than to 200, therefore, it is rounded off to 300.
Procedure Rule: To estimate a number to the nearest hundreds, we observe the immediate right digit, i.e., the
tens digit. If the tens digit is 5 or more than 5, both the tens and ones digits become 0, and the hundreds digit
is increased by 1. If the tens digit is less than 5, the tens and ones digits become 0, and the rest of the digits
remain unchanged.
For example:
=5; T and O digits become 0 <5; T and O digits become 0 >5; T and O digits become 0

(i) 6850 6900 (ii) 65840 65800 (iii) 568 600
increased by 1 remains same increased by 1
Estimation to the Nearest Thousands (By rounding off)

As the numbers 1 to 499 are nearer to 0 than to 1000, therefore these numbers are rounded off to 0.

The numbers 501 to 999 are nearer to 1000 than to 0, therefore, they are rounded off to 1000. The number 500
is rounded off to 1000.
• 1131 is closer to 1000 than to 2000; therefore, it is rounded off to 1000.
• 1746 is closer to 2000 than to 1000; therefore, it is rounded off to 2000.
Procedure Rule: To estimate a number to the nearest 1000, we observe the immediate right digit, i.e., the
hundreds digit. If the hundreds digit is 5 or more than 5, the hundreds, tens and ones digits become 0, and the
thousands digit is increased by 1. If the hundreds digit is less than 5, the hundreds, tens and ones digits become
0, and the rest of the digits remain unchanged.
For example:

<5; H, T and O digits become 0 >5; H, T and O digits become 0
(i) 2268 2000 (ii) 18987 19000
remains same increased by 1
Estimation of Sum, Difference and Multiplication

We can find the estimated sum, difference and multiplication by following the steps given below:
Step 1: For estimating a sum or difference, round off the numbers to the nearest tens, hundreds, thousands,
etc. There is no fixed rule on whether we have to round off to the nearest tens, or hundreds or thousands. It is
our requirement that decides and helps in having the nearest approximation.
For estimating a product, round off each factor of
multiplication to the greatest place, unless otherwise Remark
stated. When we round off a number to the highest
Step 2: Add, subtract or multiply the rounded off factors possible place, the accuracy of the answer
(numbers) as asked in the question. drops, but it simplifies calculations more.

86 Mathematics-6