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\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

In mathematics, estimation often refers to predicting an answer before the exact calculation is
made. It means finding a number close enough to the correct answer. The approximate value
found by observation is called an estimation. Rounding off numbers to the nearest tens, hundreds,
etc. is the foundation of estimation. To round off a given number means to find another number
close to the given number.
Before estimation, we should know how to round off a number to the nearest tens, nearest
hundreds, nearest thousands, etc. Let us follow the given rules.

Rule 1: If the digit to the right of the rounding place is 5 or greater, round up by adding 1 to
the digit at the rounding place and changing the remaining digits right to the rounding place
to zeros.

Rule 2: If the digit to the right of the rounding place is less than 5, round down by changing
the digits to the right of the rounding place to zeros.
Example 15: Round off 538 to the tens place.

Solution: 538
Rounding Place 8 > 5
In the number 538, the digit at ones place is 8 (> 5). The next digit is 3 (at the tens place). We write
4 in place of 3 and 0 in place of 8 in ones place.

Replace by 0
Therefore, 538 ≈ 540

+1
The symbol ≈ is used for “approximately equal to” or “nearly equal to”.

Example 16: Round off 3726 to the hundreds place.
Solution: 3726
Rounding Place 2 < 5
In the number 3726, the digit in the tens place is 2 (< 5). The next digit is 7 (at hundreds place). We
leave the hundreds digit as it is and write 0 in the tens and ones places.
Replace by 0

Therefore, 3726 ≈ 3700

Leave as it is
Example 17: Round off 169752 to the thousands place.
Solution: 169752
Rounding Place 7 > 5
In the number 169752, the digit at the hundreds place is 7 (> 5). The next digit is 9 (at thousands
place). We add 1 to the thousands digit and write 0 in the hundreds, tens and ones places.
Replace by 0

Therefore, 169752 ≈ 170000
+1
Example 18: Estimate the number of litres a mug, a bucket and an overhead tank can hold.
Solution: The size of these containers may vary. Though, we can estimate their capacities as follows:

Mug: 1 litre Bucket: 20 litres Overhead tank: 1,000 litres

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