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\\September 30, 2025 9:38 AM Bharat Arora P-9 Reader _________________________ Date: ___________________74

estimating the sum and differenCe

In the previous chapter, we learned about rounding off numbers to the nearest tens,

hundreds and thousands. For estimating the sum or difference, we first round off the
given numbers to their highest place and then add or subtract.

Let us understand this with the help of examples.

example 1: Estimate the sum of 4,523 and 4,103.
Solution: Rounding off 4,523 to the nearest 1000 5,000

Rounding off 4,103 to the nearest 1000 4,000
estimated Sum Actual Sum

th H T O th H T O
5 0 0 0 4 5 2 3

+ 4 0 0 0 + 4 1 0 3
9 0 0 0 8 6 2 6

Thus, 9000 is the estimated sum and 8626 is the actual sum.

example 2: Estimate the difference of 6,238 and 8,762.
Solution: Rounding off 6,238 to the nearest 1000 6,000

Rounding off 8,762 to the nearest 1000 9,000
estimated difference Actual difference

th H T O th H T O Thus, the estimated
9 0 0 0 5 12 difference is 3000 and

– 6 0 0 0 8 7 6 2 the actual difference
3 0 0 0 – 6 2 3 8 is 2524.

2 5 2 4

If we need, we can also round off a number to
the ten thousands by checking the digit in the Challenge Question

thousands place. We round up if the digit in the Find two 5-digit palindromes
thousands place is 5 or greater; otherwise, we X and Y such that X + Y = 111111.
round down.

example 3: Estimate the sum of 42,726 and 46,365.

Solution: Rounding off 42,726 to the nearest ten thousands 40,000

(Since the thousands digit, i.e. 2 < 5)
Rounding off 46,365 to the nearest ten thousands 50,000

(Since the thousands digit, i.e. 6 > 5)

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