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For two-digit numbers, we can round the number to the nearest tens place. That is only one place estimates.
For three-digit numbers, we can round the number to the nearest tens and hundreds place. That is, there are two place estimates (tens and hundreds).
For four-digit numbers, we can round the number to the nearest tens, hundreds and thousands place. That is, there are three place estimates (tens, hundreds and thousands).
Proceeding in the same way we can extend our nearest estimation for different places.
We should estimate the numbers before finding the sum, difference, product or quotient of it.
Before estimate sum or difference, you should have an idea of why you need to round off and therefore the place to which you would round off. The rounding off place merely depends on the provided number.
Important!
Your rounding off should be meaningful and quick. It means the estimated outcome should be reasonable to the exact value, and we should calculate it in less time.
General rule: Rounding each number to its greatest place, then add or subtract the rounded-off numbers.
Example:
1. Estimate: \(2567 + 4128\)
As both the numbers \(2567\) and \(4128\) are in thousands, we can round off both to the nearest \(1000\).
The nearest \(1000's\) of \(2567\) is \(3000\) because \(5\) (change to next value \(2 ->3\) is present in the hundreds place.
The nearest \(1000's\) of \(4128\) is \(4000\) because \(1\) is present in the hundreds place.
Thus, the estimated sum becomes \(3000 + 4000 = 7000\).
Let us verify with actual sum \(2567 + 4128 = 6695\). Thus, the estimated sum is roughly nearer to the actual sum.
2. Estimate: \(8732 - 267\)
Here one among the number is in the thousands place and another present in hundreds.
Let us round off both to \(1000\).
The nearest \(1000's\) of \(8732\) is \(9000\) because \(7\) (change to next value \(8 ->9\)) is present in the hundreds place.
The nearest \(1000's\) of \(267\) is \(0\) because \(2\) is present in the hundreds place.
Thus, the estimated sum becomes \(9000 - 0 = 9000\).
But this estimation is not reasonable.
Let us verify with the actual difference \(8732 - 267 = 8465\). Thus, the predicted estimated difference is not meaningful.
Let us round both \(8732\) and \(267\) to the nearest hundreds.
The nearest \(100's\) of \(8732\) is \(8700\) because \(7\) is present in the hundreds place.
The nearest \(100's\) of \(247\) is \(300\) because \(6\) (change to next value \(2 ->3\)) is present in the tens place.
Thus, the estimated sum becomes \(8700 -300 = 8400\). Thus, the estimated difference is roughly nearer to the actual difference.
And this is how we need to fix place nearest estimation. That is depending upon the problem requirement.
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