Estimation in calculation
Estimation is a way of speeding up calculation. Usually, the resulting number is less accurate and less precise than the actual value, although this is not always the case, as we’ll see below.
Reformulation strategies
‘Reformulation’ means changing the numbers of a sum to make it easier to calculate. This results in a less accurate answer.
Approximation
We can get the approximate values of numbers before evaluating the sum. We usually round up, down or off first. We can round the number to the same number of places or the same number of significant figures, depending on the situation. Here are some examples:
Note that in (b) in the above example, it is inappropriate to round the second sum to the nearest integer (since that would make it difficult to calculate) or the nearest tenth or hundredth (since that would result in the divisor being zero and an undefined answer.)
Sometimes, it is enough to round off only one of the numbers. This is particularly common in subtraction:
When we estimate an addition or multiplication problem, we can find the range of the answer (between the rounded-up value and the rounded-down value.)
Compatible numbers
Sometimes, we can tinker with the numbers so that they ‘agree’ with each other. There are several ways to do this. Look at these examples:
In a), we changed 8200 to 8100, which is divisible by nine.
In b), we changed the tens place so that the hundred, tens and units places of the two numbers all match. That way, we can obtain the estimated value of -2000 immediately.
In c), we changed the two numbers so that they add up to exactly 3000.
Clusters
Clustering is a strategy that involves both reformulation and translation.
Vocabulary table
- Reformulation
- Cluster
- Compatible number
- Translation
- Compensation
Written for younger readers
Estimation in calculation, in simpler words
This version comes from Wikijunior, a set of books written for children aged 8 to 11. It is shorter and uses plainer language than the article above.
From Wikijunior: The Book of Estimation
Estimation is a way of speeding up calculation. Usually, the resulting number is less accurate and less precise than the actual value, although this is not always the case, as we’ll see below.
‘Reformulation’ means changing the numbers of a sum to make it easier to calculate. This results in a less accurate answer.
We can get the approximate values of numbers before evaluating the sum. We usually round up, down or off first. We can round the number to the same number of places or the same number of significant figures, depending on the situation. Here are some examples:
Note that in (b) in the above example, it is inappropriate to round the second sum to the nearest integer (since that would make it difficult to calculate) or the nearest tenth or hundredth (since that would result in the divisor being zero and an undefined answer.)
Sometimes, it is enough to round off only one of the numbers. This is particularly common in subtraction:
When we estimate an addition or multiplication problem, we can find the range of the answer (between the rounded-up value and the rounded-down value.)
Sometimes, we can tinker with the numbers so that they ‘agree’ with each other. There are several ways to do this. Look at these examples:
In a), we changed 8200 to 8100, which is divisible by nine.
In b), we changed the tens place so that the hundred, tens and units places of the two numbers all match. That way, we can obtain the estimated value of -2000 immediately.
In c), we changed the two numbers so that they add up to exactly 3000.
Clustering is a strategy that involves both reformulation and translation.
- Reformulation
- Cluster
- Compatible number
- Translation
- Compensation
Where this page comes from
The article above is adapted from “Estimation in calculation” on Simple English Wikipedia, by its contributors. We removed reference markers, navigation boxes and tables, expanded measurement templates into readable numbers, and kept the prose otherwise intact. The simpler version is adapted from Wikijunior on Wikibooks.
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