Estimation and Rounding

Background

Sometimes we want to use exact numbers in a calculation or use an exact number as a result. Oftentimes though, we want to use an estimate or get an approximation as a result.

Question

Find the following:

1. Round to the nearest whole number: 6.2, 6.5, 6.7
2. Round up to the nearest whole number: 4.2, 4.5, 4.7
3. Round down to the nearest whole number: 7.2, 7.5, 7.7
4. Estimate 4.32 x 2.1 

Answer

1. 6, 7, 7
2. 5, 5, 5
3. 7, 7, 7
4. 4 x 2 = 8 

Analysis

When we're asked to round a number, we look at the digit position we're asked to round to. In Question 1, we're rounding to the nearest whole number, and so we're rounding to the 1's position:



We're looking at the Ones position to see if changes or not. To see if it does change, we look at the next position to the right, in this case, the Tenths.

When we're rounding (sometimes called "rounding off"), we keep the Ones as is if the Tenths is either 0, 1, 2, 3, or 4. We'll increase the Ones by 1 if the Tenths is either 5, 6, 7, 8, or 9.

In 6.2, the tenths place is 2, so we round to 6.
In 6.5 and 6.7, the tenths place is 5 and 7, respectively, and so we round up to 7.

Question 2

Sometimes we need to round up, which means that if the number we're looking at is even a little bit over, we round to the next value up.

Looking at our numbers in question 2 and rounding up to the next whole number, we can look at the numbers in question:

4.2 is over 4 so we round up to 5.
4.5 is over 4 so we round up to 5.
4.7 is over 4 so we round up to 5.

Question 3

Sometimes we need to round down, which means that if the number we're looking at is even a little bit under, we drop down to the next value down.

Looking at our numbers in question 3 and rounding down to the next whole number, we can look at the numbers in question:

7.2 is under 8 so we round down to 7.
7.5 is under 8 so we round down to 7.
7.7 is under 8 so we round down to 7.

Question 4

When we estimate, we calculate using rounded or approximated numbers to end up with an answer that is close to what is the "true" answer. There isn't an absolute "correct" way to do this - but the better the estimate, the closer our answer will be to the "true" answer.

4.32 x 2.1

One way we can handle this is to round to the whole numbers: 4 x 2 = 8

We could round 4.32 to 4 but keep 2.1 as is to get 4 x 2.1 = 8.4

We could also round 4.32 to the nearest tenth and round 2.1 to 2: 4.3 x 2 = 8.6

In all of these cases, we can assume that the "true" answer is above 8 and approaching 9. (It turns out that the true answer is 9.072).

Vocabulary used:

For more information check out these links (comment to add your favourite link):

Where might you have come from?

Fact-orials Index

Numbers:

• Real Numbers
• Scientific Notation

Where might we go?

Numbers:

• Pi