Topics
1. Number and place value
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AustraliaNSW
Stage 3

1.06 Estimation

Lesson
Practice
Lesson

Are you ready?

Do you remember how to  round numbers  to the nearest 10,\, 100, or 1000?

Examples

Example 1

Round 936 to the nearest ten.

Worked Solution
Create a strategy

Use a number line starting with the tens value and ending with the next tens value.

Apply the idea

Start the number line at 930 and end with 940. Plot 936.

930935940

936 is closer to 940 than 930.

The rounded value is 940.

Idea summary

When rounding a number to the nearest 10:

  • Use a number line to check if it is closer to the ten above, or the ten below the number.

  • If a number is exactly in the middle, round to the higher number.

Estimate addition and subtraction

How can we estimate the answer to an addition or subtraction problem?

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Examples

Example 2

Look at the number sentence:

6266-143=⬚

a

6266-143 will be in the:

A
6200s
B
6100s
C
6000s
Worked Solution
Create a strategy

Round each number to the nearest ten, then plot the first number on a number line and jump back with the rounded value of the second number.

Apply the idea

6266 rounded to the nearest ten is 6270. 143 rounded to the nearest ten is 140.

Start the number line with 6000 and end with 6300. Plot 6270 and jump back 140.

6000610062006300

On the number line we ended up between 6100 and 6200. So we are in the 6100s. The correct answer is B.

b

Find the value of 6266-143.

Worked Solution
Create a strategy

Put the numbers in a place value table.

Apply the idea

The numbers 6266 and 143 are written in a place value table.

ThousandsHundredsTensUnits
6266
- 143
=6 123

By subtracting each column starting from the units we get: 6266-143=6123

Reflect and check

We can see that the final answer was in the 6100s as predicted in part (a).

Idea summary

Rounding can assist us in estimating an answer to a number problem as we don't always need to determine the precise solution.

Estimate multiplication and division

We can also estimate our answer to multiplication and division problems. In fact, the process is not that different to addition and subtraction. Let's see how, in this video.

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Examples

Example 3

Let’s estimate the solution to 24 \times 24 by rounding the digits first.

a

Rewrite the calculation but use rounded numbers to the nearest 10.

Worked Solution
Create a strategy

Plot the digit on a number line.

Apply the idea

Start the number line with 20 and end with 30.

2021222324252627282930

24 is closer to 20 than 30. So the rounded value of 24 is 20.

The rounded calculation is 20 \times 20.

b

Calculate 20 \times 20.

Worked Solution
Create a strategy

Split up both numbers into a product of 10.

Apply the idea
\displaystyle 20 \times 20\displaystyle =\displaystyle (2\times 10) \times (2\times 10)Write as a product of 10
\displaystyle =\displaystyle 4\times 10 \times 10Multiply 2 by 2
\displaystyle =\displaystyle 4\times 100Multiply 10 by 10
\displaystyle =\displaystyle 400Multiply 4 by 100
c

Is 400 going to be larger or smaller than the actual result of 24 \times 24?

Worked Solution
Create a strategy

Compare the value of the original numbers and rounded numbers.

Apply the idea

We know that 20 \lt 24. Rounding 24 down in our estimate will give us a smaller result. So 20 \times 20 will be less than the product of 24 \times 24.

The correct answer is A.

Idea summary

Same with the process of addition and subtraction, we don't always need to work out the exact answer to a number problem, so rounding can help us estimate an answer. This means we can check that our answer seems reasonable.

Outcomes

MA3-5NA

selects and applies appropriate strategies for addition and subtraction with counting numbers of any size

MA3-6NA

selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation

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