Estimating decimal calculations | Year 6

01 / LEARN

Understand the idea.

Choose an estimate for the question

Choose nearby numbers that are easy to calculate mentally. For a quick size check, $28.75 + 9.9$ is close to $29 + 10 = 39$ . Use words such as about, or the symbol $\approx$ , to show that rounding changed the calculation.

The needed precision depends on the decision. A rough estimate may catch an extra zero, but may not decide whether a purchase fits just under a budget. Calculate exactly when rounding could change the conclusion.

Use the estimate to investigate an error

Compare the exact result with the estimate and investigate a large mismatch. Check the operation, the place values and the original numbers. An estimate points to a possible error; it does not justify changing digits without recalculating.

Keep the original precision through an exact calculation and round at the end if needed. Rounding several separate costs too early can build up an error, even when each rounded value seems close on its own.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Worked example 1

Estimate, then calculate $12.87 + 7.14 + 3.96$ .

Worked solution

1
Estimate using whole numbers.
$12.87 + 7.14 + 3.96 \approx 13 + 7 + 4 = 24$
All three rounded numbers are close to the original addends.
2
Add the first two amounts exactly.
$12.87 + 7.14 = 20.01$
Matching decimal columns preserves hundredths.
3
Include the final amount.
$20.01 + 3.96 = 23.97$
No rounding has been used in the exact calculation.
4
Compare the two results.
$24 - 23.97 = 0.03$
The exact sum is only three hundredths below the estimate, so the sizes agree.

Answer

Estimate about 24; exact sum 23.97.

EXAMPLE 02

Worked example 2

A student writes $48.6 \div 10 = 486$ . Use an estimate to check and correct it.

Worked solution

1
Make a nearby easy estimate.
$48.6 \div 10 \approx 50 \div 10 = 5$
The quotient should be near five.
2
Test the proposed result’s size.
$486 > 48.6$
Dividing a positive number by ten must make it smaller, so 486 cannot be correct.
3
Recalculate using place value.
$48.6 \div 10 = 4.86$
Each digit becomes worth one tenth as much.
4
Check the correction.
$4.86 \times 10 = 48.6$
The corrected value reverses to the original and is near the estimate of five.

Answer

The correct answer is 4.86, near the estimate of 5.

03 / YOUR TURN

Try it yourself.

Check your understanding

Which is the better quick estimate for $9.86 + 20.12$ : 3 or 30?

Show answer & reasoning

30.

$9.86$ is near $10$ and $20.12$ is near $20$ . Their sum is therefore near $30$ , making $30$ the better quick estimate.

Keep practising

6 worksheet questions · 12 marks

Open worksheet Worked solutions

Read the questions online

Estimate $28.75 + 9.9$ using whole numbers, then calculate it exactly.
2 marks
Estimate $12.04 - 3.87$ , then calculate it exactly.
2 marks
Estimate the cost of 40 items at 2.99 dollars each. Then find the exact cost.
2 marks
Estimate $89.6 \div 20$ , then calculate it exactly.
2 marks
A bottle holds 4.8 L. After 1.95 L is poured out, about how much remains? Then calculate the exact amount.
2 marks
A budget is 25 dollars. Two prices are 12.49 and 12.49 dollars. Is rounding both prices to 12 dollars enough to decide exactly how much money remains? Explain.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Estimate $28.75 + 9.9$ using whole numbers, then calculate it exactly.
2 marks
$29 + 10 = 39$ .
$28.75 + 9.90 = 38.65$ .
Estimate 39; exact sum 38.65.
Estimate $12.04 - 3.87$ , then calculate it exactly.
2 marks
$12 - 4 = 8$ .
$12.04 - 3.87 = 8.17$ .
Estimate 8; exact answer 8.17.
Estimate the cost of 40 items at 2.99 dollars each. Then find the exact cost.
2 marks
$3 \times 40 = 120$ .
$2.99 \times 4 \times 10 = 11.96 \times 10 = 119.6$ .
Estimate 120 dollars; exact cost 119.60 dollars.
Estimate $89.6 \div 20$ , then calculate it exactly.
2 marks
$90 \div 20 = 4.5$ .
$89.6 \div 2 \div 10 = 44.8 \div 10 = 4.48$ .
Estimate 4.5; exact answer 4.48.
A bottle holds 4.8 L. After 1.95 L is poured out, about how much remains? Then calculate the exact amount.
2 marks
$5 - 2 = 3$ is a quick estimate.
$4.80 - 1.95 = 2.85$ .
About 3 L; exactly 2.85 L.
A budget is 25 dollars. Two prices are 12.49 and 12.49 dollars. Is rounding both prices to 12 dollars enough to decide exactly how much money remains? Explain.
2 marks
Rounding gives 24 dollars and would overstate the money left.
No. Calculate the exact total 24.98 dollars, leaving 0.02 dollars.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Addition/subtraction; multiplication/division by multiples of powers of ten; estimation.

Official curriculum source ↗

In this lesson

Understand the idea.

Choose an estimate for the question

Use the estimate to investigate an error

See the method in action.

Worked example 1

Estimate using whole numbers.

Add the first two amounts exactly.

Include the final amount.

Compare the two results.

Worked example 2

Make a nearby easy estimate.

Test the proposed result’s size.

Recalculate using place value.

Check the correction.

Try it yourself.

Check your understanding

Keep practising