The idea, step by step
Choose an estimate for the question
Rounding makes numbers easier to handle mentally. When the aim is a quick size check, 28.75+9.9 can be estimated as 29+10=39. The exact sum need not equal 39 to be sensible.
For a decision close to a budget limit, a rough whole-number estimate may not be enough. Calculate more carefully if the rounded answer could change the decision. State that your estimate is approximate.
Use the estimate to investigate an error
Compare the exact result with the estimate. A very large difference can reveal a wrong operation or a misplaced decimal digit. Check the original numbers and units instead of simply changing the answer to match the estimate.
Keep enough precision while working, then round at the end when the context needs it. Early rounding can accumulate, particularly when several costs or measurements are combined.
A common trap
An estimate is wrong unless it matches every digit of the exact answer.
Instead: An estimate deliberately uses easier nearby numbers. Judge it by whether it is useful for the decision or checking task.
See the thinking
Worked example 1
Estimate, then calculate .
- Round to whole numbers: 13+7+4=24.
- Calculate exactly: 12.87+7.14=20.01; 20.01+3.96=23.97.
- 23.97 is close to 24, so the estimate supports the exact result.
Worked example 2
A student writes . Use an estimate to check and correct it.
- Use 50÷10=5 as a quick check.
- 486 is much larger than the starting number, but dividing a positive number by 10 must make it smaller.
- The correct place-value calculation is 48.6÷10=4.86.
Check your understanding
Which is the better quick estimate for : 3 or 30?
Show answer
30.
10+20=30; both original numbers are close to those whole numbers.
Your turn
6 questions · 12 marks · Work at your own pace.
Read the questions online
- Estimate using whole numbers, then calculate it exactly.2 marks
- Estimate , 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 , 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 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 , 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
3×40=120.
2.99×4×10=11.96×10=119.6.
Estimate 120 dollars; exact cost 119.60 dollars. - Estimate , then calculate it exactly.2 marks
90÷20=4.5.
89.6÷2÷10=44.8÷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.
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 ↗