Estimation and rounding | Year 7

01 / LEARN

The idea, step by step

Choose the required place

To round a whole number, identify the place being kept and inspect the digit immediately to its right. A digit from 0 to 4 leaves the kept digit unchanged; a digit from 5 to 9 increases it by one. Replace later whole-number digits with zeros.

The rounding place must be stated. The same number can round differently to the nearest ten, hundred or thousand. Rounding makes a useful approximation, not a new exact value.

Estimate with convenient numbers

Choose nearby values that make the calculation easy. To estimate $387 \times 21$ , use $400 \times 20 = 8000$ . That helps judge whether an exact result such as 8,127 is a sensible size.

An estimate is not required to equal the exact answer. Explain the rounding choices, then decide whether the approximation is useful for the context. If enough money or seats must be provided, also consider whether rounding down creates a shortage.

A common trap

An estimate is wrong whenever it differs from the exact answer.

Instead: An estimate deliberately uses convenient nearby values. It is useful when it gives the right scale and enough accuracy for the decision.

02 / WORKED EXAMPLES

See the thinking

Example 1

Round to a stated place

Round 48,762 to the nearest thousand.

Keep the thousands place.
The hundreds digit is 7, so increase 48 thousands to 49 thousands.
Replace hundreds, tens and ones with zeros.

49,000

Example 2

Check a product with an estimate

Estimate $387 \times 21$ , then compare with the exact product.

Use the nearby convenient numbers 400 and 20.
$400 \times 20 = 8000$ .
The exact product is $387 \times 20 + 387 = 7740 + 387 = 8127$ , close to 8000.

An estimate is 8,000; the exact answer is 8,127.

Check your understanding

Round 7,250 to the nearest hundred.

Show answer

7,300

The tens digit is 5, so 72 hundreds rounds up to 73 hundreds.

03 / WORKSHEET

Your turn

6 questions · 13 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Round 34,876 to the nearest hundred.
2 marks
Round 96,450 to the nearest thousand.
2 marks
Estimate $198 \times 31$ using convenient whole numbers.
2 marks
Estimate $592 \div 19$ using convenient whole numbers.
2 marks
There are 51 tickets at 19 dollars each. Estimate the total, then find the exact cost.
3 marks
Round 4,650 to the nearest thousand.
2 marks

Read the worked solutions

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

Round 34,876 to the nearest hundred.
2 marks
Keep the hundreds position.
The tens digit is 7, so round 8 hundreds up to 9 hundreds.
34,900
Round 96,450 to the nearest thousand.
2 marks
The hundreds digit is 4.
Keep 96 thousands and replace the later digits with zeros.
96,000
Estimate $198 \times 31$ using convenient whole numbers.
2 marks
Use $198 \approx 200$ and $31 \approx 30$ .
$200 \times 30 = 6000$ .
About 6,000
Estimate $592 \div 19$ using convenient whole numbers.
2 marks
Use $592 \approx 600$ and $19 \approx 20$ .
$600 \div 20 = 30$ .
About 30
There are 51 tickets at 19 dollars each. Estimate the total, then find the exact cost.
3 marks
Estimate with $50 \times 20 = 1000$ .
Calculate $51 \times 19 = 51 (20 - 1) = 1020 - 51 = 969$ .
Estimate: 1,000 dollars; exact cost: 969 dollars.
Round 4,650 to the nearest thousand.
2 marks
The hundreds digit is 6.
Round 4 thousands up to 5 thousands.
5,000

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum

Place value and powers of ten; efficient whole-number calculations and order of operations; factors, multiples and primes; prime factorisation and exponent notation; square numbers and square roots; estimation and rounding.

Official curriculum source ↗

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