Rounding/checking | Year 4

01 / LEARN

Understand the idea.

Find the neighbouring round numbers

Rounding chooses a nearby multiple of the requested place. To round $6.438$ to hundreds, use the neighbours $6.400$ and $6.500$ . Their halfway point is $6.450$ , so $6.438$ is nearer the lower hundred.

Choose the place before making a decision. Nearest tens means a multiple of $10$ ; nearest hundreds means a multiple of $100$ . At an exact halfway point, use the higher multiple. This can carry into a new place, such as $4.950$ rounding to $5.000$ .

Estimate, calculate, check

To estimate a calculation, replace each number with a convenient rounded number, then calculate with those numbers. For $432 + 287$ , rounding each addend to hundreds gives $400 + 300 = 700$ . Say that this is an estimate so it is not mistaken for an exact count.

After calculating exactly, compare with the estimate and use an inverse check when needed. Nearby rounded values can hide small errors. Rounding also loses information: different numbers may round to the same hundred while still having different exact values.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Round at two places

Round 7,482 to the nearest ten and nearest hundred.

Worked solution

1
Find the neighbouring tens and their midpoint.
$7.480 < 7.482 < 7.485 < 7.490$
7,482 is below the midpoint 7,485, so its nearest ten is 7,480.
2
Find the neighbouring hundreds and their midpoint.
$7.400 < 7.450 < 7.482 < 7.500$
7,482 is above the midpoint 7,450, so its nearest hundred is 7,500.
3
Label the two rounded answers.
$\begin{aligned} nearest ten: & 7.480 \\ nearest hundred: & 7.500 \end{aligned}$
The requested place changes which neighbouring multiples we compare.

Answer

Nearest ten: 7,480. Nearest hundred: 7,500.

EXAMPLE 02

Use an estimate

Estimate 432 + 287 to the nearest hundred, then calculate exactly.

Worked solution

1
Round each addend to the nearest hundred.
$432 \approx 400, 287 \approx 300$
432 is closer to 400, while 287 is closer to 300.
2
Add the rounded values.
$400 + 300 = 700$
This gives a quick estimate of the total size.
3
Add the original values exactly.
$\begin{aligned} 432 + 200 & = 632 \\ 632 + 80 & = 712 \\ 712 + 7 & = 719 \end{aligned}$
The parts 200, 80 and 7 add to the original 287.
4
Compare the estimate with the exact total.
$719 - 700 = 19$
The exact total 719 is close to the estimate 700; the estimate checks its size.

Answer

Estimate 700; exact total 719.

03 / YOUR TURN

Try it yourself.

Check your understanding

Round 8,249 to the nearest hundred.

Show answer & reasoning

8,200.

The neighbouring hundreds are $8.200$ and $8.300$ . Their midpoint is $8.250$ ; $8.249$ is just below it, so the nearest hundred is $8.200$ .

Keep practising

6 worksheet questions · 9 marks

Open worksheet Worked solutions

Read the questions online

Round 3,674 to the nearest ten.
1 mark
Round 6,450 to the nearest hundred.
1 mark
Round 7,499 to the nearest thousand.
1 mark
Estimate $386 + 512$ by rounding each number to the nearest hundred.
2 marks
Estimate $1.204 - 598$ to the nearest hundred, then find the exact difference.
2 marks
2,341 and 2,349 both round to 2,300 to the nearest hundred. Does this mean they are equal? Explain.
2 marks

Read the worked solutions

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

Round 3,674 to the nearest ten.
1 mark
The ones digit is 4, so the lower ten is nearer.
3,670.
Round 6,450 to the nearest hundred.
1 mark
It is halfway, so use the higher hundred.
6,500.
Round 7,499 to the nearest thousand.
1 mark
It is below the halfway point 7,500.
7,000.
Estimate $386 + 512$ by rounding each number to the nearest hundred.
2 marks
386 rounds to 400; 512 rounds to 500.
$400 + 500 = 900$ .
900.
Estimate $1.204 - 598$ to the nearest hundred, then find the exact difference.
2 marks
$1.200 - 600 = 600$ .
$1.204 - 600 + 2 = 606$ .
Estimate 600; exact difference 606.
2,341 and 2,349 both round to 2,300 to the nearest hundred. Does this mean they are equal? Explain.
2 marks
$2.349 - 2.341 = 8$ .
Rounding groups nearby values; it does not make them equal.
No. Their exact values differ by 8.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Place-value revision; odd/even properties; addition/subtraction strategies; missing values; rounding/checking.

Official curriculum source ↗

In this lesson

Understand the idea.

Find the neighbouring round numbers

Estimate, calculate, check

See the method in action.

Round at two places

Find the neighbouring tens and their midpoint.

Find the neighbouring hundreds and their midpoint.

Label the two rounded answers.

Use an estimate

Round each addend to the nearest hundred.

Add the rounded values.

Add the original values exactly.

Compare the estimate with the exact total.

Try it yourself.

Check your understanding

Keep practising