KS3 · Maths

Rounding to decimal places

£21.58 on a receipt, 1.35 m on a height chart — most numbers you meet are rounded. And rounding to 1, 2 or 3 decimal places is really one question.

Zoom in

Which neighbour is it nearer?

We're rounding to 1 decimal place, so on this stretch of line the only possible answers are 145.6, 145.7 and 145.8. Drag each tag to where it really sits. Start with the halfway point between 145.6 and 145.7 — then decide, for each number, which neighbour it is nearer.

Half — Halfway between 145.6 and 145.7Place 145.63Place 145.66Place 145.72Place 145.75

The quick way: use the place value columns

Problem

Round 65.83 to 1 decimal place, 45.8749 to 2 decimal places, and 25.3065 to 3 decimal places.

Spot the slip

Where does this answer go wrong?

Round 0.3098 to 3 decimal places.

A pupil's answer — which line goes wrong?

3 decimal places means the thousandths column.
In 0.3098 the thousandths digit is 9.
The next digit is 8, which is 5 or more, so the 9 must increase by one.
9 + 1 = 10, so write 10 in the thousandths place: 0.3010.
So 0.3098 ≈ 0.3010 to 3 decimal places.

What do you think?

Writing a rounded answer

A class was asked what matters when you write down a rounded answer. Here are four things pupils said.

Which one is closest to what you think right now?

5.99 to 1 decimal place is 6. There's no need to write 6.0 — it's the same number.A number exactly halfway, like 135 to the nearest 10, can go either way — it isn't nearer to either.5,672 to the nearest 10 is 70 — you only need to round the end of the number.A rounded answer must stay close to the original and show its accuracy — even if that means a zero on the end.

How sure are you?

I'm sureI think soI'm guessing

5.99 to 1 decimal place is 6. There's no need to write 6.0 — it's the same number.

This is a common misconception

6 and 6.0 have the same value, but they don't tell the same story. The 0 is a real digit in the tenths column: it says 'I rounded to 1 decimal place'. Written as just 6, it looks as if you rounded to the nearest whole number, or forgot a digit. So 5.99 ≈ 6.0 (1 d.p.), and 1.9037 to 2 decimal places is 1.90, not 1.9.

A number exactly halfway, like 135 to the nearest 10, can go either way — it isn't nearer to either.

This is a common misconception

You're right that it's no nearer to 130 than to 140 — and that's exactly why everyone needs to agree on one rule. The rule is: exactly halfway always rounds UP to the larger value. So 135 ≈ 140 to the nearest 10.

5,672 to the nearest 10 is 70 — you only need to round the end of the number.

This is a common misconception

Rounding gives a number that is approximately the SAME value, and 70 is nowhere near 5,672. The answer must keep its place value: 5,672 sits between 5,670 and 5,680, and it's nearer 5,670. So 5,672 ≈ 5,670 to the nearest 10.

A rounded answer must stay close to the original and show its accuracy — even if that means a zero on the end.

This matches the evidence

Exactly. That's why 0.0495 to 3 decimal places is written 0.050: the final 0 shows the thousandths were considered. And you can show that a number has been rounded with the 'approximately equal to' sign: 15,865 ≈ 15,870 (to the nearest 10).

Three checks on every rounded answer. Is it about the same size as the original? Does it show the accuracy — zeros included? And if the number was exactly halfway, did it go up?

Real life

Round as normal — or not?

Work out each answer, then decide: do you round as normal, or does the situation force you to round up or down?

Still to sort

Round as normal (0)

The nearest value makes sense here.

Must round up (0)

Rounding down would leave someone or something short.

Where the line is: Ask: if I round down, is anything left uncovered or anyone left out?

Must round down (0)

Rounding up would need more than you actually have.

Where the line is: Ask: if I round up, do I have enough to make that last one?

5 of 5 still to sort.

How big can a tiny slip get?

The last piece of plank

A 300 cm plank should be cut into ten 30 cm pieces. But each cut is made 1 mm too far along, so the first nine pieces are each 30.1 cm long. How long is the last piece?

Your estimate

28cm

A 300 cm plank should be cut into ten 30 cm pieces. But each cut is made 1 mm too far along, so the first nine pieces are each 30.1 cm long. How long is the last piece? Estimate between 25cm and 31cm.

25cm31cm

WHAT YOU'VE LEARNED

A quick recap of today's lesson.

Every rounding question is secretly the same question: which of two neighbours is this number closer to?

What you need to know

Rounding swaps a number for one that is nearly the same value but easier to work with — for example, 561 is 560 to the nearest 10.
Find the two values either side at the accuracy you want, then the halfway point between them (half their sum). Left of halfway rounds down, right rounds up, and exactly halfway rounds up.
1 decimal place means the nearest tenth, 2 decimal places the nearest hundredth, 3 decimal places the nearest thousandth. The digit just to the right of that column tells you which way to go.
A rounded answer keeps its place value and shows its accuracy — sometimes that means writing a zero on the end.
The context decides how accurate to be: money has 2 decimal places, a length to the nearest cm written in metres has 2, and a mass to the nearest gram written in kilograms has 3. Sometimes the context even forces you to round up or down.

The big picture

To round, find the two values either side of your number at the accuracy you want, find the halfway point, and go to whichever value the number is nearer. Exactly halfway goes up. The quick version: look at the one digit just to the right of the place you're rounding to — 0 to 4 keep, 5 to 9 increase. Then write the answer honestly: keep its place value, keep any zeros that show the accuracy, and let the context decide how accurate to be and, sometimes, which way to go.

Key points

1Rounding means choosing the nearer of two neighbours; the digit just to the right is a shortcut for seeing which side of halfway you're on.

2Exactly halfway always rounds up: 135 ≈ 140 to the nearest 10.

3A 9 that increases exchanges into the next column: 0.3098 ≈ 0.310 (3 d.p.) and 54.96 ≈ 55.0 (1 d.p.).

4Keep zeros that show the accuracy (5.99 ≈ 6.0 to 1 d.p.) and keep the place value (5,672 ≈ 5,670 to the nearest 10).

5Money is written to 2 decimal places; answers usually match the accuracy of the values in the question unless you're told otherwise.

6Rounding loses information: 97,000 to the nearest thousand could have been 96,782, 97,005 or 97,499.

7Measurements are only as exact as the tool: times to the nearest hundredth of a second can give a dead heat, and small slips repeated can add up.

.we-_R_18slubsnpfiv5ubrb_ [data-we-step]{display:flex !important}.we-_R_18slubsnpfiv5ubrb_ [data-we-solution]{display:block !important}.we-_R_18slubsnpfiv5ubrb_ [data-we-reveal]{display:none !important}

Worked example

Problem

A rug is measured to the nearest centimetre as 324 cm long and 126 cm wide. Carpet costs £5.29 per square metre. Write the lengths in metres, then find the rug's area and its cost, each to a sensible degree of accuracy.

⚠ Watch out

Turning a 9 into '10' inside one column. 2.197 to 2 decimal places is not 2.110 — the hundredths 9 increases, ten hundredths exchange for one tenth, and the answer is 2.20 (zero kept to show 2 d.p.).

🧠

Memory hook

Two neighbours and a halfway line: left goes down, right goes up — and sitting on the line? Up.

✓

Check yourself

Round 7.2846 to 1 decimal place, then to 2 decimal places, then to 3 decimal places. Same number, three accuracies — which column do you look at each time? (Answers: 7.3, 7.28, 7.285.)

Flashcards

(13)

What does it mean to round a number?

Change it to a nearby value that is easier to work with, e.g. 561 ≈ 560 to the nearest 10.

How do you find the halfway point between two values?

Add them and halve: halfway between 98 and 99 is (98 + 99) ÷ 2 = 98.5.

Where does 98.6 go when rounded to the nearest whole number, and why?

99 — it lies to the right of the halfway point 98.5, so it is nearer 99.

A number is exactly halfway between the two values. Which way does it round?

Up, to the larger value.

Which column is the 2nd decimal place?

The hundredths — so rounding to 2 d.p. means rounding to the nearest hundredth.

Rounding to 3 d.p.: which digit decides?

The ten-thousandths digit — the 4th digit after the point, just right of the thousandths.

Round 0.5672 to 3 decimal places.

0.567 — the next digit is 2, less than 5, so the 7 stays.

Why write 0.0495 to 3 d.p. as 0.050 rather than 0.05?

The final 0 shows it was rounded to 3 decimal places — the thousandths were considered.

What does the symbol ≈ mean?

'Approximately equal to' — it shows a value has been rounded, e.g. 15,865 ≈ 15,870 (nearest 10).

What is a conjecture?

A statement that is thought to be true but hasn't been proved yet — like a guess at what an unrounded number was.

A mass is measured to the nearest gram and written in kilograms. How many decimal places should it have?

Three — there are 1000 g in a kilogram, so 1 g is 0.001 kg (e.g. 1,506 g = 1.506 kg).

How many decimal places is money written to?

Two — pounds and pence, e.g. £21.58.

How can two runners end up with a dead heat?

If times are measured only to the nearest hundredth of a second, two different times can show up as the same number.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

Learning with Lightbulb is opening soon

You can use this lesson now. Join the waitlist and we'll let you know when the full Lightbulb experience is ready.

Keep me posted

Which neighbour is it nearer?

Where does this answer go wrong?

Writing a rounded answer

Round as normal — or not?

The last piece of plank

More KS3 Maths topics