Unit 1 · Number
1 Rounding
Your phone says a journey takes 23.847 minutes. Nobody says that. You say “about 24 minutes”. That is rounding — and there are two different ways to do it. This lesson makes sure you never mix them up.
🎯 By the end of this you can…
- ✓Round any number to a given number of decimal places.
- ✓Round any number to a given number of significant figures.
- ✓Say which digit decides, every single time.
💡 The idea
Rounding is just: which one is it nearer to?
Every rounding question is the same question. 7.3 is nearer to 7 than to 8, so it rounds to 7. 7.8 is nearer to 8. That is all rounding ever is.
The only rule you have to memorise is what to do at the exact middle, 7.5. The rule everyone agrees on: round it up.
📋 Rounding to decimal places (dp)
- 1Count places after the decimal point. 1 dp means one digit after the point, 2 dp means two.
- 2Put your finger on the last digit you are allowed to keep.
- 3Look at the very next digit only. Just one. Ignore everything after it.
- 4Is that next digit 5 or more? Round your finger digit up by 1. Is it 4 or less? Leave your finger digit alone.
- 5Delete everything after your finger. Done.
✏️ Worked example
Round 12.5164 to 2 decimal places.
- 12 dp means keep two digits after the point: 12.51|64
- 2Finger on the 1 (the second decimal digit).
- 3The very next digit is 6.
- 46 is 5 or more, so round up: the 1 becomes a 2.
✅ Answer: 12.52
⚠️ The classic trap
Never round twice. To round 7.249 to 1 dp, look at the 4 only — so it stays 7.2.
Lots of students round 7.249 → 7.25 → 7.3. That is wrong. You look at one digit, once. The 9 at the end never gets a vote.
🎮 Decimal places — from the worksheet
⭐ 0 XP🔥 streak 0🤔 Which digit do you look at to round 5.4471 to 2 decimal places?
💡 The idea
Significant figures: the same rounding, a different starting line
Decimal places count from the decimal point. Significant figures (sf) count from the first digit that is not zero.
That is the whole difference. Everything else — the finger, the next digit, 5 or more — is identical.
In 0.003204 the first significant figure is the 3. Those three zeros in front are just holding the place. They do not count.
📋 Rounding to significant figures (sf)
- 1Find the first non-zero digit, reading left to right. That is significant figure number 1.
- 2Count along to the right from there — every digit counts now, zeros included.
- 3Put your finger on the last one you are allowed to keep.
- 4Look at the very next digit. 5 or more? Round up. 4 or less? Leave it.
- 5Refill with zeros to keep the number the right size. 4218 to 1 sf is 4000, not 4 — the zeros are place holders, not extra accuracy.
✏️ Worked example
Round 0.004718 to 1 significant figure.
- 1Read left to right. 0, 0, 0, then 4 — the first non-zero digit. That is the 1st sf.
- 2We only want 1 sf, so the finger stays on the 4.
- 3The very next digit is 7.
- 47 is 5 or more, so round the 4 up to 5.
- 5Keep the zeros in front so it is still a small number: 0.005.
✅ Answer: 0.005
⚠️ The classic trap
Rounding 4218 to 1 sf is not 4. It is 4000.
Ask yourself: is my answer roughly the same size as the number I started with? 4218 is a few thousand, so the answer must be a few thousand. Those zeros are doing a job.
🎮 Significant figures — round to 1 sf
⭐ 0 XP🔥 streak 0🎮 Significant figures — 2 sf and 3 sf
⭐ 0 XP🔥 streak 0🤔 Round 6752081 to 2 significant figures.
🏅
You finished this lesson!
Two kinds of rounding, one difference: decimal places count from the point, significant figures count from the first non-zero digit. After that, every question is the same three moves — finger, next digit, 5 or more.
Next up: using rounding backwards, to find upper and lower bounds.
Keep reading — this lesson marks itself done automatically.