The number system
Rounding decimals
It is easier to say 'an African elephant is about 3 metres tall' than 'the average height of an African elephant is 3.3 metres'. Rounding makes numbers easier to describe and understand.
The rounding rule
Look at the TENTHS digit — the first digit after the decimal point. • If it is 0, 1, 2, 3 or 4 → round DOWN to the whole number below. • If it is 5, 6, 7, 8 or 9 → round UP to the whole number above. That one digit decides everything. You never need to look further along.
Using a number line
A number line shows why the rule works. Put your number between the two whole numbers either side. 3.9 sits between 3 and 4 — and it is much closer to 4. So it rounds to 4. 0.4 sits between 0 and 1, closer to 0. So it rounds to 0 — and yes, 0 is a perfectly good answer. Drawing the line is a good check whenever you are unsure.
The halfway case
What about 4.5? It is exactly halfway between 4 and 5 — no closer to either. So mathematicians agree a rule: a tenths digit of 5 ALWAYS rounds up. That means 4.5 rounds to 5. This is a convention, not something the number line can settle for you. Everyone follows it so that we all get the same answer.
Which numbers round to a given whole number?
Turn the rule around and you can work out the whole range. Which numbers with 1 decimal place round to 5? The smallest is 4.5 — it is halfway, so it rounds up. The largest is 5.4 — a tenths digit of 4 rounds down. So everything from 4.5 to 5.4 rounds to 5. Watch out for a common mistake: 74.5 does NOT round to 74. The tenths digit is 5, so it rounds UP to 75.
Worked examples
Rounding up: 3.9 m
- Look at the tenths digit: 9.
- 9 is 5 or more, so round up.
- On a number line, 3.9 sits very close to 4.
Answer: 3.9 m rounds to 4 m
Rounding down: 7.3
- Look at the tenths digit: 3.
- 3 is 4 or less, so round down.
Answer: 7.3 rounds to 7
The halfway case: 4.5 m
- 4.5 is exactly halfway between 4 and 5.
- The rule says a tenths digit of 5 always rounds up.
Answer: 4.5 m rounds to 5 m
Rounding to zero: 0.4 m
- Look at the tenths digit: 4.
- 4 is less than 5, so round down.
- The whole number below 0.4 is 0.
Answer: 0.4 m rounds to 0 m
Is Marcus right that 74.5 rounds to 74?
- Look at the tenths digit of 74.5: it is 5.
- A tenths digit of 5 rounds UP, not down.
Answer: No — 74.5 rounds to 75
The smallest and largest number that rounds to 5
- The smallest must round up, so its tenths digit is 5: that is 4.5.
- The largest must round down, so its tenths digit is 4: that is 5.4.
Answer: Everything from 4.5 to 5.4
Where you see this in real life
- Saying an elephant is 'about 3 metres' tall instead of 3.3 metres.
- Rounding a price of $6.80 to 'about $7' when checking you have enough money.
- Reporting your height to the nearest whole centimetre instead of 142.6 cm.
Key words
- Round
- To change a number to a nearby, simpler number.
- Nearest whole number
- The closest whole number to the given number.
- Tenth
- The first place after the decimal point — one part out of ten.
- Round up
- To go to the whole number above.
- Round down
- To go to the whole number below.
- Approximately
- About; close to but not exactly.