Cambridge Primary Checkpoint · Mathematics 0096 · Stage 6 · Number
Rounding Decimals
Round numbers with two decimal places to the nearest tenth or whole number, work backwards from a rounded value, and use rounding to estimate — with number lines, worked examples and a Checkpoint-style quiz.
British & IGCSE › Checkpoint 6 › Checkpoint 6 Maths — Complete Course
- Round numbers with 2 decimal places to the nearest tenth or to the nearest whole number (6Np.04)
Rounding gives a simpler number that is close to the real one. We round to make estimates, to check answers, and to give sensible measurements ("the plank is about 1.7 m long"). In Stage 6 you round numbers with two decimal places, like 3.47, either to the nearest whole number or to the nearest tenth (one decimal place).
Key words
| Word / phrase | Meaning / use |
|---|---|
| round | يقرّب — replace a number with a simpler number that is close to it |
| nearest whole number | لأقرب عدد صحيح — the answer has no decimal places: 6.38 → 6 |
| nearest tenth | لأقرب جزء من عشرة — the answer has one decimal place: 3.47 → 3.5 |
| decimal place (d.p.) | منزلة عشرية — a place after the point; 3.47 has 2 decimal places |
| deciding digit | الرقم اللي بيحدد — the digit just to the right of the place you are rounding to |
| halfway | المنتصف — exactly in the middle of the two choices, e.g. 3.45 between 3.4 and 3.5 |
| estimate | تقدير — a quick, rough answer found with rounded numbers |
| ≈ | "is approximately equal to" — يساوي تقريبًا: 4.82 + 3.19 ≈ 8 |
1. Rounding on a number line
To round, ask: which of the two possible answers is the number closer to? A number line makes this easy to see.
2. Rounding to the nearest whole number
- Find the two whole numbers the number lies between (6.38 lies between 6 and 7).
- Look at the tenths digit only — this is the deciding digit.
- If the tenths digit is 0, 1, 2, 3 or 4, round down: keep the ones digit (6.38 → 6).
- If the tenths digit is 5, 6, 7, 8 or 9, round up: add 1 to the ones digit (6.51 → 7).
- Write the answer with no decimal places.
| Number | Tenths digit | Round | Nearest whole number |
|---|---|---|---|
| 6.38 | 3 | down | 6 |
| 6.51 | 5 | up | 7 |
| 12.49 | 4 | down | 12 |
| 0.72 | 7 | up | 1 |
| 19.63 | 6 | up | 20 (19 + 1 = 20) |
| 0.29 | 2 | down | 0 |
Notice 12.49 rounds down to 12. It is very close to 12.5, but it is still less than halfway. Only the tenths digit (4) matters — the hundredths digit (9) does not change the answer.
3. Rounding to the nearest tenth
- Find the two tenths the number lies between (3.47 lies between 3.4 and 3.5).
- Look at the hundredths digit — this is the deciding digit.
- 0–4: round down (keep the tenths digit). 5–9: round up (add 1 to the tenths digit).
- Write the answer with exactly one decimal place — even if that digit is 0.
| Number | Hundredths digit | Round | Nearest tenth |
|---|---|---|---|
| 3.47 | 7 | up | 3.5 |
| 3.42 | 2 | down | 3.4 |
| 7.45 | 5 | up | 7.5 |
| 12.05 | 5 | up | 12.1 |
| 4.96 | 6 | up | 5.0 (4.9 + 0.1 = 5.0) |
| 0.03 | 3 | down | 0.0 |
Rounding up past a 9. 4.96 lies between 4.9 and 5.0. Adding 1 tenth to 4.9 gives 5.0. Write 5.0, not 4.10 and not 5. The ".0" shows that you rounded to the nearest tenth.
4. Two important rules
Halfway rounds up. A number exactly halfway, like 7.45 (between 7.4 and 7.5) or 6.50 (between 6 and 7), is rounded up: 7.45 → 7.5 and 6.50 → 7.
Round only once, from the original number. To round 2.47 to the nearest whole number, look at the tenths digit (4) straight away: 2.47 → 2. Do not round to 2.5 first and then to 3. 2.47 is less than 2.5, so it is closer to 2.
| Number | Nearest whole number | Nearest tenth |
|---|---|---|
| 2.47 | 2 | 2.5 |
| 8.55 | 9 | 8.6 |
| 10.94 | 11 | 10.9 |
| 5.98 | 6 | 6.0 |
| 0.65 | 1 | 0.7 |
5. Working backwards: which numbers round to …?
Checkpoint often turns the question round: "A number with 2 decimal places rounds to 4.3. What is the smallest/largest it could be?"
- Find the halfway points either side of 4.3: halfway between 4.2 and 4.3 is 4.25; halfway between 4.3 and 4.4 is 4.35.
- Halfway rounds up, so 4.25 rounds to 4.3 (allowed) but 4.35 rounds to 4.4 (not allowed).
- So the 2-decimal-place numbers that round to 4.3 go from 4.25 (smallest) to 4.34 (largest).
| Rounded value | Rounded to | Smallest (2 d.p.) | Largest (2 d.p.) |
|---|---|---|---|
| 4.3 | nearest tenth | 4.25 | 4.34 |
| 0.8 | nearest tenth | 0.75 | 0.84 |
| 7 | nearest whole number | 6.50 | 7.49 |
| 10 | nearest whole number | 9.50 | 10.49 |
6. Using rounding to estimate
Round each number to the nearest whole number, then calculate. The estimate helps you check an exact answer.
- 4.82 + 3.19 ≈ 5 + 3 = 8 (exact answer 8.01 — close, so it looks right).
- 9.27 − 2.85 ≈ 9 − 3 = 6 (exact answer 6.42).
- A book costs $3.95. Four books cost about 4 × 4 = $16 (exact $15.80).
- لأقرب عدد صحيح: بص على رقم الأجزاء من عشرة (أول رقم بعد العلامة). لأقرب جزء من عشرة: بص على رقم الأجزاء من مئة (تاني رقم بعد العلامة).
- لو الرقم ٠ أو ١ أو ٢ أو ٣ أو ٤ → سيب الرقم زي ما هو. لو ٥ أو أكتر → زوّد واحد.
- قرّب مرة واحدة بس من الرقم الأصلي: ٢٫٤٧ لأقرب عدد صحيح = ٢ مش ٣.
- ٤٫٩٦ لأقرب جزء من عشرة = ٥٫٠ — اكتب الصفر!
Worked examples
Worked example 1 — Round 14.63 (a) to the nearest whole number (b) to the nearest tenth. [2 marks]
- (a) The tenths digit is 6 (5 or more), so round up: 14 → 15.
- (b) The hundredths digit is 3 (less than 5), so round down: 14.6.
Common mistake: giving 14.6 for part (a). Read the question carefully: "whole number" means no decimal places.
Worked example 2 — Round 8.97 to the nearest tenth. [1 mark]
8.97 lies between 8.9 and 9.0. The hundredths digit is 7, so round up: 8.9 + 0.1 = 9.0. Answer: 9.0. Common mistake: writing 8.10 ("9 + 1 = 10") — the tenths cannot hold 10, so you carry into the ones.
Worked example 3 — Ring all the numbers that round to 3 to the nearest whole number: 2.49 2.50 3.48 3.51 2.81 [1 mark]
- 2.49 → tenths digit 4 → rounds to 2 ✗
- 2.50 → tenths digit 5 → rounds up to 3 ✓
- 3.48 → tenths digit 4 → stays 3 ✓
- 3.51 → tenths digit 5 → rounds up to 4 ✗
- 2.81 → tenths digit 8 → rounds up to 3 ✓
Answer: ring 2.50, 3.48 and 2.81. All three must be ringed (and no others) for the mark.
Worked example 4 — A number has 2 decimal places. Rounded to the nearest tenth it is 5.7. Write the smallest and the largest number it could be. [2 marks]
Halfway between 5.6 and 5.7 is 5.65, which rounds up to 5.7 ✓. Halfway between 5.7 and 5.8 is 5.75, which rounds up to 5.8 ✗, so the largest is one hundredth less: 5.74. Answer: smallest 5.65, largest 5.74. Common mistake: giving 5.75 as the largest.
Worked example 5 — Mona buys 2.85 kg of potatoes, 1.32 kg of onions and 0.94 kg of tomatoes. Estimate the total mass by rounding each mass to the nearest whole number. [1 mark]
2.85 → 3, 1.32 → 1, 0.94 → 1. Estimate: 3 + 1 + 1 = 5 kg. (The exact total is 5.11 kg, so the estimate is good.) Show the rounded numbers — that is the method the question is testing.
Worked example 6 — Omar says: "6.45 rounded to the nearest whole number is 7, because 5 rounds up." Explain why Omar is wrong. [1 mark]
Answer: To round to the nearest whole number you look at the tenths digit, which is 4, so 6.45 rounds down to 6. (6.45 is less than 6.5, the halfway point.) Omar looked at the hundredths digit, which is only used when rounding to the nearest tenth.
- Looking at the wrong digit. Whole number → look at tenths. Nearest tenth → look at hundredths.
- Rounding twice: 2.47 → 2.5 → 3 is wrong; 2.47 → 2 is right.
- Dropping the zero: 4.96 to the nearest tenth is 5.0, not 5.
- Writing 8.10 for 8.97 rounded to one decimal place. Carry into the ones: 9.0.
- Changing the digits you keep when rounding down: 3.42 → 3.4, not 3.3.
- Giving 4.35 as the largest number that rounds to 4.3 — it rounds to 4.4.
- "Round 6.38 to the nearest whole number" / "to the nearest tenth" — answer in a box.
- "Ring the numbers that round to …" or "Tick the correct answer" — check every number, one by one.
- Complete a table: one column "nearest whole number", another "nearest tenth".
- Number lines: a point on a scale going up in hundredths, then "round it to the nearest tenth".
- Reverse questions: smallest/largest number, or use digit cards to make a number that rounds to a given value.
- Estimation: "Estimate … by rounding each number to the nearest whole number. Show your working." Write the rounded numbers.
- "Explain" questions: name the deciding digit and say whether it is less than 5 or 5 or more.
Practice
- Nearest whole number → look at the tenths digit. Nearest tenth → look at the hundredths digit.
- 0–4 round down (keep the digit); 5–9 round up (add 1). Exactly halfway rounds up.
- Round once, from the original number: 2.47 → 2, never 2.47 → 2.5 → 3.
- Keep one decimal place when rounding to the nearest tenth, even if it is 0: 4.96 → 5.0.
- Numbers that round to 4.3 (nearest tenth) go from 4.25 to 4.34.
All pages in this course
Start here
Number: integers and calculation
- Counting On and Back and Negative Numbers
- Sequences, Letters and Position-to-Term Rules
- Order of Operations, Brackets and Laws of Arithmetic
- Multiplying Whole Numbers (up to 10 000 × 2-digit)
- Dividing Whole Numbers (up to 1000 ÷ 2-digit)
- Factors, Multiples and Tests of Divisibility
- Square Numbers and Cube Numbers
Number: place value, decimals, fractions, percentages and ratio
- Place Value and Decimals to Thousandths
- Rounding Decimals
- Fractions: Division, Operators and Simplest Form
- Adding and Subtracting Fractions
- Multiplying and Dividing Fractions by Whole Numbers
- Fractions, Decimals and Percentages: Equivalence and Ordering
- Adding, Subtracting, Multiplying and Dividing Decimals
- Ratio and Direct Proportion
Geometry and measure
- Time: Decimals and Mixed Units
- Quadrilaterals: Properties and Classification
- Circles: Parts and Constructing Circles
- Angles: Measuring, Drawing and Angles in a Triangle
- Area of Rectangles and Right-angled Triangles
- 3D Shapes, Compound Shapes and Nets
- Capacity, Volume and Surface Area
- Coordinates in Four Quadrants
- Rotational Symmetry, Translation, Reflection and Rotation
Statistics and probability
Practice tests