How to Round Numbers and Estimate: KS3 Maths Guide

Rounding means replacing a number with a nearby value that is simpler to work with. At KS3 you need to round to the nearest 10, 100, or 1000, to a given number of decimal places, and to a given number of significant figures — then use those rounded values to estimate the result of a calculation.

Why do we round numbers?

Exact values are not always needed. A builder estimating materials, a scientist recording a measurement, or a student checking whether a calculator answer looks right all benefit from rounding. At KS3, rounding is also a gateway skill for significant figures at GCSE and beyond.

The key rule in rounding is the halfway rule: look at the digit immediately to the right of the position you are rounding to. If it is 5 or more, round up; if it is 4 or less, round down.

How to round to the nearest 10, 100, or 1000

Step 1 — Identify the target place value

Step 2 — Look at the digit immediately to the right

Step 3 — Apply the halfway rule

Worked example 1: round 347 to the nearest 10

The tens digit is 4. The digit to its right (ones column) is 7.
7 ≥ 5, so round up: the tens digit increases from 4 to 5, and the ones digit becomes 0.

Answer: 350

Worked example 2: round 2483 to the nearest 100

The hundreds digit is 4. The digit to its right (tens column) is 8.
8 ≥ 5, so round up: hundreds digit becomes 5.

Answer: 2500

Worked example 3: round 7249 to the nearest 1000

The thousands digit is 7. The digit to its right (hundreds column) is 2.
2 < 5, so round down: thousands digit stays at 7.

Answer: 7000

How to round to decimal places (d.p.)

Decimal places are counted from the decimal point going right. "Round to 2 d.p." means keep two digits after the decimal point.

Step 1 — Count to the required decimal place

Step 2 — Look at the digit immediately to its right

Step 3 — Apply the halfway rule; drop all digits to the right

Worked example 4: round 6.847 to 1 d.p.

The first decimal place holds 8. The digit to its right is 4.
4 < 5, so round down: keep the 8.

Answer: 6.8

Worked example 5: round 3.1459 to 2 d.p.

The second decimal place holds 4. The digit to its right is 5.
5 ≥ 5, so round up: 4 becomes 5.

Answer: 3.15

Worked example 6: round 0.9963 to 2 d.p.

The second decimal place holds 6. The digit to its right is 6.
6 ≥ 5, so round up: 6 becomes 7.

Answer: 1.00 (the second decimal place rolled over, which carried through to give 1.00 — include both zeros to show the answer is given to 2 d.p.)

How to round to significant figures (s.f.)

Significant figures count from the first non-zero digit, regardless of position. This makes the method very useful for very large or very small numbers.

Rules for counting significant figures

Start counting at the first non-zero digit.

Every digit after that counts — including zeros between non-zero digits.

Trailing zeros after a decimal point are significant (e.g. 3.40 has 3 s.f.).

Trailing zeros in a whole number are ambiguous unless a decimal point is shown.

Step 1 — Locate the first non-zero digit; this is the first significant figure

Step 2 — Count along to the required number of significant figures

Step 3 — Apply the halfway rule using the next digit; replace remaining digits with zeros (or drop them after a decimal point)

Worked example 7: round 4826 to 2 s.f.

First s.f. = 4 (thousands). Second s.f. = 8 (hundreds). Next digit = 2.
2 < 5, so round down: 8 stays as 8.

Remaining digits become zeros: 4800

Answer: 4800 (2 s.f.)

Worked example 8: round 0.003 817 to 2 s.f.

First non-zero digit: 3 (the first s.f.). Second s.f. = 8. Next digit = 1.
1 < 5, so round down.

Answer: 0.0038 (2 s.f.)

Worked example 9: round 5 953 000 to 3 s.f.

First three s.f. are 5, 9, 5. Next digit = 3.
3 < 5, so round down.

Answer: 5 950 000 (3 s.f.)

Estimation

Estimation means rounding each number in a calculation — usually to 1 significant figure — and then carrying out the simplified calculation mentally. It is a quick check on whether a calculator answer is sensible.

How to estimate a calculation

Round every number to 1 s.f. (or a convenient round number).

Perform the calculation with the rounded values.

Compare the estimate with the exact answer.

Worked example 10: estimate 38.4 × 52.7

Round to 1 s.f.: 40 × 50 = 2000

Exact answer: 38.4 × 52.7 = 2023.68

The estimate 2000 is close — confirming the calculator answer is reasonable.

Worked example 11: estimate 793 ÷ 18.6

Round: 800 ÷ 20 = 40

Exact answer: 793 ÷ 18.6 ≈ 42.6

The estimate 40 is in the right ballpark. A calculator answer of 4.26 or 426 would both be unreasonable.

Summary table

Rounding type | Look at | Rule
Nearest 10 | Ones digit | ≥ 5 round up; < 5 round down
Nearest 100 | Tens digit | ≥ 5 round up; < 5 round down
Decimal places | Digit after required d.p. | ≥ 5 round up; < 5 round down
Significant figures | Digit after required s.f. | ≥ 5 round up; < 5 round down

Common mistakes to avoid

Mistake 1 — Rounding more than once.
Always round the original number directly to the required precision. Rounding 6.847 to 1 d.p. in two steps (first to 6.85, then to 6.9) gives the wrong answer; the correct answer is 6.8.

Mistake 2 — Forgetting place-holder zeros.
When rounding 4826 to 1 s.f. you get 5000, not 5. The zeros hold the place value.

Mistake 3 — Misidentifying the first significant figure.
In 0.0038, the zeros after the decimal point are not significant — the first s.f. is 3.

Mistake 4 — Using the wrong digit for the decision.
Always look at the digit immediately to the right of your target position, not two positions to the right.

How rounding fits the KS3 national curriculum

The Department for Education's KS3 mathematics programme of study requires pupils to "round numbers and measures to an appropriate degree of accuracy" and to "use approximation through rounding to estimate answers and calculate possible resulting errors." The statutory national curriculum for Key Stage 3 and 4 treats rounding and estimation as essential number skills that appear in every Year 7–9 topic, from measurement to statistics, and underpin calculator-use checks throughout GCSE.

Frequently asked questions

What is the difference between decimal places and significant figures?

Decimal places count digits after the decimal point. Significant figures count from the first non-zero digit, wherever it appears. For example, 0.00456 rounded to 2 decimal places is 0.00 (just two decimal places, both zero), but rounded to 2 significant figures it is 0.0046 (the first s.f. is 4, the second is 5, rounded up from 56).

Why do I need to use estimation in maths?

Estimation catches errors. If you type a calculation into a calculator and misplace a decimal point or press a wrong key, your estimate tells you the answer should be roughly 2000 — so a calculator display of 20 or 200 000 is immediately suspicious. The KS3 programme of study lists estimation as a distinct skill precisely because it builds mathematical sense.

What happens when the deciding digit is exactly 5?

The standard rule at KS3 is to round up when the deciding digit is 5. So 2.45 rounded to 1 d.p. becomes 2.5, and 35 rounded to the nearest 10 becomes 40. (There are other conventions used in statistics and computing, but round-half-up is what KS3 mark schemes expect.)

Can you round a negative number?

Yes. The halfway rule still applies, but remember that rounding "up" means towards a larger value (less negative). For example, −3.7 rounded to the nearest whole number is −4, because −4 is the nearest integer (−3.5 and below rounds to −4 using the standard convention).

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