Count significant figures, round to sig figs, and perform arithmetic with correct sig fig rules — all with step-by-step solutions. Perfect for GCSE and A-Level Maths, Physics, and Chemistry.
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Significant figures (often abbreviated to sig figs or sf) are the digits in a number that carry meaningful information about its precision. They tell us how accurately a measurement was made.
If you measure a length with a ruler and record 23.5 cm, this has 3 significant figures — you measured to the nearest millimetre. If you record 23.50 cm, this has 4 significant figures — you're saying the measurement is precise to the nearest 0.01 cm. The trailing zero matters!
In science and engineering, significant figures prevent us from implying false precision. If your inputs are only accurate to 2 sig figs, your answer shouldn't be reported to 10 decimal places.
Every digit from 1 to 9 is significant, no matter where it appears.
Zeros between non-zero digits are always significant. They're "trapped" and cannot be removed.
Zeros before the first non-zero digit are just placeholders. They show where the decimal point is, nothing more.
If there's a decimal point, trailing zeros show intentional precision.
Without a decimal point, we can't tell if trailing zeros are significant or just rounding artifacts. Use scientific notation to clarify.
To round a number to N significant figures:
1. Skip leading zeros: 0.004567
2. The 3rd sig fig is 6, and the next digit is 7
3. Since 7 ≥ 5, round up: 6 → 7
4. Answer: 0.00457
The answer has the fewest sig figs of the inputs.
2.3 × 4.567
= 2.3 (2 sf) × 4.567 (4 sf)
= 10.5041 → round to 2 sf
= 11
The answer rounds to the fewest decimal places of the inputs.
12.1 + 3.456
= 12.1 (1 dp) + 3.456 (3 dp)
= 15.556 → round to 1 dp
= 15.6
Scientific notation removes all ambiguity about significant figures. Every digit in the coefficient is significant, and the exponent doesn't affect the count.
All three represent 1200, but each communicates a different level of precision. This is why scientific notation is preferred in science — it's unambiguous.
One of the most common confusions in GCSE and A-Level maths and science is mixing up decimal places (dp) and significant figures (sf). They measure different things: decimal places count digits after the decimal point, while significant figures count all meaningful digits from the first non-zero digit.
| Number | Decimal Places | Significant Figures |
|---|---|---|
| 0.0025 | 4 | 2 |
| 3.50 | 2 | 3 |
| 1200 | 0 | 2, 3, or 4 (ambiguous) |
| 100.0 | 1 | 4 |
| 0.500 | 3 | 3 |
| 42 | 0 | 2 |
Decimal places and significant figures are different concepts. A number like 0.0025 has 4 decimal places but only 2 significant figures. Use our Compare mode above to explore more examples and build your intuition.
Counting leading zeros
✓ Fix: Leading zeros are placeholders, never significant. 0.003 has 1 sf.
Forgetting trailing zeros after decimal
✓ Fix: 2.50 has 3 sf, not 2. The trailing zero indicates precision.
Using wrong rule for arithmetic
✓ Fix: × and ÷ use fewest sig figs. + and − use fewest decimal places.
Dropping trailing zeros when rounding
✓ Fix: 1500 rounded to 2 sf is still 1500, not 15. Or write 1.5 × 10³.
Confusing decimal places with sig figs
✓ Fix: 0.0025 has 2 sf but 4 decimal places. They are different concepts.
Rounding intermediate steps
✓ Fix: Only round the FINAL answer. Keep extra precision in intermediate calculations.
Leading zeros (0.00) — not significant
3 — non-zero, significant
4 — non-zero, significant
0 — trailing zero after decimal, significant
Answer: 3 significant figures
The 2nd sig fig is 4, next digit is 5
Since 5 ≥ 5, round up: 34 → 35
Fill remaining digits with zeros: 3500
Answer: 3500
2.30 has 3 sf, 1.5 has 2 sf
For multiplication: use fewest sf → 2 sf
Raw: 2.30 × 1.5 = 3.45
Round to 2 sf: 3.45 → 3.5
Answer: 3.5 (2 sf)
12.1 has 1 dp, 3.456 has 3 dp
For addition: use fewest dp → 1 dp
Raw: 12.1 + 3.456 = 15.556
Round to 1 dp: 15.556 → 15.6
Answer: 15.6 (1 dp)
Move decimal right until one non-zero digit before it: 4.5
Moved 4 places to the right → negative exponent
Coefficient: 4.5, Exponent: −4
Sig figs: 2 sf (the 4 and 5)
Answer: 4.5 × 10⁻⁴ (2 sf)
100.0 has 4 sf (decimal makes trailing zeros significant)
3 has 1 sf
For division: use fewest sf → 1 sf
Raw: 100.0 ÷ 3 = 33.333...
Round to 1 sf: 33.33 → 30
Answer: 30 (1 sf)
Significant figures are the digits in a number that carry meaning about its precision. They include all non-zero digits, trapped zeros, and trailing zeros after a decimal point.
Count from the first non-zero digit. Include trapped zeros and trailing zeros after a decimal. Exclude leading zeros.
After a decimal point: yes. In whole numbers without a decimal point: ambiguous. Use scientific notation to clarify.
No, never. Leading zeros are placeholders. 0.003 has 1 sf.
Count from the first non-zero digit to the 3rd sig fig. Look at the 4th digit: ≥5 round up, <5 round down.
The answer should have the same number of sig figs as the input with the fewest sig figs.
The answer should be rounded to the fewest decimal places of the inputs (not fewest sig figs).
They communicate measurement precision and prevent implying false accuracy in experimental results.
Scientific notation removes ambiguity — every digit in the coefficient is significant.
Decimal places count digits after the point. Sig figs count all meaningful digits from the first non-zero digit.
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