Scientific Tool
Significant Figures Calculator
Count sig figs, convert to scientific notation, round numbers, and perform operations with step-by-step explanations.
Significant Figures Calculator
5.00 + 5.00Addition
12.3 × 5.0Multiplication
0.003050Leading zeros
100.0Trailing zeros
25.1 + 2.03Mixed decimals
1.23e4Scientific
Round to:
sig figs
Understanding Significant Figures
Significant figures (also called sig figs or significant digits) are the digits in a number that carry meaningful information about its precision. They’re essential in science, engineering, and mathematics to avoid false precision in calculations.
How to Use This Significant Figures Calculator
- Type a number or expression into the input field, or use the keypad below it.
- For a single number (e.g.,
0.003050), the calculator counts sig figs and shows scientific notation instantly. - For expressions (e.g.,
5.00 + 5.00), click Solve to get the result with full step-by-step sig fig working. - Use the Round to buttons to round any number to your chosen number of sig figs, then click Round.
- Switch between Basic, Operations, and Scientific keypads as needed.
- Click the quick example chips to load common problems instantly.
What Are Significant Figures?
Significant figures are all the meaningful digits in a number — the ones you can actually trust based on the precision of the measurement or calculation. They tell the reader “how precise is this number?”
For example, the number 12.3 has 3 sig figs — it’s measured to the nearest tenth. But 12.30 has 4 sig figs — it’s measured to the nearest hundredth, which is more precise.
Significant Figures Rules
Use these five rules to determine whether any digit in a number is significant:
- Rule 1 — Non-zero digits are always significant.
1234→ 4 sig figs.3.14→ 3 sig figs. - Rule 2 — Zeros sandwiched between non-zero digits are significant.
20.05→ 4 sig figs.1001→ 4 sig figs. - Rule 3 — Leading zeros (before the first non-zero digit) are NEVER significant.
0.0025→ 2 sig figs.0.50→ 2 sig figs. - Rule 4 — Trailing zeros are significant ONLY if the number has a decimal point.
100.0→ 4 sig figs.100→ 1 sig fig.1.500→ 4 sig figs. - Rule 5 — Exact numbers have infinite significant figures.
Counted quantities (12 eggs) or definitions (1 km = 1000 m) don’t limit sig figs in calculations.
Quick tip: Are trailing zeros significant? Yes — but ONLY if there’s a decimal point. 100 has 1 sig fig. 100. has 3 sig figs. 100.0 has 4 sig figs.
Significant Figures Reference Table
| Number | Sig Figs | Why |
|---|---|---|
| 1234 | 4 | All non-zero digits |
| 0.0025 | 2 | Leading zeros not significant |
| 0.003050 | 4 | Leading zeros not sig; middle 0 and trailing 0 are |
| 100 | 1 | Trailing zeros without decimal not significant |
| 100. | 3 | Trailing zeros WITH decimal are significant |
| 100.0 | 4 | All digits including trailing zero significant |
| 1.23 × 10⁴ | 3 | Scientific notation: mantissa digits only |
| 5.00 | 3 | Trailing zeros after decimal are significant |
| 20.05 | 4 | Sandwiched zero is significant |
| 0.50 | 2 | Leading zero not sig; trailing zero after decimal is sig |
Significant Figures in Mathematical Operations
Addition and Subtraction — Use Decimal Places
When adding or subtracting, the result must have the same number of decimal places as the number with the fewest decimal places.
Example: 5.00 + 5.00 = ?
5.00has 2 decimal places and 3 sig figs.5.00has 2 decimal places and 3 sig figs.- Fewest decimal places = 2.
- Raw sum:
5.00 + 5.00 = 10.00 - Round to 2 decimal places:
10.00 - Answer: 10.00 (4 sig figs)
Example: 25.1 + 2.03 = ?
25.1has 1 decimal place (3 sig figs).2.03has 2 decimal places (3 sig figs).- Fewest decimal places = 1 (from 25.1).
- Raw sum:
25.1 + 2.03 = 27.13 - Round to 1 decimal place:
27.1 - Answer: 27.1 (3 sig figs)
Example: 1000 – 15.5 = ?
1000has 0 decimal places (1 sig fig — no decimal point).15.5has 1 decimal place (3 sig figs).- Fewest decimal places = 0 (from 1000).
- Raw difference:
1000 - 15.5 = 984.5 - Round to 0 decimal places:
985 - Answer: 985 → rounded to hundreds: 1000 (1 sig fig)
Multiplication and Division — Use Significant Figures
When multiplying or dividing, the result must have the same number of significant figures as the number with the fewest significant figures.
Example: 12.3 × 5.0 = ?
12.3has 3 sig figs.5.0has 2 sig figs.- Fewest sig figs = 2 (from 5.0).
- Raw product:
12.3 × 5.0 = 61.5 - Round to 2 sig figs:
62 - Answer: 62 (2 sig figs)
Example: 100.0 / 3.00 = ?
100.0has 4 sig figs.3.00has 3 sig figs.- Fewest sig figs = 3 (from 3.00).
- Raw quotient:
100.0 / 3.00 = 33.333... - Round to 3 sig figs:
33.3 - Answer: 33.3 (3 sig figs)
Scientific Notation and Sig Figs
Scientific notation is the clearest way to express significant figures. The form is M × 10ⁿ where M (the mantissa) has exactly as many digits as there are sig figs.
100(1 sig fig) →1 × 10²100.(3 sig figs) →1.00 × 10²0.0025(2 sig figs) →2.5 × 10⁻³1234.5(5 sig figs) →1.2345 × 10³
FAQs
Are trailing zeros significant?
Trailing zeros are significant only if the number contains a decimal point. For example:
100 has 1 sig fig, 100. has 3 sig figs, and 100.0 has 4 sig figs. This is one of the most searched sig fig questions — KD only 15!Are leading zeros significant?
No — leading zeros are never significant. They only serve to place the decimal point. Example:
0.0052 has 2 significant figures (5 and 2). The zeros before 5 are not counted.What is 5.00 + 5.00 in significant figures?
Answer: 10.00 (4 sig figs). Both numbers have 2 decimal places, so the result is rounded to 2 decimal places. The sum is 10.00, which has 4 significant figures. Try it in the calculator above!
How do sig figs work in addition vs multiplication?
They use different rules:
Addition/Subtraction: Match the fewest decimal places of any number in the problem.
Multiplication/Division: Match the fewest significant figures of any number in the problem.
Addition/Subtraction: Match the fewest decimal places of any number in the problem.
Multiplication/Division: Match the fewest significant figures of any number in the problem.
How many sig figs does 0.0 have?
0.0 is ambiguous. The zero before the decimal is not significant. The trailing zero after the decimal is significant. So 0.0 could be considered to have 1 significant figure. It’s clearer to write 0 or use scientific notation.Is zero a significant figure?
Zero can be significant or not — it depends on its position. Zeros between non-zero digits are always significant (e.g.,
204 → 3 sig figs). Trailing zeros with a decimal point are significant (e.g., 5.00 → 3 sig figs). Leading zeros are never significant (e.g., 0.005 → 1 sig fig).What is the difference between significant figures and decimal places?
Decimal places count the digits after the decimal point. Significant figures count all meaningful digits in the number. Example:
0.0050 has 4 decimal places but only 2 significant figures (5 and 0). Sig Fig Rules
1
Non-zero digits are always significant.
2
Sandwiched zeros (between non-zeros) are significant.
3
Leading zeros are NEVER significant.
4
Trailing zeros are significant only with a decimal point.
5
Exact numbers have infinite sig figs.
Operation Rules
+
Addition/Subtraction: Result has fewest decimal places.
×
Multiplication/Division: Result has fewest sig figs.
!
Mixed: Apply rules step-by-step following PEMDAS.
Common Examples
| Number | SF |
|---|---|
| 0.0025 | 2 |
| 5.00 | 3 |
| 100 | 1 |
| 100.0 | 4 |
| 0.003050 | 4 |
| 1.23×10⁴ | 3 |
| 20.05 | 4 |
| 0.50 | 2 |
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