Significant figures (sig figs) are the digits in a measurement that carry real information about its precision. A ruler marked in millimeters can report 12.3 cm, but not 12.34 cm; a lab balance might report 0.004050 g with four meaningful digits. Counting them correctly is the first step in every sig-fig problem, from rounding a result to deciding how precise a calculated answer can be. This counter color-codes every digit and names the rule behind it.
How to use the significant figures counter
- Type the number exactly as it was recorded, including any trailing zeros and the decimal point. Scientific notation such as
3.20e4or3.20 × 10^4is accepted. - Read the count on the tape. If trailing zeros are ambiguous, the tape shows the possible range.
- The colored display marks significant digits in blue, placeholder zeros struck through and ambiguous zeros in amber. The table explains each digit.
The rules for counting significant figures
| Rule | Example | Sig figs |
|---|---|---|
| 1. Non-zero digits are always significant | 4.72 | 3 |
| 2. Zeros between non-zero digits (captive zeros) are significant | 3,005 | 4 |
| 3. Leading zeros are never significant | 0.0072 | 2 |
| 4. Trailing zeros after a decimal point are significant | 7.200 | 4 |
| 5. Trailing zeros in a whole number with a decimal point are significant | 450. | 3 |
| 6. Trailing zeros in a whole number without a decimal point are ambiguous | 4,500 | 2 (maybe 3 or 4) |
| 7. In scientific notation, every digit of the coefficient is significant | 4.50 × 10³ | 3 |
A quick way to apply rules 1–5: if the number has a decimal point, start at the first non-zero digit on the left and count every digit to the end. If it has no decimal point, start at the first non-zero digit on the right and count every digit to the beginning.
Worked example: 0.004050
Leading zeros: 0.00 — placeholders, not significant (rule 3)
Non-zero digits: 4 and 5 — significant (rule 1)
Captive zero: the 0 between 4 and 5 — significant (rule 2)
Trailing zero: the final 0, after a decimal point — significant (rule 4)
Total: 4 significant figures. In scientific notation: 4.050 × 10⁻³
Why trailing zeros cause confusion
The number 4,500 might be a rough estimate to the nearest hundred (2 sig figs) or a careful count to the nearest unit (4 sig figs). Without more information you cannot tell, so textbooks treat the zeros as not significant. Writers avoid the ambiguity by:
- adding a decimal point: 4500. has four significant figures,
- using scientific notation: 4.5 × 10³ (two), 4.50 × 10³ (three), 4.500 × 10³ (four),
- or placing a bar over the last significant zero, a convention used in some textbooks.
The scientific notation converter rewrites any value in scientific form, which is the cleanest way to show precision.
Special cases
- Zero itself. A reading of 0 or 0.00 has no non-zero digit to start counting from. Its precision is better described by decimal places — 0.00 g is known to the hundredths place.
- Negative signs don’t affect the count: −305.0 has four significant figures.
- Exact numbers — counts, conversion definitions such as 100 cm = 1 m, and pure math constants written in full — are never the limiting factor in a calculation.
- Commas used as thousands separators are ignored. Write decimals with a period.
What to do next
Once you know how many significant figures each measurement has, the significant figures calculator applies the addition and multiplication rules to a calculation, and the significant figures rounding calculator rounds any number to a chosen count. Reporting a lab result? Pair it with the percent error calculator.
Frequently asked questions
How many significant figures are in 0.004050?
Four. The three leading zeros are placeholders and don't count. The 4 and 5 are non-zero, the zero between them is captive and counts, and the final zero counts because the number has a decimal point.
How many significant figures does 1200 have?
By the usual convention, two — trailing zeros in a whole number without a decimal point are treated as not significant. The writer may have meant three or four, so the number is ambiguous. Writing 1.20 × 10³ or 1200. (with a decimal point) makes the intent clear.
Are zeros after a decimal point significant?
Trailing zeros after a decimal point are significant: 2.50 has three significant figures and 2.500 has four. Zeros at the start of a decimal, as in 0.025, are not.
How do I count significant figures in scientific notation?
Count every digit in the coefficient. 6.02 × 10²³ has three and 6.020 × 10²³ has four. The power of ten only moves the decimal point; it never changes the count.
Do exact numbers have significant figures?
Counted quantities (12 students) and defined values (1 foot = 12 inches exactly) are treated as having unlimited significant figures, so they never limit a calculated answer. The rules on this page apply to measured values.