Significant Figures
4 sig figs
Rounded
0.00456
Scientific
4.56e-3
Supports integers, decimals, and scientific notation (e.g., 3.45e6)
Significant Figures
4
0.00456
4.56e-3
Leading zeros are never significant
All non-zero digits are significant
Trailing zeros after a decimal point are significant
Count from first non-zero digit, applying 5 rulesNon-zero digits always count. Captive zeros count. Leading zeros never count. Trailing zeros after a decimal count. Trailing zeros in whole numbers are ambiguous.
Where:
Non-zero= Always significant (1-9)Captive zero= Zero between non-zero digits (always significant)Leading zero= Zeros before first non-zero digit (never significant)Trailing zero= Significance depends on decimal point presenceround(x, N) = round to N digits from first significant digitStart from the leftmost significant digit, count N digits, and round based on the (N+1)th digit. If >= 5, round up; otherwise truncate.
Where:
x= The number to roundN= Desired number of significant figuresInputs
Result
The leading zeros (0.00) are not significant. The digits 4, 5, 6 are non-zero (significant). The trailing 0 after the decimal is significant. Total: 4 sig figs.
Inputs
Result
Count 3 significant digits from left: 9, 8, 7. The next digit is 6 (>= 5), so round up: 98800.
Inputs
Result
1 is non-zero (significant). The two zeros between 1 and 3 are captive zeros (significant). 3 is non-zero (significant). The two trailing zeros after decimal are significant. Total: 6 sig figs.
Significant figures (sig figs) are the meaningful digits in a number that contribute to its precision. They matter in science and engineering because they communicate measurement accuracy. Reporting extra digits implies false precision.
| Number | Sig Figs | Precision Level |
|---|---|---|
| 1200 | 2 | Nearest hundred |
| 1200. | 4 | Nearest unit |
| 1200.0 | 5 | Nearest tenth |
| 0.0045 | 2 | Two significant digits |
| 0.004500 | 4 | Four significant digits |
Follow five rules: (1) all non-zero digits are significant, (2) zeros between non-zero digits (captive zeros) are significant, (3) leading zeros are never significant, (4) trailing zeros after a decimal point are significant, (5) trailing zeros in a whole number are ambiguous.
| Number | Sig Figs | Rule Applied |
|---|---|---|
| 305 | 3 | Captive zero counts |
| 0.0070 | 2 | Leading zeros ignored, trailing counts |
| 8.040 | 4 | Captive + trailing after decimal |
| 100 | 1 | Trailing zeros ambiguous |
| 100. | 3 | Decimal point makes trailing significant |
Count from the first significant digit to your desired number, then round the next digit. If the next digit is 5 or more, round up; if less than 5, round down. For example, 0.004560 rounded to 2 sig figs = 0.0046.
| Original | 2 Sig Figs | 3 Sig Figs | 4 Sig Figs |
|---|---|---|---|
| 3.14159 | 3.1 | 3.14 | 3.142 |
| 0.004560 | 0.0046 | 0.00456 | 0.004560 |
| 98765 | 99000 | 98800 | 98770 |
| 1.005 | 1.0 | 1.01 | 1.005 |
For multiplication and division, the result should have the same number of sig figs as the input with the fewest sig figs. For addition and subtraction, the result should have the same number of decimal places as the input with the fewest decimal places.
| Operation | Calculation | Rule | Result |
|---|---|---|---|
| Multiply | 2.5 × 3.42 | 2 sig figs (fewest) | 8.6 |
| Divide | 45.0 / 3.1 | 2 sig figs (fewest) | 15 |
| Add | 1.2 + 3.45 | 1 decimal place | 4.7 |
| Subtract | 100.0 - 1.234 | 1 decimal place | 98.8 |
Decimal places count digits after the decimal point regardless of significance. Significant figures count all meaningful digits from the first non-zero digit. The number 0.00450 has 5 decimal places but only 3 significant figures.
| Number | Decimal Places | Sig Figs |
|---|---|---|
| 3.14 | 2 | 3 |
| 0.00450 | 5 | 3 |
| 1200 | 0 | 2 (ambiguous) |
| 100.0 | 1 | 4 |
| 0.10 | 2 | 2 |
Significant figures communicate the precision of a measurement in science and engineering.
The five rules for counting sig figs cover non-zero digits, captive zeros, leading zeros, and trailing zeros.
Proper use of significant figures ensures calculated results do not imply false precision.
Last Updated: Mar 9, 2026
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