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 |
0.004560 has exactly 4 significant figures — the leading zeros are placeholders, not measurements. The five rules determine which digits carry real information: (1) all non-zero digits are significant, (2) captive zeros between non-zero digits are significant, (3) leading zeros are never significant, (4) trailing zeros after a decimal point are significant, (5) trailing zeros in whole numbers without a decimal point are ambiguous.
Rule 5 is the most common source of confusion. Does 1200 have 2 sig figs (1.2 × 10³) or 4 sig figs (1200.)? Without additional context, convention assumes 2. Adding a decimal point (1200.) explicitly communicates 4 sig figs. Scientific notation eliminates ambiguity entirely: 1.200 × 10³ = 4 sig figs, 1.2 × 10³ = 2 sig figs.
The number 100.00 has 5 significant figures: the 1 (non-zero), the two captive zeros between 1 and the decimal (captive), and the two trailing zeros after the decimal. Each additional trailing zero communicates greater precision. The Scientific Notation Calculator provides an unambiguous way to express any number with a specific sig fig count.
| Number | Sig Figs | Rule(s) Applied |
|---|---|---|
| 456 | 3 | All non-zero digits |
| 1002 | 4 | Captive zeros count |
| 0.0045 | 2 | Leading zeros ignored |
| 2.300 | 4 | Trailing after decimal counts |
| 1500 | 2 (ambiguous) | Trailing zeros in whole number |
| 1500. | 4 | Decimal point makes trailing significant |
Multiplication and division: the result gets the same number of sig figs as the input with the fewest. 2.5 × 3.42 = 8.55 on a calculator, but 2.5 has only 2 sig figs, so the answer rounds to 8.6. Dividing 45.0 (3 sig figs) by 3.1 (2 sig figs) gives 14.516..., rounded to 15 (2 sig figs).
Addition and subtraction: the result gets the same number of decimal places as the input with the fewest. 100.0 + 1.234 = 101.234 on a calculator, but 100.0 has only 1 decimal place, so the answer rounds to 101.2. This rule preserves the absolute precision of the least precise measurement rather than relative precision.
Exact numbers (counted quantities, defined conversions) have infinite sig figs and never limit results. Counting 12 eggs is exact — it does not have 2 sig figs. Similarly, 1 inch = 2.54 cm is an exact definition. Only measured values carry finite precision. The Rounding Calculator can round any result to the correct number of significant figures or decimal places.
| Operation | Calculation | Rule | Correct Result |
|---|---|---|---|
| Multiply | 2.5 × 3.42 | Fewest sig figs (2) | 8.6 |
| Divide | 45.0 / 3.1 | Fewest sig figs (2) | 15 |
| Add | 100.0 + 1.234 | Fewest dec places (1) | 101.2 |
| Subtract | 50.00 − 0.567 | Fewest dec places (2) | 49.43 |
A bathroom scale measuring 70.0 kg has 3 sig figs (precision to 0.1 kg). Reporting your weight as 70.000 kg implies precision to 1 gram — a claim your scale cannot support. This false precision can propagate through calculations: if you compute BMI using that inflated precision, every decimal in the result is meaningless noise.
In chemistry, a titration endpoint measured as 12.45 mL (4 sig figs) combined with a concentration of 0.10 M (2 sig figs) limits the moles calculation to 2 sig figs: n = 0.10 × 0.01245 = 0.001245, rounded to 0.0012 mol. Reporting 0.001245 implies the concentration was measured to 4 sig figs when it was measured to only 2.
Engineering tolerances use sig figs implicitly. A part dimensioned as 12.5 mm implies tolerance of ±0.05 mm (3 sig figs). Specifying 12.50 mm tightens the tolerance to ±0.005 mm (4 sig figs), which requires more precise machining and costs significantly more. The Percentage Calculator can compute the relative error: ±0.05/12.5 = ±0.4% for 3 sig figs versus ±0.04% for 4.
In multi-step calculations, keep 1–2 extra sig figs through intermediate steps and round only the final answer. This prevents rounding errors from accumulating. Spreadsheets and calculators naturally do this by storing full precision internally.
Last Updated: Mar 26, 2026
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