Significant Figures Calculator
Significant Figures Rules
Non-zero digits are always significant
1234 → 4 sig figs
Zeros between non-zero digits are significant
1002 → 4 sig figs
Leading zeros are NOT significant
0.00123 → 3 sig figs
Trailing zeros after decimal ARE significant
12.300 → 5 sig figs
Trailing zeros without decimal are ambiguous
1200 → 2, 3, or 4 sig figs (unclear)
Quick Examples
Related Calculators
Understanding Significant Figures
What Are Significant Figures?
Significant figures (also called significant digits) are the digits in a number that carry meaningful information about its precision. They indicate the reliability of a measurement or calculation.
Why Sig Figs Matter
In science and engineering, a measurement of 5.00 meters is more precise than 5 meters. The trailing zeros indicate that the measurement was taken to the hundredths place, giving three significant figures instead of one.
Rules for Counting Significant Figures
Rule 1: Non-Zero Digits
All non-zero digits are significant.
Example: 1234 has 4 sig figs; 7.89 has 3 sig figs
Rule 2: Sandwiched Zeros
Zeros between non-zero digits are significant.
Example: 1002 has 4 sig figs; 3.07 has 3 sig figs
Rule 3: Leading Zeros
Leading zeros (before the first non-zero digit) are NOT significant.
Example: 0.00123 has 3 sig figs; 0.5 has 1 sig fig
Rule 4: Trailing Zeros (with decimal)
Trailing zeros after a decimal point ARE significant.
Example: 12.300 has 5 sig figs; 5.0 has 2 sig figs
Rule 5: Trailing Zeros (without decimal)
Trailing zeros in a whole number without a decimal point are ambiguous.
Example: 1200 could have 2, 3, or 4 sig figs (use scientific notation to clarify)
Operations with Significant Figures
Addition/Subtraction
Result should have the same number of decimal places as the least precise number.
(not 12.41)
Multiplication/Division
Result should have the same number of significant figures as the least precise number.
(not 6.384)
Practice Examples
| Number | Sig Figs | Explanation |
|---|---|---|
| 48923 | 5 | All non-zero |
| 3.967 | 4 | All non-zero |
| 900.06 | 5 | Zeros between non-zeros count |
| 0.0001 | 1 | Leading zeros don't count |
| 8.1000 | 5 | Trailing zeros after decimal count |
| 501.040 | 6 | All zeros count (sandwiched + trailing) |
Tip: Use Scientific Notation
When precision is ambiguous (like 1200), use scientific notation to be clear: 1.2 × 10³ (2 sig figs), 1.20 × 10³ (3 sig figs), or 1.200 × 10³ (4 sig figs).
Frequently Asked Questions
Are trailing zeros significant?
It depends on whether there's a decimal point. With a decimal (12.300), trailing zeros ARE significant (5 sig figs). Without a decimal (1200), trailing zeros are ambiguous - could be 2, 3, or 4 sig figs. Use scientific notation (1.20 x 10 cubed) to be clear.
How many sig figs should my answer have?
For multiplication/division: use the fewest sig figs of any input. For addition/subtraction: use the fewest decimal places. Example: 2.5 x 3.42 = 8.6 (2 sig figs, not 8.55). And 12.11 + 0.3 = 12.4 (1 decimal place).
Why do leading zeros not count as significant?
Leading zeros (0.00456) are placeholders showing magnitude, not precision. The measurement 0.00456 meters is the same as 4.56 millimeters - both have 3 significant figures. The zeros just indicate where the decimal point is relative to the significant digits.
Are exact numbers subject to sig fig rules?
No. Exact numbers (counting numbers like 12 eggs, defined constants like 100 cm per meter) have infinite significant figures and don't limit your answer. Only measured values with inherent uncertainty follow sig fig rules.