Math Tool

Significant Figures Calculator

Count significant figures in any number instantly and round to any number of sig figs. Shows all 5 sig fig rules with examples.

Count Sig Figs-Round to N Sig Figs-All 5 Rules

Count Significant Figures

Round to Sig Figs

significant figures

Quick Examples

Sig Fig Rules

1
Non-zero digits
Always significant
1, 2, 3...
2
Leading zeros
Never significant
0.0025 has 2 sig figs
3
Captive zeros
Always significant
1007 has 4 sig figs
4
Trailing zeros (no decimal)
Ambiguous
1500 may have 2-4 sig figs
5
Trailing zeros (with decimal)
Always significant
1500. has 4 sig figs
Scientific Notation

Use scientific notation to eliminate ambiguity: 1.5 x 10^3 clearly has 2 sig figs, while 1.500 x 10^3 has 4 sig figs.

Significant Figures in Operations

OperationRuleExampleAnswer
MultiplicationFewest sig figs in inputs4.56 × 1.46.4 (2 sig figs)
DivisionFewest sig figs in inputs9.89 ÷ 2.14.7 (2 sig figs)
AdditionFewest decimal places12.52 + 349.0361.5 (1 decimal)
SubtractionFewest decimal places45.67 - 2.343.4 (1 decimal)
MixedApply rule to each step(2.1 + 3.45) × 1.26.7 (2 sig figs)

Why Significant Figures Matter

Significant figures are not just a classroom convention - they communicate the precision of a measurement. When a scientist reports a result as 12.3 grams, the three significant figures tell other scientists that the measurement was made with a precision of about plus or minus 0.1 grams. Reporting it as 12.30 grams (4 sig figs) implies precision to 0.01 grams.

The rules for significant figures ensure that calculated results don't appear more precise than the original measurements allow. This concept is called precision propagation. If you measure a box as 1.2 meters and 3.456 meters and multiply to get the area, reporting 4.1472 square meters implies you measured to 0.0001 square meter precision - but your first measurement was only good to 0.1 meters.

Common Mistakes to Avoid

The most common mistake is confusing significant figures with decimal places. Decimal places count digits after the decimal point. Significant figures count all meaningful digits starting from the first non-zero digit. The number 0.0045 has 0 digits before the decimal but 2 significant figures (4 and 5).

Frequently Asked Questions

How do you count significant figures?⌄
Apply these rules: (1) All non-zero digits are significant. (2) Leading zeros are never significant (0.0025 has 2). (3) Captive zeros between non-zeros are significant (1007 has 4). (4) Trailing zeros with a decimal point are significant (2.50 has 3). (5) Trailing zeros without decimal are ambiguous (1500 may be 2, 3, or 4 sig figs).
How many significant figures does 0.00420 have?⌄
Three significant figures. The leading zeros (0.00) are not significant. The digits 4, 2, and the trailing 0 after the decimal are all significant. The trailing zero is significant because it appears after a decimal point.
What is the rule for significant figures in multiplication and division?⌄
The result should have the same number of sig figs as the measurement with the fewest sig figs. For example, 4.56 × 1.4 = 6.384, but rounded to 2 sig figs (from 1.4), the answer is 6.4.
What is the rule for significant figures in addition and subtraction?⌄
The result should have the same number of decimal places as the measurement with the fewest decimal places. For example, 12.52 + 349.0 + 8.24 = 369.76, rounded to 369.8 (one decimal place, matching 349.0).
How do you round to 3 significant figures?⌄
Identify the first 3 significant digits, look at the 4th digit to decide rounding. Example: 0.004567 rounded to 3 sig figs = 0.00457 (digits are 4, 5, 6; the 7 rounds up the 6 to 7).
Are all zeros in 100.0 significant?⌄
Yes. 100.0 has 4 significant figures. The decimal point clarifies that all zeros are intentionally written, making the trailing zeros significant. Without the decimal, 100 has ambiguous trailing zeros.
What is scientific notation used for in sig figs?⌄
Scientific notation eliminates ambiguity. Instead of 1500 (2-4 sig figs ambiguous), write 1.5 x 10^3 (2 sig figs) or 1.500 x 10^3 (4 sig figs). Only digits in the coefficient are significant.
How many sig figs should I use in everyday calculations?⌄
Match the precision of your least precise measurement. For lab work, typically 3-4 sig figs. For engineering, 3 sig figs is standard. More precision is not always better - reporting 12.4567 when your ruler only reads to 0.1 is false precision.

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