EducationMarch 23, 2026

Significant Figures: Rules, Examples, and Calculator

By The hakaru Team·Last updated March 2026

Significant figures (also called significant digits or sig figs) are the meaningful digits in a measured or calculated number that indicate its precision. They include all certain digits plus one estimated digit. Mastering significant figure rules is essential in chemistry, physics, and engineering, where reporting false precision can lead to errors in experimental results.

Quick Answer

1. 6 rules: all non-zero digits are significant; zeros between non-zero digits are significant; leading zeros are not; trailing zeros in decimals are; trailing zeros in whole numbers are ambiguous.
2. Multiplication/division: round to the fewest sig figs among inputs. Addition/subtraction: round to the fewest decimal places.
3. Sig figs express measurement uncertainty: the last digit has an implied uncertainty of +/-1 in its place value.
4. Exact numbers (definitions, counts) have infinite sig figs and never limit calculation precision.

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The 6 Rules for Counting Significant Figures

Rule 1: All Non-Zero Digits Are Significant

Every digit from 1 through 9 always counts as significant, regardless of its position.

4,827 has 4 significant figures
52.3 has 3 significant figures
7 has 1 significant figure

Rule 2: Zeros Between Non-Zero Digits Are Significant (Captive Zeros)

A zero sandwiched between non-zero digits is always significant because it represents a measured value.

1,007 has 4 significant figures
40.05 has 4 significant figures
20,309 has 5 significant figures

Rule 3: Leading Zeros Are Not Significant

Zeros that appear before the first non-zero digit are merely placeholders and do not count.

0.045 has 2 significant figures (only 4 and 5)
0.0009 has 1 significant figure
0.00320 has 3 significant figures (3, 2, and the trailing 0)

Rule 4: Trailing Zeros in a Decimal Number Are Significant

When a number has a decimal point, trailing zeros indicate measured precision.

2.50 has 3 significant figures
100.0 has 4 significant figures
0.500 has 3 significant figures

Rule 5: Trailing Zeros in a Whole Number Are Ambiguous

Without a decimal point, trailing zeros in a whole number may or may not be significant. The number 1500 could have 2, 3, or 4 sig figs. Scientific notation removes the ambiguity:

1.5 x 10³ = 2 sig figs
1.50 x 10³ = 3 sig figs
1.500 x 10³ = 4 sig figs

Some textbooks use a trailing decimal point (1500.) to indicate all four digits are significant, but this convention is not universal.

Rule 6: Exact Numbers Have Infinite Significant Figures

Numbers from definitions (1 meter = 100 centimeters), counting (12 eggs), and some mathematical constants are exact and never limit the sig figs in a calculation.

Significant Figures in Calculations

Multiplication and Division: Match the Fewest Sig Figs

The result of multiplication or division should have the same number of significant figures as the input with the fewest sig figs.

Example: 4.56 x 1.4 = 6.384, rounded to 6.4 (2 sig figs, limited by 1.4 which has 2 sig figs).

Example: 8.315 / 2.1 = 3.959523..., rounded to 4.0 (2 sig figs, limited by 2.1).

Addition and Subtraction: Match the Fewest Decimal Places

The result of addition or subtraction should have the same number of decimal places as the input with the fewest decimal places.

Example: 12.11 + 0.3 + 1.013 = 13.423, rounded to 13.4 (one decimal place, limited by 0.3).

Example: 100.0 - 7.23 = 92.77, which stays as 92.77 (two decimal places, limited by 7.23; 100.0 has one decimal place, so actually the answer rounds to 92.8).

Mixed Operations: Follow Order of Operations

For calculations with both multiplication/division and addition/subtraction, keep track of sig figs through each step. Complete the multiplication/division first, noting the number of sig figs, then apply the addition/subtraction rule to the final result. Many chemistry instructors recommend keeping one extra "guard digit" during intermediate steps and rounding only the final answer.

Rounding Rules for Significant Figures

When rounding to the correct number of significant figures:

If the digit to be dropped is less than 5, drop it and leave the preceding digit unchanged. (4.32 rounded to 2 sig figs = 4.3)
If the digit to be dropped is greater than 5, increase the preceding digit by one. (4.36 rounded to 2 sig figs = 4.4)
If the digit to be dropped is exactly 5 (with nothing after it), round to the nearest even digit. This is the "round half to even" or "banker's rounding" rule, which reduces systematic bias. (4.35 rounds to 4.4; 4.25 rounds to 4.2)

Common Mistakes With Significant Figures

Confusing leading zeros with significant digits: 0.005 has 1 sig fig, not 3. The zeros are placeholders.
Using the multiplication rule for addition: 12.1 + 1.15 should round to one decimal place (13.3), not three sig figs.
Reporting calculator output without rounding: Your calculator shows 12 digits. If your measurements have 3 sig figs, your answer should have 3 sig figs.
Rounding intermediate steps: Round only the final answer. Rounding at each step introduces cumulative rounding error.
Ignoring ambiguous trailing zeros: If a measurement is reported as 2500 mL, clarify whether 2, 3, or 4 sig figs are intended, or convert to scientific notation.

Practice Problems

Test your understanding with these examples:

Number	Sig Figs	Explanation
0.00820	3	Leading zeros not significant; trailing zero after 2 in decimal is significant
10,200	3 (ambiguous)	Trailing zeros without decimal are ambiguous; likely 3 sig figs
1.020 x 10⁴	4	Scientific notation makes it clear: 1, 0, 2, 0 all count
500.	3	Trailing decimal point indicates all digits are significant
6.022 x 10²³	4	Avogadro's number reported to 4 sig figs

The Bottom Line

Significant figures are the scientific convention for communicating measurement precision. The rules are straightforward: non-zero digits always count, captive zeros count, leading zeros do not, and trailing zeros depend on context. In calculations, use the fewest sig figs rule for multiplication/division and the fewest decimal places rule for addition/subtraction. When in doubt, express numbers in scientific notation to eliminate ambiguity.

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Frequently Asked Questions

How many significant figures does 0.00340 have?

0.00340 has 3 significant figures. The leading zeros (0.00) are not significant because they only serve as placeholders to show the position of the decimal point. The digits 3, 4, and the trailing 0 are all significant. The trailing zero after the 4 is significant because it appears after a non-zero digit in a decimal number, indicating that the measurement was precise to the hundred-thousandths place.

Are trailing zeros significant?

It depends on whether a decimal point is present. Trailing zeros in a number with a decimal point are always significant: 2.50 has 3 sig figs, and 100.0 has 4 sig figs. Trailing zeros in a whole number without a decimal point are ambiguous: 1500 could have 2, 3, or 4 sig figs depending on the precision of the measurement. To remove ambiguity, use scientific notation: 1.5 x 10^3 (2 sig figs), 1.50 x 10^3 (3 sig figs), or 1.500 x 10^3 (4 sig figs).

What are the sig fig rules for addition vs multiplication?

For multiplication and division, the result should have the same number of significant figures as the measurement with the fewest sig figs. For example, 4.56 x 1.4 = 6.384, rounded to 6.4 (2 sig figs, matching 1.4). For addition and subtraction, the result should have the same number of decimal places as the measurement with the fewest decimal places. For example, 12.11 + 0.3 = 12.41, rounded to 12.4 (one decimal place, matching 0.3). These are different rules, and mixing them up is one of the most common errors in chemistry and physics courses.

Do exact numbers have significant figures?

Exact numbers have an infinite number of significant figures and never limit the precision of a calculation. Exact numbers come from definitions (1 foot = 12 inches exactly), counting (there are exactly 5 beakers on the table), or mathematical constants with defined values. When you multiply a measurement by an exact number, the significant figures of the result are determined only by the measurement. For example, the circumference of a circle with a measured radius of 3.45 cm is 2 x pi x 3.45 = 21.7 cm (3 sig figs, determined by the radius measurement, not by the 2 or pi).

Why do significant figures matter in science?

Significant figures communicate the precision of a measurement. Reporting 9.80 m/s^2 for gravitational acceleration tells the reader the value was measured to three significant figures (the hundredths place). Writing 9.8 m/s^2 communicates lower precision (two sig figs). Writing 9.800 m/s^2 claims four sig figs of precision. Overstating precision (reporting more sig figs than your instrument can measure) is scientifically dishonest and can propagate errors through calculations. In fields like pharmaceuticals, engineering, and analytical chemistry, correct sig fig usage is essential for safety and regulatory compliance.

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