Maths5 min readUpdated Apr 28, 2026

Significant Figures Cheat Sheet: All Sig Fig Rules with Examples

A complete sig figs cheat sheet covering the 5 counting rules, the multiplication and division rule, the addition and subtraction rule, scientific notation, and the special logarithm rule for pH, all with worked examples and a quick reference table for common numbers.

Key Takeaways

Non-zero digits, captive zeros, and trailing zeros after a decimal are always significant.
Leading zeros are never significant. Trailing zeros in a whole number with no decimal are ambiguous.
Multiplication and division: the result uses the fewest sig figs of any input.
Addition and subtraction: the result uses the fewest decimal places of any input, not sig figs.
Logarithms have a special rule: input sig figs map to log decimal places (mantissa).

The 5 Counting Rules at a Glance

These five rules cover every digit you will ever need to count. Memorize them once and you can read any number correctly.

#	Rule	Example
1	All non-zero digits are significant	482 has 3 sig figs
2	Captive zeros (between non-zeros) are significant	1005 has 4 sig figs
3	Leading zeros are NEVER significant	0.0032 has 2 sig figs
4	Trailing zeros AFTER a decimal are significant	2.500 has 4 sig figs
5	Trailing zeros in a whole number are ambiguous	1200 has 2, 3, or 4 sig figs

If rule 5 leaves you uncertain, scientific notation removes the ambiguity. Writing 1.20 x 10^3 is unmistakably 3 sig figs; 1.200 x 10^3 is 4.

Operation Rules: Sig Figs vs Decimal Places

The rule that governs the answer depends on the operation. This is the single most-confused topic in sig fig math, and the source of most lost points on chemistry and physics exams.

Operation	Rule for the Result	Worked Example
Multiplication	Fewest SIG FIGS of any input	4.56 x 1.4 = 6.4 (limited by 1.4)
Division	Fewest SIG FIGS of any input	25.36 / 4.2 = 6.0 (limited by 4.2)
Addition	Fewest DECIMAL PLACES of any input	12.52 + 1.7 = 14.2 (1 decimal place)
Subtraction	Fewest DECIMAL PLACES of any input	45.876 - 0.34 = 45.54 (2 decimals)

Multiplication and division track relative precision (a percentage of the value). Addition and subtraction track absolute precision (which decimal place is uncertain). They are not interchangeable.

The Logarithm and pH Rule

Logarithms break the normal pattern. The integer part of a log (the characteristic) only sets the order of magnitude, so all the precision lives in the decimal part (the mantissa).

Direction	Rule
Forward log	Sig figs in input = Decimal places in log result
Antilog (10^x)	Decimal places in input = Sig figs in result

Worked example for pH: if [H+] = 2.5 x 10^-4 (2 sig figs), then pH = 3.60 (2 decimal places). The "3" is just the order of magnitude; the ".60" carries the precision. This rule applies identically to natural log (ln) and to any pX-style scale: pKa, pKb, pOH, all the same.

Quick Reference: Sig Fig Counts for Common Numbers

Here is a lookup table for numbers that come up constantly in homework and lab work. If your number is not listed, apply the 5 counting rules to derive the answer.

Number	Sig Figs	Reason
40	1 (ambiguous)	Trailing zero in whole number, no decimal
40.	2	Decimal point makes the 0 significant
40.0	3	Trailing zero after decimal counts
40.00	4	Two trailing zeros after decimal
100	1 (ambiguous)	Trailing zeros in whole number
100.0	4	Decimal makes all zeros significant
100.00	5	All trailing zeros after decimal count
200	1 (ambiguous)	Trailing zeros in whole number
0.001	1	Leading zeros do not count
0.002	1	Only the 2 is significant
0.009	1	Only the 9 is significant
0.020	2	Trailing zero after decimal counts
0.0030	2	Trailing zero after decimal counts
0.500	3	All three digits after decimal count
0.00340	3	3, 4, and trailing 0 all count
1200	2, 3, or 4	Ambiguous; use scientific notation
4.0	2	Trailing zero after decimal
70.0	3	Trailing zero after decimal
500.0	4	Decimal makes all zeros significant
76.00	4	Two trailing zeros after decimal

Scientific Notation Removes All Ambiguity

Whenever rule 5 leaves you stuck, switch to scientific notation. The number of digits in the coefficient equals the sig fig count, full stop.

Written	Scientific Notation	Sig Figs
1200	1.2 x 10^3	2
1200	1.20 x 10^3	3
1200	1.200 x 10^3	4
0.00340	3.40 x 10^-3	3
3,450,000	3.45 x 10^6	3

This is why scientific publications, lab reports, and exams always express precision-sensitive results in scientific notation. There is no other way to communicate "exactly 3 sig figs" for a number like 4500.

Common Mistakes and Edge Cases

A few traps catch students even after they know the rules. **Rounding intermediate steps.** Never round in the middle of a multi-step calculation. Carry one or two extra digits and round only the final answer. Early rounding compounds error. **Treating exact numbers as if they had limited sig figs.** Counts (12 eggs), defined conversions (1 inch = 2.54 cm exactly), and stoichiometric coefficients (the "2" in 2H2O) all have unlimited sig figs and never limit your answer. **Catastrophic cancellation in subtraction.** If you subtract two close numbers like 5.67 and 5.64, the result 0.03 has only 1 sig fig even though both inputs had 3. This is a real precision loss, not a quirk of the rule. **Forgetting that addition follows decimal places, not sig figs.** 99.5 + 1.3 = 100.8 has 4 sig figs, even though both inputs had 3. The decimal place rule is what governs the answer.

Frequently Asked Questions

How many sig figs does 40.0 have?

40.0 has 3 significant figures. The 4 is non-zero (rule 1), the 0 in the ones place is significant because there is a decimal point following it (rule 4), and the trailing 0 after the decimal is also significant.

How many sig figs does 100.00 have?

100.00 has 5 significant figures. Without the decimal point, "100" would be ambiguous (rule 5). With the decimal and trailing zeros, every digit becomes significant under rule 4.

How many sig figs does 0.500 have?

0.500 has 3 significant figures. The leading zero before the decimal does not count (rule 3), the 5 is non-zero (rule 1), and both trailing zeros after the decimal are significant (rule 4).

How many sig figs does 1200 have?

It is ambiguous. 1200 could have 2, 3, or 4 sig figs depending on how the measurement was made. Writing it as 1.2 x 10^3 fixes it at 2 sig figs, 1.20 x 10^3 at 3, and 1.200 x 10^3 at 4. Scientific notation is the only unambiguous way.

How many sig figs does 0.0030 have?

0.0030 has 2 significant figures. Leading zeros (0.00) are never significant. The 3 counts, and the trailing 0 after the decimal also counts.

Are captive zeros always significant?

Yes. A zero between two non-zero digits (a captive zero) is always significant, no matter where the decimal sits. So 1005, 10.05, and 0.01005 all have 4 significant figures.

Why is 100 ambiguous when 100.0 is not?

A whole number with trailing zeros has no marker telling you which zeros were measured precisely. The decimal point in 100. or 100.0 acts as that marker, declaring those zeros to be measured values, not placeholders.

How do sig figs work in pH calculations?

pH uses the logarithm rule. The number of significant figures in the hydrogen ion concentration becomes the number of decimal places in the pH. For [H+] = 2.5 x 10^-4 (2 sig figs), pH = 3.60 (2 decimal places).

What is the rule for multiplying with sig figs?

The product has the same number of significant figures as the input with the fewest sig figs. For 4.56 x 1.4: 4.56 has 3, 1.4 has 2, so the answer is rounded to 2 sig figs (6.4).

Is the rule for adding sig figs the same as multiplying?

No. Addition and subtraction use decimal places, not sig figs. The result is rounded to the same decimal place as the input with the fewest decimal places. Mixing these rules is the most common sig fig mistake.

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Significant Figures Cheat Sheet: All Sig Fig Rules with Examples

Key Takeaways

The 5 Counting Rules at a Glance

Operation Rules: Sig Figs vs Decimal Places

The Logarithm and pH Rule

Quick Reference: Sig Fig Counts for Common Numbers

Scientific Notation Removes All Ambiguity

Common Mistakes and Edge Cases

Frequently Asked Questions

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