Significant Figures in Addition and Subtraction
The rule for addition and subtraction is about decimal places, not sig fig count. Learn why — with worked examples and common mistakes.
Reviewed by the Sig Figs Calc Editorial Team · Last updated April 2025 · See methodology
The rule for addition and subtraction
The answer must have the same number of decimal places as the input with the fewest decimal places.
For example: 12.11 + 0.3 = 12.4
The raw sum is 12.41. But 0.3 has only 1 decimal place — so the answer is limited to 1 decimal place: 12.4.
Notice that we are counting decimal places — not total sig figs. This is what makes the addition rule different from the multiplication rule.
Why decimal places control the result
When you add or subtract, precision is determined by position — specifically, which column (tenths, hundredths, thousandths) the last significant digit occupies.
If one number is precise to the tenths place (0.3) and another is precise to the hundredths (12.11), the result can only be trusted to the tenths place. The hundredths digit in the answer is unreliable because one of the inputs had no information there.
This is different from multiplication
Multiplication and division use total sig fig count — not decimal places. See the multiplication and division guide →
How to apply the rule — step by step
Write out each number
Line them up at the decimal point. This makes it easy to see which number has the fewest decimal places.
Identify the fewest decimal places
Find the input with the least decimal places. That is your limit — the answer cannot be more precise than this.
Perform the addition or subtraction
Calculate the full raw answer using all digits given.
Round the answer to the limiting decimal places
Round the raw result to match the fewest decimal places from step 2. Apply standard rounding rules — if the next digit is ≥ 5, round up.
Express the result with correct sig figs
The final answer should show no more precision than the least precise input. Do not add or remove trailing zeros arbitrarily.
Worked examples
Four examples, from simple to multi-operand.
12.11 + 0.3
0.3 has only 1 decimal place. The raw sum 12.41 rounds to 12.4.
1.002 + 0.0040
1.002 limits to 3 decimal places. 1.0060 rounds to 1.006.
100.0 − 0.036
100.0 limits to 1 decimal place. 99.964 rounds to 100.0.
5.8 + 0.004 + 2.31
5.8 has only 1 decimal place. The sum 8.114 rounds to 8.1.
What about mixed operations?
When an expression contains both addition/subtraction and multiplication/division, evaluate step by step. Apply the correct rule for each operation type as you go, carrying the appropriate precision through each step.
Example
(1.2 + 3.45) × 2.0
Step 1: 1.2 + 3.45 → limited to 1 dp → 4.6
Step 2: 4.6 × 2.0 → both have 2 sf → 9.2
Common errors
✗ Using sig fig count instead of decimal places
This is the most common error. For addition and subtraction, the rule is decimal places — not total sig figs. 12.11 has 4 sig figs but 2 decimal places. 0.3 has 1 sig fig and 1 decimal place. The answer is limited by decimal places: 1.
✗ Rounding before you calculate
Do the full calculation first, then round the final answer. If you round each operand first, rounding errors compound. Calculate with all digits, then apply the rule once at the end.
✗ Applying this rule to multiplication and division
Multiplication and division use a completely different rule: fewest sig figs, not fewest decimal places. Make sure you apply the right rule for the right operation.
✗ Forgetting that whole numbers have zero decimal places
If you add 1.23 + 5, the integer 5 has 0 decimal places — which would round the answer to a whole number. If that seems too imprecise, the integer may actually be exact (like a count), which has unlimited sig figs.
Frequently asked questions
Common questions about sig figs in addition and subtraction.
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