Arithmetic rule

Adding and Subtracting Significant Figures

When adding or subtracting significant figures, round the final answer to the least precise decimal place—not the fewest significant figures.

Use the calculator

The addition and subtraction sig fig rule

For addition and subtraction, the final answer is rounded to the least precise decimal place among the measured inputs. This rule is about place value, not the total number of significant figures.

Step 1: line up the decimal points

Write each measured value by place value so you can compare the last reliable decimal place.

Step 2: find the least precise place

Identify the input whose last reliable digit is farthest to the left. That decimal place controls the final answer.

Step 3: calculate with guard digits

Add or subtract without rounding the intermediate result, so an early rounding choice does not change the answer.

Step 4: round the final answer

Round the raw result once to the controlling decimal place, then include the correct unit when the values are measurements.

Addition and subtraction sig fig examples

Each example shows the raw result, the limiting decimal place, and the correctly rounded final answer.

Example: 12.5 + 0.003

The raw result is 12.503. Since 12.5 is precise only to tenths, the final answer is 12.5.

Example: 2.34 + 1.2

2.34 is precise to hundredths, while 1.2 is precise to tenths. The raw sum 3.54 is reported as 3.5.

Example: 105.6 - 2.45

The raw result is 103.15. Because 105.6 is precise to tenths, report 103.2.

Do not use the fewest sig figs rule here

A value can have many significant figures but still control the answer by decimal place. That is why addition and subtraction are different from multiplication and division.

Rule contrast

Fewest significant figures controls multiplication and division, not addition and subtraction.

Why this matters

12.5 has 3 significant figures, but it still controls 12.5 + 0.003 because it only reaches the tenths place.

Line up the decimal points

When solving by hand, line up decimal points so the place values are visible. This makes it easier to see which input has the least precise decimal place.

Workflow check

Write the raw arithmetic first, keep guard digits while calculating, then round only the final result.

Subtraction follows the same rule

Subtraction uses the same decimal-place rule as addition. The final result should not claim more decimal precision than the least precise measured value supports.

Example: 20.00 - 0.113

The raw result is 19.887. Since 20.00 is precise to hundredths, report 19.89.

Units stay with the rounded answer

In lab work, the unit is part of the reported result. Round the number according to the decimal-place rule, then keep the correct unit with the final answer.

Example: 12.5 mL + 0.003 mL

Report 12.5 mL because the least precise input is measured to tenths of a milliliter.

Same-unit check

Only add or subtract values after the units match. If a problem mixes mL and L, convert first, then apply the decimal-place precision rule.

Common mistakes in addition and subtraction

The biggest mistakes are using the multiplication rule, rounding intermediate values too early, or counting decimal places after the arithmetic instead of before the final rounding choice.

Mistake: using fewest sig figs

12.5 + 0.003 is reported as 12.5, not because of the fewest-sig-fig rule, but because tenths is the least precise decimal place.

Mistake: over-reporting decimals

Reporting 12.503 would imply precision to thousandths, which the 12.5 measurement does not support.

Lab report wording

A clear report sentence names the rounded value and the decimal-place rule. Keep it short so the reason is easy to check.

Copy-ready answer

The result should be reported as 12.5 because addition and subtraction follow the least precise decimal place.