Significant Figures in Addition and Subtraction

When adding or subtracting measured values, significant-figure rules are slightly different from the rules used for multiplication and division. The final answer is determined by the number of decimal places in the values being added or subtracted, not simply by counting their significant figures.

The basic rule is simple:

For addition and subtraction, round the final result to the same number of decimal places as the value with the fewest decimal places.

This rule prevents a calculated result from appearing more precise than the least precise measurement used in the calculation.

If you are learning significant figures for the first time, start with our guide to What Are Significant Figures? You can also review the complete Rules of Significant Figures before working through the examples below.

The Rule for Addition and Subtraction

For addition and subtraction:

Look at the number of decimal places in each value.
Identify the value with the fewest decimal places.
Perform the addition or subtraction.
Round the final result to that same number of decimal places.

Notice that this rule is based on decimal places, not the total number of significant figures.

Example

Calculate:

12.11 + 0.3

The numbers have:

12.11 → 2 decimal places
0.3 → 1 decimal place

The least precise value is 0.3, which has 1 decimal place.

First calculate:

12.11 + 0.3 = 12.41

Then round to 1 decimal place:

12.4

Therefore:

12.11 + 0.3 = 12.4

Why Decimal Places Matter

In addition and subtraction, the position of the last reported digit determines the precision of the result.

Consider:

18.42 + 3.1

Here:

18.42 is reported to the hundredths place.
3.1 is reported to the tenths place.

The second number is less precise because its final reported digit is in the tenths place.

Calculate:

18.42 + 3.1 = 21.52

Round the result to the tenths place:

21.5

The answer is therefore:

21.5

Even though 21.52 contains four significant figures, reporting all four would imply more decimal-place precision than the original values support.

Addition With Significant Figures: Step-by-Step Examples

Example 1: Two decimal numbers

Calculate:

4.25 + 3.6

Decimal places:

4.25 → 2
3.6 → 1

Calculate:

4.25 + 3.6 = 7.85

Round to 1 decimal place:

7.9

Answer:

4.25 + 3.6 = 7.9

Example 2: Three values

Calculate:

12.35 + 4.2 + 0.678

Decimal places:

12.35 → 2
4.2 → 1
0.678 → 3

The fewest decimal places is 1.

Calculate:

12.35 + 4.2 + 0.678 = 17.228

Round to 1 decimal place:

17.2

Answer:

17.2

Example 3: Values with trailing zeros

Calculate:

5.20 + 2.3

The written precision matters:

5.20 → 2 decimal places
2.3 → 1 decimal place

Calculate:

5.20 + 2.3 = 7.50

Round to the least precise decimal place, which is the tenths place:

7.5

Answer:

7.5

The trailing zero in 5.20 communicates that the original value was reported to the hundredths place, but the result cannot be reported beyond the tenths place because of 2.3.

Subtraction With Significant Figures

The same decimal-place rule applies to subtraction.

Example 1

Calculate:

15.67 − 2.4

Decimal places:

15.67 → 2
2.4 → 1

Calculate:

15.67 − 2.4 = 13.27

Round to 1 decimal place:

13.3

Answer:

15.67 − 2.4 = 13.3

Example 2

Calculate:

100.00 − 25.6

Decimal places:

100.00 → 2
25.6 → 1

Calculate:

100.00 − 25.6 = 74.40

Round to 1 decimal place:

74.4

Answer:

74.4

What If There Is No Decimal Point?

Whole numbers can make addition and subtraction more complicated because trailing zeros may not clearly communicate their intended precision.

For example:

1200 + 35

The written form 1200 may be ambiguous. It may represent a value measured to the nearest hundred, nearest ten, or potentially an exact or defined quantity, depending on the context.

In situations where the intended precision matters, scientific notation can make it explicit.

For example:

1.2 × 10³ → precision to the hundreds place
1.20 × 10³ → precision to the tens place
1.200 × 10³ → precision to the ones place

The context of the measurement should always be considered rather than assuming that every trailing zero has the same meaning.

For more information, see our Significant Figures Rules guide.

Addition and Subtraction With Negative Numbers

The same precision rule applies when negative values are involved.

Example

Calculate:

15.6 + (−2.34)

This is equivalent to:

15.6 − 2.34

The decimal places are:

15.6 → 1
2.34 → 2

Calculate:

15.6 − 2.34 = 13.26

Round to 1 decimal place:

13.3

Answer:

13.3

The sign of a number affects the arithmetic, but it does not change how decimal-place precision is determined.

Addition and Subtraction in Measurements

Significant figures are especially important when adding or subtracting measured quantities.

For example, suppose two lengths are measured as:

12.4 cm + 3.25 cm

The measurements have different decimal-place precision:

12.4 cm → tenths of a centimeter
3.25 cm → hundredths of a centimeter

Calculate:

12.4 + 3.25 = 15.65 cm

The least precise measurement is 12.4 cm, so the result should be rounded to the tenths place:

15.7 cm

The final reported value is therefore:

15.7 cm

The units should also be carried through the calculation.

Do Not Count Significant Figures for This Rule

One of the most common mistakes is to look at the number of significant figures instead of decimal places.

Consider:

123.4 + 5.67

The numbers contain:

123.4 → 4 significant figures
5.67 → 3 significant figures

It might seem that the answer should contain 3 significant figures. That is not the addition/subtraction rule.

Instead, look at decimal places:

123.4 → 1 decimal place
5.67 → 2 decimal places

Calculate:

123.4 + 5.67 = 129.07

Round to 1 decimal place:

129.1

Correct answer:

129.1

The number of significant figures in the final answer happens to be four, but that is not what determined the rounding.

Addition and Subtraction vs. Multiplication and Division

This distinction is essential.

Operation	Rule
Addition	Round to the fewest decimal places
Subtraction	Round to the fewest decimal places
Multiplication	Round to the fewest significant figures
Division	Round to the fewest significant figures

For example:

Addition

12.11 + 0.3 = 12.4

because the least precise value has 1 decimal place.

Multiplication

4.5 × 2.13 = 9.6

because 4.5 has only 2 significant figures.

For more detail on identifying significant digits, see Significant Figures Rules. For rounding procedures, see Rounding Significant Figures.

What About Mixed Calculations?

Some problems contain addition, subtraction, multiplication, and division in the same expression.

In these cases, follow the normal mathematical order of operations rather than treating the entire expression as one addition or subtraction problem.

For example, in a calculation containing multiplication followed by addition:

2.5 × 3.42 + 1.2

you first perform the multiplication:

2.5 × 3.42 = 8.55

Then add:

8.55 + 1.2 = 9.75

The final addition is limited by the tenths place because 1.2 has one decimal place.

Therefore, the final reported result is:

9.8

In multi-step calculations, avoid unnecessary rounding of intermediate values. Keep extra digits during the calculation when appropriate and apply the relevant precision rule at the required stage.

Detailed multi-operation handling can vary with the context and the instructions provided for a particular course, laboratory, or technical calculation.

Do You Round Before or After Adding?

For ordinary addition and subtraction problems, perform the calculation first and then round the result according to the least precise decimal place.

For example:

15.67 + 2.4

Do not round 15.67 before calculating.

Calculate:

15.67 + 2.4 = 18.07

Then round to the tenths place:

18.1

Rounding an input unnecessarily before performing the calculation can introduce additional rounding error.

Common Mistakes

Mistake 1: Using the fewest significant figures

This rule belongs to multiplication and division, not addition and subtraction.

For addition and subtraction, use the fewest decimal places.

Mistake 2: Counting digits after the decimal incorrectly

Remember that decimal places mean the number of digits to the right of the decimal point.

For example:

4.5 → 1 decimal place
4.50 → 2 decimal places
4.500 → 3 decimal places

Mistake 3: Rounding before the calculation

Do not unnecessarily round the original values before performing the operation.

Mistake 4: Ignoring the written precision

5.2 and 5.20 have the same numerical value but communicate different decimal-place precision.

Mistake 5: Assuming trailing zeros always mean the same thing

Whole-number trailing zeros can be ambiguous. Use the context or scientific notation when necessary.

Quick Reference: Addition and Subtraction Rule

When adding or subtracting values:

1. Count the decimal places in every value.

2. Find the value with the fewest decimal places.

3. Perform the calculation without unnecessary intermediate rounding.

4. Round the final result to the same decimal place.

Quick example

8.245 + 3.1 + 0.52

Decimal places:

8.245 → 3
3.1 → 1
0.52 → 2

Fewest decimal places = 1

Calculate:

8.245 + 3.1 + 0.52 = 11.865

Round to 1 decimal place:

11.9

Frequently Asked Questions

What is the rule for significant figures in addition?

When adding measured values, round the final result to the same number of decimal places as the value with the fewest decimal places.

What is the rule for significant figures in subtraction?

Subtraction follows the same rule as addition: round the final result to the fewest decimal places present in the values being subtracted.

Do I use significant figures or decimal places for addition?

Use decimal places for addition and subtraction.

Why does addition use decimal places instead of significant figures?

Addition and subtraction depend on the position of the last reported digit. The decimal-place rule prevents the result from implying greater positional precision than the least precise input.

What is 12.11 + 0.3 with significant figures?

First calculate:

12.11 + 0.3 = 12.41

The least precise value has one decimal place, so the final answer is:

12.4

What is 15.67 − 2.4 with significant figures?

Calculate:

15.67 − 2.4 = 13.27

Round to one decimal place:

13.3

Do trailing zeros affect addition and subtraction?

Yes. Written trailing zeros can communicate the decimal-place precision of a value. For example, 5.20 is reported to two decimal places, while 5.2 is reported to one.

Should I round intermediate answers?

Avoid unnecessary intermediate rounding. Retaining additional digits can reduce accumulated rounding error, while the final reported result should follow the applicable precision rule.

What is the difference between addition/subtraction and multiplication/division rules?

Addition and subtraction use the fewest decimal places. Multiplication and division generally use the fewest significant figures.

Can a calculator handle significant figures in addition and subtraction?

A significant figures calculator can help check calculations when its supported functions include arithmetic with significant-figure rules. You can use the Significant Figures Calculator on this site to verify supported calculations.