Rules for Adding Significant Figures

Significant figures show how exact a number is.
When you add numbers in science or math, you must follow special rules. These rules help you decide how many digits to keep in your final answer. This keeps your math honest and your results correct.

This will help you learn the rules for adding and rounding with significant figures.

What Are Significant Figures?

Significant figures are the important digits in a number.
They tell how much we trust the number. The more digits that matter, the more exact the number is.

1. The number 7.2 has 2 significant figures: 7 and 2
2. The number 0.0050 has 2 significant figures: 5 and 0 (the leading zeros do not count)

You must follow special rules when you add numbers with different levels of precision.

What Is the Rule for Adding Significant Figures?

When adding, you round based on decimal places, not the total number of digits.

The number with the fewest digits after the decimal point decides how many to keep in the answer. This is the main rule for adding significant figures.

Rule 1: Match the Decimal Places

When adding, look at the number of digits after the decimal point.
The number with the smallest number of decimal digits controls how many the answer gets.

4.51 + 1.2 = 5.71 → round to 5.7

Why? Because 1.2 has only one decimal place. So your answer can only have one as well.

This is the core of all addition rules for significant figures.

Rule 2: Line Up the Decimal Point

Always line up the decimal points before adding.
This helps you see which digits match and where to round.

3.400 + 2.1 = 5.500 → round to 5.5

You add the full numbers, then round your answer to match the correct place.

Rule 3: Round the Final Answer Only

Never round early. Do all adding first. Then round.

If you round too soon, your final number might be wrong.

5.345 + 4.2 = 9.545 → round to 9.5

Why? Because 4.2 has one digit after the decimal point. Your answer must match that.

This is very important for adding significant figures the right way.

Rule 4: Zeros Can Be Important

Zeros after the decimal point count when they come after real digits.

They show that the number is more exact. If a number ends in 0 but has a decimal point, that 0 is important.

• 2.00 has 3 significant digits (the zero counts)
• 3.20 shows that the number is exact to the hundredths place
• 400 has just 1 significant digit, unless written as 400.

Rule 5: Use Decimal Places, Not Total Digits

When adding, count only the number of decimal digits not the full number of significant figures.

This rule is different from multiplication and division, where total significant digits are used.

Common Mistakes to Avoid

Mistake 1: Rounding before adding
Fix: Add the full numbers, then round

Mistake 2: Using total significant figures to round
Fix: Use only decimal places to decide

Mistake 3: Forgetting that trailing zeros matter
Fix: If there’s a decimal point, those zeros count

More Examples to Practice

Example 1:

• 6.123 + 2.1 = 8.223 → round to 8.2

2.1 has 1 decimal digit. So the answer keeps only 1.

Example 2:

• 5.000 + 1.22 = 6.220 → round to 6.22

Here, 1.22 has 2 digits after the decimal. Keep 2.

Example 3:

• 12.0 + 0.35 = 12.35 → round to 12.4

12.0 has 1 digit after the decimal. Final answer keeps just 1.

Subtraction Follows the Same Rule

Just like with addition, subtraction also uses decimal places to round.

Example:

• 9.50 − 2.1 = 7.40 → round to 7.4

Since 2.1 has 1 decimal place, your answer does too.

Quick Reference Table

Expression	Raw Answer	Rounded Answer	Why?
2.4 + 3.10	5.50	5.5	2.4 has 1 decimal
4.321 + 5.1	9.421	9.4	5.1 has 1 decimal
3.00 + 2.05	5.05	5.05	Keep 2 decimals
7.15 − 1.2	5.95	6.0	Round to 1 decimal
9.456 − 4.33	5.126	5.13	Keep 2 decimal places

People Also Ask

Final Thoughts

If you are in school or doing science homework, you must follow the right rules for adding significant figures. These help you give answers that make sense and match your tools.

Here is what to remember:

• Line up decimal points
• Add all digits fully
• Round only at the end
• Match the decimal places of the shortest number
• Ignore total digits when adding only look at decimals

Use a significant figures calculator if you want help checking your answers.

Written by Paul Meehan, PhD chemistry

References:

1. 3.16: Significant Figures. LibreTexts libraries.
2. Rules for Significant Figures. Columbia University.