When you add or subtract measurements, significant figures follow a different rule than multiplying or dividing. For adding and subtracting, it’s all about decimal places!

The Rule for Adding and Subtracting

When you add or subtract numbers from measurements, your final answer can only be as exact as the measurement that has the least number of decimal places.

Here’s how to apply it:

  1. Do the Math: First, add or subtract your numbers just like normal. Write down the full answer your calculator gives you (your “raw answer”).
  2. Count Decimal Places in Each Original Number: For each number you started with, count how many digits it has after the decimal point.
  3. Find the Smallest Count: Look at all the counts from Step 2. Which number had the fewest decimal places? This is your “limiting number.”
  4. Round Your Final Answer: Round your raw answer (from Step 1) so it has the same number of decimal places as your “limiting number” (from Step 3).

Example 1: Addition

Problem: Add 5.24 m and 0.003 m.

Solution:

  1. Do the Math: \(5.24 + 0.003 = 5.243\) (raw answer)

  2. Count Decimal Places in Each Original Number:
    • 5.24 has 2 decimal places.
    • 0.003 has 3 decimal places.

  3. Find the Smallest Count: The smallest count is 2 (from 5.24). Our final answer must have 2 decimal places.

  4. Round Your Final Answer: Round 5.243 to 2 decimal places. Final Answer: 5.24 m

Example 2: Subtraction

Problem: Subtract 2.1 kg from 12.567 kg.

Solution:

  1. Do the Math: \(12.567 - 2.1 = 10.467\) (raw answer)

  2. Count Decimal Places in Each Original Number:
    • 12.567 has 3 decimal places.
    • 2.1 has 1 decimal place.

  3. Find the Smallest Count: The smallest count is 1 (from 2.1). Our final answer must have 1 decimal place.

  4. Round Your Final Answer: Round 10.467 to 1 decimal place. Final Answer: 10.5 kg

Why This Rule Matters

This rule makes sure your answer doesn’t look more exact than the numbers you started with. When you add or subtract, your answer can only be as exact as the number that had the fewest decimal places to begin with.

Audio Explanation

Prefer to listen? Here's a quick audio summary of significant figures in addition and subtraction.

💡 Quick Concept Check:

When adding two measurements, one ending in the tenths place (e.g., 15.1) and another ending in the thousandths place (e.g., 0.345), to which decimal place should you round your final answer, and why?

Click to Reveal Answer
You should round your final answer to the tenths place. In addition (and subtraction), the result must be rounded to match the measurement with the fewest decimal places. The tenths place (1 decimal place) is less precise than the thousandths place (3 decimal places).

Ready to apply these rules? Learn the steps and see worked examples on these related skills pages:

Practice Problems

Test your understanding with these problems:

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