When you multiply or divide measurements, the rules for significant figures are different from adding or subtracting. Here, we focus on the total number of significant figures in your starting numbers.

The Rule for Multiplying and Dividing

When you multiply or divide numbers from measurements, your final answer can only be as exact as your least exact starting number.

Here’s the simple rule:

Your final answer should have the same number of significant figures as the original measurement that had the FEWEST significant figures.

Let’s break it down:

  1. Do the Math: First, multiply or divide your numbers just like normal. Write down the full answer your calculator gives you (your “raw answer”).
  2. Count Sig Figs in Each Original Number: For each number you started with, count how many significant figures it has.
  3. Find the Smallest Count: Look at all the counts from Step 2. Which number had the smallest number of significant figures? This is your “limiting number.”
  4. Round Your Final Answer: Round your raw answer (from Step 1) so it has the same number of significant figures as your “limiting number” (from Step 3).

Examples

Let’s see how this rule works with some examples.

Example 1: Multiplication

Problem: Multiply 2.5 m by 4.15 s.

Solution:

  1. Do the Math: \(2.5 \times 4.15 = 10.375\) (raw answer)

  2. Count Sig Figs in Each Original Number:
    • 2.5 has 2 significant figures.
    • 4.15 has 3 significant figures.

  3. Find the Smallest Count: The smallest count is 2 (from 2.5). This means our final answer must have 2 significant figures.

  4. Round Your Final Answer: Round 10.375 to 2 significant figures. Final Answer: 10. m·s (or $1.0 \times 10^1 \text{ m} \cdot \text{s}$ for extra clarity).

Example 2: Division

Problem: Divide 125.0 g by 5.0 mL.

Solution:

  1. Do the Math: \(\frac{125.0}{5.0} = 25\) (raw answer)

  2. Count Sig Figs in Each Original Number:
    • 125.0 has 4 significant figures.
    • 5.0 has 2 significant figures.

  3. Find the Smallest Count: The smallest count is 2 (from 5.0). Our final answer must have 2 significant figures.

  4. Round Your Final Answer: Round 25 to 2 significant figures. Final Answer: 25 g/mL

Why This Rule Matters

This rule makes sure your answer doesn’t look more exact than the numbers you started with. You can’t magically get more precision just by multiplying or dividing! Your answer should always reflect the precision of your least precise starting measurement.

Audio Explanation

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

💡 Quick Concept Check:

When multiplying two measurements, one with 3 significant figures and one with 5 significant figures, how many significant figures should your final answer have, and why?

Click to Reveal Answer
Your final answer should have 3 significant figures. In multiplication (and division), the result must be rounded to match the number of significant figures in the least precise measurement (the one with the fewest significant figures). In this case, 3 is fewer than 5.

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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