Significant figures are a way to show how precise a measurement is. Knowing which digits are “significant” helps us avoid pretending our measurements are more accurate than they really are.

What are Significant Figures?

Significant figures (often called “sig figs”) are the digits in a measurement that carry meaning and contribute to its precision. They include all the digits you are certain of, plus one estimated digit.

For example, if you measure a length as 5.2 cm with a ruler, the ‘5’ is certain, and the ‘2’ is your best estimate between the marks. Both are significant. If you then measure it with a more precise tool as 5.23 cm, the ‘3’ becomes the estimated digit, and you have more significant figures.

Rules for Counting Significant Figures

Here are the main rules to determine which digits in a number are significant:

  1. Non-zero digits are always significant.
    • Example: 23.45 has 4 significant figures.
  2. Zeros between non-zero digits are significant (called “sandwich zeros”).
    • Example: 1005 has 4 significant figures.
  3. Leading zeros (zeros before non-zero digits) are NOT significant. They are just placeholders.
    • Example: 0.0025 has 2 significant figures. (The zeros before ‘2’ are not significant).
  4. Trailing zeros (zeros at the end of the number):
    • Significant if the number contains a decimal point.
      • Example: 1200. has 4 significant figures.
      • Example: 2.00 has 3 significant figures.
    • NOT significant if the number does NOT contain a decimal point.
      • Example: 1200 has 2 significant figures. (The zeros are just placeholders).

Interactive: Identify Significant Figures

Click on the boxes below the digits you think are significant. Then, click “Check Answer” to see how you did!

Interactive Match: Significant Figures

Test your understanding of the key terms and rules for significant figures.

Click a term and then its matching meaning. Match all pairs to complete!

At its core, the reason we use significant figures is to show the uncertainty of a measurement. The last significant digit is always the one you are estimating, and it tells us exactly how precise the tool was.

For example, a measurement of $12.3 \text{ cm}$ (with 3 sig figs) suggests your ruler was precise to about $0.1 \text{ cm}$. The last digit, the 3, is the one you estimated. It’s really a quick way to say the measurement is $12.3 \pm 0.1 \text{ cm}$. .

Using significant figures is a common shortcut for reporting uncertainty in science.

Audio Explanation

Prefer to listen? Here's a quick audio summary of significant figures rules.

💡 Quick Concept Check:

How many significant figures are in the measurement 0.004050 meters?

Click to Reveal Answer
There are four significant figures. The leading zeros (0.00) are not significant. The '4' and '5' are significant. The zero between '4' and '5' is a sandwich zero, so it's significant. The trailing zero after '5' is significant because there's a decimal point in the number.

Ready to apply your understanding of significant figures? Check out these related skills:

Practice Problems

Test your understanding with these problems:

↑ Back to top