You did the chemistry perfectly. Right setup, right units, right calculator steps. Then your answer came back marked wrong because you wrote 6.384 instead of 6.4. Sound familiar? Significant figures trip up a lot of students, mostly because the rules get taught as a list of exceptions instead of one simple idea. So what are the significant figures rules, and how do you use them without losing points?
The significant figures rules tell you which digits in a measurement are meaningful and how many digits your calculated answer is allowed to keep. All nonzero digits count, zeros between nonzero digits count, leading zeros never count, and trailing zeros count only when there’s a decimal point. When you add or subtract, round to the fewest decimal places. When you multiply or divide, round to the fewest significant figures. Exact numbers like counted objects and defined conversions don’t limit your answer, and you should round only once, at the very end.
Why Do Significant Figures Exist?
Significant figures exist because every measurement has a limit to how precise it can be. Your answer can’t be more precise than the tools you used to get it.
Picture measuring a pencil with a ruler marked in millimeters. You can read the whole millimeters for sure, and then you can estimate one more digit between the marks, maybe 14.36 cm. That last digit is your best guess, and it still counts. Writing 14.3628 cm would be pretending your ruler is something it isn’t.
I find this kind of beautiful. Sig figs are how scientists tell each other “here’s how much you can trust this number” without writing a paragraph about it. A chemist who reads 2.50 g knows the balance was good to the hundredths place. A chemist who reads 2.5 g knows it wasn’t.
Significant Figures Rules for Counting Digits
There are four counting rules, and they’re really about zeros. Every nonzero digit is always significant, so the only real question is what each zero is doing.
- Nonzero digits always count. 4.56 has three sig figs.
- Captive zeros count. Zeros between nonzero digits are significant. 1002 has four.
- Leading zeros never count. Zeros in front just hold the decimal place. 0.0045 has two.
- Trailing zeros count if there’s a decimal point. 3.040 has four, and 25.00 has four.
The messy case is a whole number with trailing zeros and no decimal point, like 2500. Most textbooks treat those zeros as not significant, giving two sig figs, but the number is ambiguous. Scientific notation fixes that. Write 2.5 × 103 for two sig figs, 2.50 × 103 for three or 2.500 × 103 for four. Some courses also accept a trailing decimal point, like “2500.”, to show four.
Quick trick: in scientific notation, every digit in the front number is significant. That’s one reason chemists love it.
How Do You Round When Adding or Subtracting?
When you add or subtract, round your answer to the same number of decimal places as the measurement with the fewest decimal places. You’re lining up the decimal points, and the least precise column wins.
12.11 + 18.0 + 1.013 = 31.123, which rounds to 31.1
The number 18.0 only goes to the tenths place, so the answer can only go to the tenths place. Notice that you don’t count sig figs here at all. 31.1 has three sig figs, even though 12.11 had four. That surprises most people.
Subtraction works the same way, and sometimes the rounded answer ends in a zero you have to keep:
20.42 − 1.322 = 19.098, which rounds to 19.10
Both 20.42 and 19.10 go to the hundredths place. The trailing zero has to stay, because it tells the reader the answer is good to the hundredths.
How Do You Round When Multiplying or Dividing?
When you multiply or divide, round your answer to the same number of significant figures as the measurement with the fewest sig figs. Decimal places don’t matter here. Only the count does.
4.56 × 1.4 = 6.384, which rounds to 6.4
Since 1.4 has two sig figs, the answer gets two. Here’s a division example:
75.0 ÷ 3.1 = 24.19…, which rounds to 24
75.0 has three sig figs and 3.1 has two, so the answer keeps two. This rule covers density, molarity and most stoichiometry, because those problems are chains of multiplication and division. If you’re setting up those chains, my guide to dimensional analysis pairs well with this one.
What about mixed operations?
For a problem that mixes both, follow the order of operations and apply the right rule at each step. Keep extra digits in your calculator, but track how many are significant.
(12.5 − 2.31) × 1.30
First, 12.5 − 2.31 = 10.19. By the subtraction rule, that’s good to the tenths place, so it carries three sig figs (10.2). Then multiply by 1.30, which also has three. The calculator gives 13.247, and the final answer is 13.2.
What Are Exact Numbers?
Exact numbers are values with no uncertainty, so they have unlimited significant figures and never limit your answer. There are two main kinds:
- Counted numbers, like 3 test tubes, 12 eggs or the 2 in front of H2O in a balanced equation
- Defined conversions, like 1 L = 1000 mL, 1 kg = 1000 g or 1 inch = 2.54 cm exactly
So if you convert 0.250 L to milliliters, the answer is 250. mL with three sig figs. The “1000” in the conversion factor doesn’t drag your answer down to one sig fig, because it’s a definition.
Practice Table: Test Yourself on the Significant Figures Rules
Cover the right column and try each one before you check.
| Problem | Answer | Why |
|---|---|---|
| How many sig figs in 0.00450? | 3 | Leading zeros don’t count; the trailing zero after the decimal does |
| How many sig figs in 1002? | 4 | Captive zeros count |
| How many sig figs in 0.0700? | 3 | The 7 and both trailing zeros count |
| How many sig figs in 2.500 × 103? | 4 | Every digit in the front number counts |
| 8.6 + 2.15 | 10.8 | 8.6 goes to the tenths place (10.75 rounds up) |
| 3.0 × 4.123 | 12 | 3.0 has two sig figs (12.369 rounds to 12) |
| 9.80 ÷ 2.0 | 4.9 | 2.0 has two sig figs |
What Mistakes Cost the Most Points?
The most expensive mistake is rounding in the middle of a problem. If you round each step, small errors pile up and your final answer can drift off. Keep everything in the calculator and round once at the end.
Other common slip-ups:
- Using the decimal-place rule for multiplication, or the sig-fig rule for addition
- Dropping a meaningful trailing zero, like writing 19.1 when the answer is 19.10
- Letting exact numbers like 1000 mL/L limit your answer
- Copying every digit the calculator shows
That last one is easy to fall into because calculators happily show ten digits. Knowing your calculator well helps, too, and the guide to choosing a calculator for chemistry class covers the features that matter for gen chem.
For the official version of these rules with more examples, the free OpenStax textbook has a solid section on measurement uncertainty, accuracy and precision. To practice sig figs inside full exam-style calculations, work through our Gen Chem 1 ACS practice exam and check your rounding against each worked solution.
Every Digit Tells the Truth
The significant figures rules come down to honesty about precision. Count nonzero digits, captive zeros and trailing zeros after a decimal point. Use decimal places for adding and subtracting, sig figs for multiplying and dividing, and let exact numbers ride for free. Round once, at the end.
Cover the answers and run through the practice table one more time. If you can do all seven in under two minutes, sig figs are handled, and those lost half-points on exams will start coming back.