Significant figures are usually the very first topic of the year, which means they get taught fast and then never fully revisited, even though they quietly affect the "correctness" of an answer for the rest of the course.
The counting rules
- All nonzero digits are significant. 342 has three significant figures.
- Zeros between nonzero digits are significant. 4009 has four significant figures.
- Leading zeros are never significant. 0.0025 has two significant figures, the 2 and the 5.
- Trailing zeros after a decimal point are significant. 3.400 has four significant figures.
- Trailing zeros with no decimal point are ambiguous. 1200 could have two, three, or four significant figures depending on how precisely it was measured. Scientific notation removes the ambiguity entirely.
The rules for calculations
Addition and subtraction: match decimal places
The answer can only have as many decimal places as the number in the calculation with the fewest decimal places. Example: 12.11 + 18.0 = 30.1, rounded to one decimal place because 18.0 only has one.
Multiplication and division: match significant figures
The answer can only have as many significant figures as the number in the calculation with the fewest significant figures. Example: 4.56 × 1.4 = 6.4, rounded to two significant figures because 1.4 only has two.
Why this actually matters on the exam
On the AP exam, a numerically correct answer reported with the wrong number of significant figures can lose the point tied to precision, separate from whether the calculation itself was right. It's treated as part of communicating the answer correctly, not just decoration.
Where students actually lose points here
Using the multiplication rule for an addition problem
These two rules genuinely use different criteria, decimal places versus total significant figures, and mixing them up is the single most common sig fig mistake.
Forgetting that counted or exact numbers don't limit sig figs
A number like "3 trials" or a conversion factor defined exactly, such as 100 cm in a meter, is treated as having infinite significant figures and never limits the final answer's precision.
Rounding in the middle of a multi step calculation
Rounding too early compounds small errors through several steps. Carry extra digits through the calculation and round only at the very end.
A small rule with a long reach
Significant figures come back on nearly every numerical answer for the rest of the year, in both Honors and AP Chemistry, which is exactly why getting them automatic early on pays off all year.
Common questions
Do significant figures matter on the AP Chemistry exam?
Yes. A correct calculation reported with the wrong number of significant figures can lose the point tied to precision, separately from whether the math itself was right.
How many significant figures are in the number 100?
As written, it's ambiguous, it could be one, two, or three significant figures depending on how precisely it was measured. Writing it in scientific notation, like 1.00 × 10², removes the ambiguity.
What's the difference between precision and accuracy?
Precision describes how consistent repeated measurements are with each other. Accuracy describes how close a measurement is to the true or accepted value. A set of measurements can be precise without being accurate.