Rules guide
Learn which digits count, when zeros are significant, and which rounding rule applies to each kind of calculation.
Use the calculatorEvery non-zero digit is significant. These digits communicate measured precision directly, so you count them whether the number is a whole number, a decimal, or written in scientific notation.
The digits 3, 4, and 7 all count, so 347 has 3 significant figures.
Leading zeros appear before the first non-zero digit. They only locate the decimal point, so they do not add precision to the measurement.
The significant digits are 4, 5, and the final decimal zero, so the count is 3.
Captive zeros are zeros between non-zero digits. They are significant because they are part of the measured value, not just placeholders before or after the number.
Both zeros sit between non-zero digits, so the number has 4 significant figures.
Trailing zeros after a decimal point count because the decimal point makes the written precision explicit. Whole-number trailing zeros without a decimal point are ambiguous.
100 is ambiguous, while 100. makes the decimal point explicit and normally shows 3 significant figures.
2.50 has 3 significant figures because the final zero after the decimal point records measured precision.
Scientific notation separates the measured digits from the power of ten. Count the digits in the coefficient; the exponent changes the size of the number, not its precision.
The coefficient 3.76 has 3 significant figures. The exponent 4 does not add or remove significant figures.
This notation shows that 100 should be read with 3 significant figures.
For addition and subtraction, do not round by the fewest significant figures. Instead, round the final answer to the least precise decimal place among the measured inputs.
12.5 is precise to tenths, while 0.003 is precise to thousandths. The raw result 12.503 is reported as 12.5.
For multiplication and division, count the significant figures in each measured input. The final answer should have the same number of significant figures as the least precise measured input.
2.50 has 3 significant figures and 3.1 has 2. The raw product 7.75 is reported as 7.8.
Counted values and defined constants are exact in many chemistry and physics problems. They usually do not reduce the number of significant figures in the final measured answer.
If you repeat a measurement 3 times, the counted number 3 is exact. The measured values determine the significant figures.
In most lab calculations, keep extra digits while you work. Rounding too early can create a final answer that is less accurate than the measurement supports.
Use the significant-figures rule or decimal-place rule after the arithmetic is complete, unless your class explicitly tells you otherwise.
Most significant-figures mistakes come from treating every zero the same, using the wrong arithmetic rule, or rounding too early. Check the notation first, then check the operation.
The zeros in 0.00450 do not all behave the same. The leading zeros do not count, but the final decimal zero does.
Addition and subtraction use decimal places. Multiplication and division use the fewest significant figures.
