Significant figures are the digits in a measured or calculated value that carry meaningful information about precision. They tell you how carefully a quantity was measured, not just how large it is. For example, 12.30 cm is more precise than 12.3 cm because the final zero shows the measurement was recorded to the hundredths place.
Scientists and engineers use significant figures so that answers do not claim more precision than the measurements allow.
The main idea is that every calculation is limited by the least precise measurement used in it. In multiplication and division, the answer should have the same number of significant figures as the measurement with the fewest significant figures. In addition and subtraction, the answer should be rounded to the same decimal place as the least precise measurement.
Learning these rules helps you report measurements honestly and compare results in labs, engineering, chemistry, physics, and everyday data analysis.
Key Facts
- All nonzero digits are significant, so 12.3 has 3 significant figures.
- Zeros between nonzero digits are significant, so 1002 has 4 significant figures.
- Leading zeros are not significant, so 0.0045 has 2 significant figures.
- Trailing zeros after a decimal point are significant, so 12.30 has 4 significant figures.
- For multiplication and division, the result has the same number of significant figures as the factor with the fewest significant figures.
- For addition and subtraction, the result is rounded to the least precise decimal place, such as 12.30 + 1.4 = 13.7.
Vocabulary
- Significant figure
- A significant figure is a digit in a number that shows reliable information about the precision of a measurement.
- Precision
- Precision describes how closely repeated measurements agree or how finely a measurement is recorded.
- Leading zero
- A leading zero is a zero before the first nonzero digit, and it is used only to locate the decimal point.
- Trailing zero
- A trailing zero is a zero at the end of a number, and it is significant when it appears after a decimal point.
- Rounding
- Rounding is the process of adjusting a number to a chosen place value or number of significant figures.
Common Mistakes to Avoid
- Counting leading zeros as significant is wrong because zeros in numbers like 0.0025 only show the position of the decimal point.
- Dropping a final zero after a decimal is wrong when reporting precision because 12.30 cm and 12.3 cm do not show the same measurement precision.
- Using the multiplication rule for addition is wrong because addition and subtraction depend on decimal places, not total significant figures.
- Rounding too early in a multi-step calculation is wrong because it can create extra rounding error; keep extra digits until the final answer.
Practice Questions
- 1 How many significant figures are in each number: 0.00340, 1200., 1200, and 45.060?
- 2 Calculate 3.42 cm x 2.1 cm and report the answer with the correct number of significant figures.
- 3 A student measures a length as 8.0 cm using a ruler and another student writes the same length as 8 cm. Explain what information is lost in the second measurement.