When reporting values that were the result of a measurement or calculated using measured values, it is important to have a way to indicated the certainty of the measurement. This is accomplished through the use of significant figures.
Significant figures are the digits in a value that are known with some degree of confidence. As the resolution of the measuring instrument increases (e.g. more scale graduations on a ruler), so does the number of significant figures and thus the measurement is more certain. Watch the video below to learn more!
Video Summary
Non zero numbers are significant.
Leading zeros are never significant.
Trapped zeros are always significant.
Trailing zeros are significant only if the decimal point is specified.
Hint: Change the number to scientific notation. It is easier to see.
Calculations with Significant Figures
When completing calculations using measurements, the uncertainties in all of your measured quantities should propagate through the calculation. However, the topic of error propagation through calculations is outside the scope of this course. Thus, consider the simpler rules below for determining the approximate number of significant figures in a calculated result.
With Addition and Subtraction, the final result should have the same number of decimal places as the value with the smallest number of decimal places (the least precise number).
With Multiplication and Division, the final result should only have as many significant figures as the term with the least number of significant figures.
The calculator gives 0.013099698. All numbers in the calculation have 3 significant figures, but if you break up the calculation into steps, 1 significant figure is needed.
Exact numbers are known with infinite precision and do not affect the significant figures in a calculation. For example if there are 3 trials performed for a measurement, that number is an exact number. Similarly, physical constants such as the charge of an electron do not affect significant figures.
Practice
Test your understanding by completing the significant figures quiz below. Use the Khan Academy website for extra practice if needed.