Measurement and Significant Figures
When a scientist makes a measurement she uses a measurement device that will allow for a set level of accuracy that depends upon the physical characteristics of the device. For example, look at the ruler being used to make the length measurement below. One can say for sure that the measurement is greater than 11.6 cm, but the second decimal place in the measurement would only be a guess.
The number of significant figures in a measurement represents all the digits that are known for sure PLUS one digit that is a guess. The measurement made above might then be 11.65 cm. But it would still be a valid measurement if someone used this ruler and claimed that the measurement was 11.64 cm. Each of the measurements contains four significant figures.
The College Board expects students who take the AP* Physics exams to understand the role of significant figures in measurement and to be able to determine the number of significant figures in the answers to problems involving the multiplication, division, addition and subtraction of measurements. Since students taking this course are expected to have already taken a chemistry course, wherein the concept of significant figures should have already been covered, the rules below should act as a reminder of how significant figures are used...not as a tutorial. If you want to see more information on significant figures click here to find an entry on Wikipedia.
A quick note regarding significant figures and unit expression...you will notice that attention to significant figures is not always a high priority when computations are done during the presentations for this course. Reasonableness in rounding is the rule when the concept being described is more important than attention to significant figures. In other words, if the presenation is about magnetism, all the work shown will exhibit reasonable rounding in computations but not always strict adherence to the rules of significant figures. Additionally, much of the work done will only show the units in the final answer of the calculation rather than in each step along the way. Again, priority is given to efficiency in learning the concept at hand rather than making the problem look busy with unit notations.
The rules that you should know in this regard are are follows:
1. All non-zero numbers are significant.
2. Zeros within significant digits are always significant. (Ex: 809 has three significant figures)
3. Zeros that are "place-holders" are not significant. (Ex: 0.0082 has two significant figures)
4. Trailing zeros that aren't needed to hold the decimal point are significant. (Ex: 20.00 has four significant figures)
5. When measurements are added or subtracted, the answer can contain no more decimal places than the least accurate measurement. (Ex: 21.47 + 1.1 = 22.6)
6. When measurements are multiplied or divided, the answer can contain no more significant figures than the least accurate measurement. (Ex: 5.156 x 2.3 = 12 because there are only two significant digits in one of the measurements being multiplied)
7. When answers are rounded off it is generally acceptable to round up if the last digit is 5 or greater and round down if the last digit is less than 5. Different sources may site different rules in this regard.
(You might want to print this information and place it in a binder for future reference)