Referring to the example of the ball point pen, we see that in each case the final digit is somewhat uncertain. In part b, three of the digits were known with certainty and the last was the result of an estimation. In the value 12.46 all four digits have an experimental meaning and are said to be significant figures. Another definition of the term is that significant figures are those digits which have actually been the result of a measurement process; this excludes leading zeroes which serve only to locate a decimal point.
It is through proper use of significant digits that the measurement uncertainty is conveyed. Much more will be said about measurement uncertainty throughout the course. The student is cautioned to always evaluate the measurement device and report the results of the measurement to the number of significant digits that is justified by the measurement process.
Most experiments performed in this course involve more than one measurement; some calculation is made to yield a final result. It is important that these manipulations be done in such a way as to properly represent the uncertainty in the final value. The guiding principle in arithmetic operations involving the results of measurements is that the arithmetic cannot improve or deteriorate the uncertainty of the result. Some of the important rules are summarized below.
Addition and Subtraction - (1) the numbers are arranged in columnar form and the operation performed; (2) the result is rounded back to the column of the first uncertain digit.
9.62 | 2 decimal places | ||||
3.1 | 1 decimal place | ||||
14.216 | 3 decimal places | ||||
26.936 | 26.9 | 1 decimal place |
2.761
5.5 |
= 0.502 0.50 |