1. Significant Digits p. 940 – 941 or significant figures or sigfigs or sf

2. Accuracy and precision Accuracy describes the degree to which the result of an experiment or calculation approximates the true value – how correct it is. Precision describes the exactness and repeatability of a value – ie. 10.23 mm is more precise than 10.2 mm. We will make use of a system to ensure the precision of a calculated value reflects the precision of the inputs. The system involves significant figures. What follows are the rules used to determine the number of significant figures in a given value.

3. When digits are significant All non-zero digits are significant. i.e. 562 has three sigfigs, 49 has two sigfigs Any zeros between two non-zero digits are significant. i.e. 4008 has four sigfigs, 106 has three sigfigs Any zeros to the right of both the decimal point and a non-zero digit are significant. i.e. 7.0 has two sigfigs, 1.900 has four sigfigs All digits used in scientific notation are significant. i.e. 4.00 x 10 7 has 3 sigfigs

4. When digits are not significant Note that these two rules are to ensure that precision is maintained when converting units. Any zeros to the right of the decimal point but preceding a non-zero digit are not significant. ie. 0.0019 kg = 1.9 g two sigfigs Any zeros to the right of a non-zero digit are not significant; they are placeholders. ie. 4.72 m = 4720 mm three sigfigs A special case: With the rules above, the measurement 230 cm would need to be written in scientific notation to show three sigfigs. As a shortcut, we use 230. cm to indicate that the zero in this case is significant.

5. Some practice 1.67 2.802 3.4.560 4.5.10 x 10 7 5.0.0031 6.0.087000 7.3070 8.90.

6. Calculations As a general rule, accuracy is maintained through mathematical calculations by ensuring that the final answer has the same number of significant figures as the least precise number used during the calculations. ie. 2.39 x 98 = 230 (3 sf x 2 sf  2 sf)