Significant Figures, Accuracy and Precision

Significant Figures

A calculation based upon measurement is only as accurate as the device that made the measurement.

The degree to which a measurement is accurate is expressed by the number of significant figures used in the numeric result. These are rules for dealing with numbers and calculations based upon measurement:

  1. All digits (1 to 9) are significant.
  2. Zeros between significant digits are always significant. Ex: 103
  3. Trailing zeros are significant only if the number contains a decimal point. Ex: 10.
  4. Leading zeros used to place the decimal point are not significant. Ex: 0.23
  5. Zeros following the decimal are always significant. Ex: 10.00
  6. For multiplication and division: the answer has the same number of sig figs as the lowest measurement's sig figs.
  7. For addition and subtraction: the answer has the same number of decimal places as the measurement with the fewest decimal places.

Accuracy and Precision

Precision is how close the measurements are to each other. This is the reproducibility.

Accuracy is how close the measurement is to the actual value.

Types of Error

  1. Random error: these produce readings both above and below the actual value and are always present.
  2. Systemic error: readings are either all higher or lower than the actual value. Caused by experiment equipment or procedure.
 

Results for Measurement of Pb Density

Data Set A:

Trial Reading
1 11.3
2 11.2
3 11.4
4 11.2

Data Set C:

Trial Reading
1 12.0
2 14.0
3 11.2
4 12.8

Data Set B:

Trial Reading
1 14.1
2 14.2
3 14.2
4 14.4

Data Set D:

Trial Reading
1 14.5
2 12.0
3 14.0
4 12.5

Directions:

  1. On separate graphs, graph each of the data sets. Be sure to annotate the graphs completely.
  2. Above each graph, describe the precision and accuracy as either HIGH or LOW. Example: HIGH precision and LOW accuracy. The actual density of Pb is 11.35 g/cm3
  3. Using a petri dish and ruler, draw four 'dart boards' on your paper.
  4. By placing dots on the 'dart boards' to represent darts, create patterns to show the four combinations of low and high precision and accuracy.