# 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:

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

**Random error:**these produce readings both above and below the actual value and are always present.**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:

- On separate graphs, graph each of the data sets. Be sure to annotate the graphs completely.
- 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/cm
^{3} - Using a petri dish and ruler, draw four 'dart boards' on your paper.
- By placing dots on the 'dart boards' to represent darts, create patterns to show the four combinations of low and high precision and accuracy.