# 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.

Data Set A:

1 11.3
2 11.2
3 11.4
4 11.2

Data Set C:

1 12.0
2 14.0
3 11.2
4 12.8

Data Set B:

1 14.1
2 14.2
3 14.2
4 14.4

Data Set D: