**Uncertainty & Error**

**Uncertainties**

- Experiments involve using laboratory apparatus and taking measurements.
- Almost all measurements have an
**inherent**degree of uncertainty. - Uncertainty is a measure of the
**amount of error**that might be present in the measurements you have taken. - Uncertainty is usually due to errors in experimental design and operation, of which there are two types.

**Systematic errors**

**Source**- Systematic errors occur due to a persistent flaw with equipment or incorrect use of equipment e.g. consistently taking a burette reading from a height (error of parallax) instead of at eye level.

**How to identify**- A systematic error would affect the entire data set so you would get a regular pattern but on analysis the pattern would not be the expected one.
- Systematic errors reduce accuracy.

**How to correct**- Improvements in the experimental technique or by using apparatus with a greater degree of accuracy.
- Measuring
**larger amounts**decreases the uncertainty. For example in a rate of reaction experiment, increasing the length of time between measuring the amount of products formed will reduce the uncertainty.

**Random errors**

**Source**- Random errors occur due to issues over which the scientist has no direct control e.g. changes in room temperature when measuring the effect of heat on the rate of a reaction.

**How to identify**- A random error would usually show up as an anomalous result, which is a data point that does not fit the pattern.
- Random errors reduce reliability.

**How to correct**- Using apparatus with a greater degree of accuracy, increasing the number of measurements taken or taking measurements more carefully.

**Calculating Uncertainty**

**From an Instrument**

- The smallest change that an instrument can measure is called its
**resolution.** - For example a thermometer that has a mark every 0.5°C has a resolution of 0.5°C and this is a
**higher resolution**than a thermometer that has a mark every 1°C. - Uncertainties when mathematically calculated are represented using the symbol ± placed before the uncertainty.
- The uncertainty of an instrument can be calculated using the equation:

#### Uncertainty = Resolution ÷ 2

- For a
**digital instrument**the uncertainty is the value obtained when you divide the last displayed digit by 2. - For example a reading of 8.05g from a balance thus has an uncertainty of 0.052= ±0.025g.
- This means that the true value lies somewhere between 8.025g and 8.075g.

**From a Set of Results**

- Each time you take a measurement there is a level of uncertainty.
- The mean calculated from a set of results also has an implicit level of uncertainty involved.
- The uncertainty in a mean can be calculated using the following equation, where the
**range**is the**difference**between the**largest**value and the**smallest**value:

#### % error = Range ÷ 2

- The larger the value of the range then the greater will be the level of uncertainty as the results are less precise .
- Uncertainties when mathematically calculated are represented using the symbol ± placed before the uncertainty.
- An answer of 10.0 with an uncertainty of ± 0.5 cm
^{3}indicates that the actual “true” value lies somewhere between 9.50 and 10.50 cm^{3}.

**Example**

### Author: Morgan

Morgan’s passion for the Periodic Table begun on his 10th birthday when he received his first Chemistry set. After studying the subject at university he went on to become a fully fledged Chemistry teacher, and now works in an international school in Madrid! In his spare time he helps create our fantastic resources to help you ace your exams.