# 3.24 Uncertainties

## Uncertainties

• Uncertainties can be represented in a number of ways:
• Absolute Uncertainty: where uncertainty is given as a fixed quantity
• Fractional Uncertainty: where uncertainty is given as a fraction of the measurement
• Percentage Uncertainty: where uncertainty is given as a percentage of the measurement
• Percentage uncertainty is defined by the equation:

Percentage uncertainty = × 100 %

• To find uncertainties in different situations:
• The uncertainty in a reading: ± half the smallest division
• The uncertainty in a measurement: at least ±1 smallest division
• The uncertainty in repeated data (e.g. the mean): half the range i.e. ± ½ (largest - smallest value)
• The uncertainty in digital readings: ± the last significant digit unless otherwise quoted How to calculate absolute, fractional and percentage uncertainty

• Always make sure your absolute or percentage uncertainty is to the same number of significant figures as the reading

#### Combining Uncertainties

• When combining uncertainties, the rules are as follows:

• Add together the absolute uncertainties #### Multiplying / Dividing Data

• Add the percentage or fractional uncertainties #### Raising to a Power

• Multiply the percentage uncertainty by the power #### Exam Tip

Remember:

• Absolute uncertainties have the same units as the quantity
• Percentage uncertainties have no units
• The uncertainty in numbers and constants, such as π, is taken to be zero

In Edexcel International A level, the uncertainty should be stated to at least one few significant figures than the data but no more than the significant figures of the data.

For example, the uncertainty of a value of 12.0 which is calculated to be 1.204 can be stated as 12.0 ± 1.2 or 12.0 ± 1.20. ### Get unlimited access

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