# Physics - Uncertainty

> Source: https://ollybritton.com/notes/a-level/physics/topics/uncertainty/ · Updated: 2020-09-13 · Tags: ankify, year-1, school, physics

# Uncertainty
##### What are the two types of uncertainty??
* Absolute uncertainty
* Percentage uncertainty

##### What is absolute uncertainty??
* A number that gives the range of values for an experiment.
* E.g. $7.3mm \pm 0.2mm$

##### What is percentage uncertainty equal to for a single measurement??
The resolution of the equipment.

##### What is percentage uncertainty equal to for multiple measurements??
The range of values divided by two.

##### What is the percentage uncertainty for $0.65mm, 0.58mm, 0.62mm$??
$\pm 0.3mm$

##### How do you calculate percentage uncertainty??
$$
\frac{\text{Absolute uncertainty}}{\text{Actual value}} \times 100\%
$$

##### How does multiplication by a constant affect percentage uncertainties??
They are left the same.

##### How does multiplication by a constant affect absolute uncertainties??
They are multiplied by the constant.

##### How does addition or subtraction of quantities affect absolute uncertainties??
The uncertainties are added together.

##### How does multiplication or division of quantities affect percentage uncertainties??
The uncertainties are added together.

##### How does raising a value to a power affect percentage uncertainties??
The percentage uncertainty is multiplied by the power.

##### How do you deal with absolute uncertainties after using an operation like $\sin(x)$ or $\ln(x)$??
* Calculate the difference between the two min and max values after being put into the operation.

### 2021-11-09
##### How can you calculate the $\text{percentage uncertainty}$ from the $\text{range}$ and the $\text{mean}$??
$$
\frac{\text{range}}{2\text{percentage uncertainty}}
$$

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