1.3.2 Measure the uncertainty in the derived quantity.

1. ADDITION AND SUBTRACTION:
           When performing additions and subtractions we simply need to add together the absolute uncertainties.

Example:

Add the values 1.2 ± 0.1, 12.01 ± 0.01, 7.21 ± 0.01

1.2 + 12.01 + 7.21 = 20.42
0.1 + 0.01 + 0.01 = 0.12
20.42 ± 0.12

2. MULTIPLICATION, DIVISION AND POWERS:
          When performing multiplications and divisions, or, dealing with powers, we simply add together the percentage uncertainties.

Example:

Multiply the values 1.2 ± 0.1, 12.01 ± 0.01

1.2 x 12.01 = 14
0.1 / 1.2 x 100 = 8.33 %
0.01 / 12.01 X 100 = 0.083%
8.33 + 0.083 = 8.413 %

14 ± 8.413 %

3. OTHER FUNCTIONS:
           For other functions, such as trigonometric ones, we calculate the mean, highest and lowest value to determine the uncertainty range. To do this, we calculate a result using the given values as normal, with added error margin and subtracted error margin. We then check the difference between the best value and the ones with added and subtracted error margin and use the largest difference as the error margin in the result.

Example:

Calculate the area of a field if it's length is 12 ± 1 m and width is 7 ± 0.2 m.

Best value for area:
12 x 7 = 84 m²

Highest value for area:
13 x 7.2 = 93.6 m²

Lowest value for area:
11 x 6.8 = 74.8 m²

If we round the values we get an area of:
84 ± 10 m²