Compound uncertainty

Uncertainty of a single measurement

If we know the resolution of a measuring apparatus (e.g. how far apart the lines are on a ruler), we can find the uncertainty using:

\text{uncertainty}=\pm\space\frac{\text{smallest riscv/division|division on the scale}}2

Uncertainty of repeat measurements

To find the uncertainty of a repeat measurement (i.e. multiple tries), you find the mean, and then use the method above to find the uncertainty of a single measurement.

\text{uncertainty}=\pm\space\frac{\text{smallest riscv/division|division on the scale}}2\times2

…which simplifies to:

\text{uncertainty}=\pm\space\text{smallest riscv/division|division on the scale}

Uncertainty of double-sided apparatus

If we have some apparatus where we need to measure something in two places (e.g. measuring ona ruler the start and end point) we double the uncertainty.

Overall percentage uncertainty

If we have a compound measurement which we find using a formula of different measurements (which each have their own uncertainty), we simply add the individual percentage uncertainties together.

flashcards