Measurements

The 7 SI units

Derived Quantities and Units

Note: when the question tells you to present units as SI units, you have to break up derived quantities into the SI units

Instead of memorising what are the SI units of derived physical quantities, this can be done through looking at the following (simpler) equations and deriving the base SI units from there.

An example of how this is done:

 As such, we can repeat this method for the other derived quantities:

Systematic Errors

• An error is systematic if repeating the measurement under the same conditions yields readings with error of same magnitude and sign. 
• Systematic errors has constant deviations of a reading from its true value.
• A reading is is accurate when there are small systematic errors.

Random Errors

• An error is random if repeating the measurement under the same conditions yields readings with error of different magnitude and sign.
• Random errors have errors scattered about the mean reading.
• A reading is precise when there are small random errors.

Uncertainty Calculations

Uncertainties attributed to measuring instruments are taken to half the smallest graduation.

A = (Aavg ± ∆A) [SI Units]

Uncertainties are always quoted to 1s.f.
And correspondingly the number of decimal places for the value Aavg follow that of ∆A the uncertainty
For working in such questions express all answers in intermediate steps to 3 additional decimal places more than usual so that there will not be rounding errors in your final answer

Calculating ∆A:

• Note:

 gives you percentage uncertainty