Measurements in physics

The Système International d’Unités (SI) has been used as the preferred language of science and technology across the globe and reflects current best measurement practice.

All physical quantities have units that can be expressed in terms of seven fundamental quantities.

*Not covered in IBDP Physics

• All other quantities have derived units, i.e., combinations of the fundamental units. $\rm E.g.$, The derived unit the newton is $\rm kg~m~s^{-2}$ (using $\rm F = ma$).
• The significant figures recorded for a measurement should reflect the precision. $\rm E.g.$, a measurement of $\rm 1.0~ cm$ is more precise than one of $\rm 1~ cm$. The uncertainty in the first measurement is $\rm\pm 0.1~cm$ and that in the second $\rm\pm 1~cm$.
• The number of significant figures in any answer should reflect the number of significant figures in the given data.
• When data is multiplied or divided the answer should be quoted to the same number of significant figures as the least precise.
• When data is added or subtracted the answer should be quoted to the same number of decimal places as the least precise value.
• The use of standard form makes the precision of a measurement explicit.
• The measurement of $100$ s is ambiguous whereas a value of $\rm 1.0 \times 10^2~s$ has two significant figures and one of $\rm 1.00 \times 10^2~s$ has three significant figures.
• The most common prefixes:
  

  $\rm n~ 10^{-9}$

  $\mu~ 10^{-6}$

  $\rm m~ 10^{-3}$

  $\rm c~ 10^{-2}$

  $\rm k~ 10^3$

  $\rm M~ 10^6$

• When data is multiplied or divided the answer should be quoted to the same number of significant figures as the least precise.
• When data is added or subtracted the answer should be quoted to the same number of decimal places as the least precise value.
• When adding or subtracting measurements the total absolute uncertainty is the sum of the absolute uncertainties.
• When multiplying or dividing measurements the total percentage uncertainty is the sum of the individual percentage uncertainties. The absolute uncertainty can then be calculated from the percentage uncertainty.

Physics deals with the very big and the very small. It is good to have an approximate idea of the size, mass and duration of various quantities and processes. Estimation is a key skill in physics which can be used to check calculations.