S0.3 Numbers
[A] Order of magnitude
- The order of magnitude of a physical quantity is an estimate to within a power of 10.
- It is useful in assessing whether an effect is important or measurable.
Example
Reveal
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![\[F = \frac{G M m}{r^2} \]](mastermathpng-0.png)

Example
Does your mass affect the trajectory of your snooker ball?
The physics:
![\[F = \frac{G M m}{r^2} \]](mastermathpng-0.png)
The estimates:
your mass M | ∼ | 102 kg |
ball mass m | ∼ | 10-1 kg |
separation r | ∼ | 1 m |
gravitational constant G | ∼ | 10-10 N m2 kg-2 |
The conclusion: F∼10-9 N …which seems negligible
[B] Precision
- The precision claimed for the value of some quantity is expressed in the number of digits (‘significant figures’, ‘sf’) used when it is quoted.
- You must not write down ‘insignificant’ figures.
- Experimental results are usually quoted with an error bound.
Learning Resources
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