Title 1.1.1-Orders-of-Magnitude-and-significant-figures.pdf ✅

Topic 1 - Measurements and Uncertainties Orders of magnitude In physics, we deal with a wide range of magnitudes. We use tiny values such as the mass of an electron and huge ones such as the mass of the observable universe. To easily understand the magnitude of these quantities, we need a way to express them in a simple form. To do this, we simply write them to the nearest power of ten (rounding up or down as appropriate). That is, instead of writing a number such as 10000, we write 104 . Orders of magnitude are used to get an idea of the scale and differences in scale between values. It is not an accurate representation of a value. For example, if we take 300, it’s order of magnitude is 102 , which when we calculate it gives 10 x 10 = 100. Although this is three times less than the actual value, the point of orders of magnitude is to get a sense of the scale of the number (‘ball park’), in this case we know the number is within the 100’s. The ranges of magnitudes of quantities that occur in the Universe (smallest to largest): Masses: • mass of electron: 10-30 kg • mass of universe: 10+50 kg Distances: • nucleons (protons, neutrons): 10-15 m • size of the visible universe: 10+25m Times: • light to pass across a nucleus: 10-23 s • age of the universe: 10+18 s Ratios of quantities as differences of orders of magnitude: Using orders of magnitude makes it easy to compare quantities. For example, if we want to compare the size of an atom (10-10m) to the size of a single proton (10-15m), we would take the difference between them to obtain the ratio. Here, the difference is of magnitude 105 meaning that an atom is 105 or 100000 times bigger than a proton.