Order of Magnitude

## Order of Magnitude

In performing rough calculations, estimates, or comparisons, we occasionally round off a number to zero significant figures - which is the nearest power of 10. A number rounded to the nearest power of 10 is called an order of magnitude. For example, let's say the average height of a human being is about 1.7 meters (about 5'7"). For the sake of simplicity, let's round off 1.7 meters to the nearest power of 10, which is 100 m (or 1 m). We are not saying that the average height of a person is a mere 1 meter, but rather the average height is closer to 1 meter (or 100 meters) than it is to 10 meters (or 101 meters). Similarly, rounding the height of an ant, which is about 8 x 10-4 meters, to the nearest power of ten results in 10-3 meters. Another way of saying this is that the order of magnitude of the height of an ant is 10-3 meters. Now, if we compare the height of a human being (100 meters) with the height of an ant (10-3 meters), we come up with the ratio human height/ant height = 100/10-3 = 100 - (-3) = 103 = 1000. A human being is roughly 1000 times (or 103 times) taller than an ant. In other words, a human being is 3 orders of magnitude (3 powers of 10) taller than an ant. The table below shows some interesting comparisons.

 Order of Magnitude of some Masses Order of Magnitude of some Lengths MASS grams LENGTH meters electron 10-27 radius of proton 10-15 proton 10-24 radius of atom 10-10 virus 10-16 radius of virus 10-7 amoeba 10-5 radius of amoeba 10-4 raindrop 10-3 height of human being 100 ant 100 radius of earth 107 human being 105 radius of sun 109 pyramid 1013 earth-sun distance 1011 earth 1027 radius of solar system 1013 sun 1033 distance of sun to nearest star 1016 milky way galaxy 1044 radius of milky way galaxy 1021 the Universe 1055 radius of visible Universe 1026