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 10^{0} 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 10^{0} meters) than it is to 10 meters (or 10^{1} 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 (10^{0} meters) with the height of an ant (10^{-3} meters), we come up with the ratio human height/ant height = 10^{0}/10^{-3} = 10^{0 - (-3)} = 10^{3} = 1000. A human being is roughly 1000 times (or 10^{3} 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 | 10^{0} |
ant | 10^{0} |
radius of earth | 10^{7} |
human being | 10^{5} |
radius of sun | 10^{9} |
pyramid | 10^{13} |
earth-sun distance | 10^{11} |
earth | 10^{27} |
radius of solar system | 10^{13} |
sun | 10^{33} |
distance of sun to nearest star | 10^{16} |
milky way galaxy | 10^{44} |
radius of milky way galaxy | 10^{21} |
the Universe | 10^{55} |
radius of visible Universe | 10^{26} |