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 |