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