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