bholderness wrote:Hi, I'm doing a design project about space and thought it would be interesting to find out what fraction of the total volume of the earth an average human brain is. I have both figures in cubic meters:

human brain: .0013 cubic meter

earth: 1, 097, 509, 500, 000, 000, 000, 000 cubic meters

due to the gigantic disparity between the two numbers I am unsure how to convert this into a fraction that would make sense to non math people as to the magnitude of it.

Please let me know if you have any ideas. Thanks a lot!

It was for reasons like this that Archimedes invented a notation for expressing large numbers.

In Archimedes' The Sand Reckoner, addressed to Gelon, King of Syracuse, he attempted to count the number of grains of sand required to fill the entire universe. Assuming that one poppy-head would not contain more than 10,000 grains of sand, and that its diameter is not less than 1/40th of a finger's breadth, and assuming that the sphere of the fixed stars, which was to Archimedes the boundary of the universe, was less than 107 times the sphere exactly containing the orbit of the sun as a great circle, he found that the number of grains of sand required to fill the universe turns out to be less than 10 raised to the 63rd power.

In modern notation, this would be written as 1x10^63, or 1.0e63.

Using that notation:

0.0013 mÂ³ = 1.3e-3 (1.3 with the decimal point moved 3 spaces to the left)

1,097,509,500,000,000,000,000 mÂ³ = 1.0975095e+21 (1.0975095 with the decimal point moved 21 spaces to the right)

Now, we can divide these really large numbers:

1.3e-3

-------------------- = 1.184e-24

1.0975095e+21

Now to convert this to a percentage: 1.184e-24 / 100 = 1.184e-26

So, the average brain is 1.184e-26 (or 0.000,000,000,000,000,000,000,000,0184) percent of the size of the earth.

By way of comparison, the total number of atoms in your body is about 1.0e+28. The total number of particles in the universe has been variously estimated at numbers from 1.0e+72 up to 1.0e+87. If the universe were packed solid with neutrons, there would still be only 1.0e+128 particles.

William J. Knight

Health Physicist

Los Alamos National Labs