If a cube of `1.0` cm length is cut in all the three directions so as to produce eight cubes each of `0.5`cm edge
length which are then further sub-divided into eight cubes of `0.25` cm edge length and so on. How many
successive subdivisions are required to reduce the cube to colloidal dimensions?

Explanation

We find that every division in two equal halves also reduces the size of edge lengths to one half.
In first subdivision 1 cm is reduceds to `0.5 cm = (1)/(2) cm.`
In second subdivision 0.5 cm is reduced to `0.25 cm = (1)/(4) cm = ((1)/(2))^(2) cm`
In n subdivision 1 cm is reduced to `((1)/(2))^(n)`. Size of colloidal particles lies between 1 to 1000 mm.
Thus to make n subdivision required particle size may be attained.
`((1)/(2))^(n) = 100 nm = 100 xx 10^(-9) m = 100 xx 10^(-7) cm.`
n log 2 = 5
`n xx 0.3010 = 5.`
`n = (5)/(0.3010) = 16.61 = 17` subdivisions are required for dimension of 100 nm.