Question

A very small unit of length is the femtometer (fm). One fm= 10^-15 meters and 2.54 cm = 1
inch. One cubic inch is how many cubic femtometers? (using dimensional analysis)

Answer 1

1 in^3 = (2.54 cm)^3
= (2.54 x 10^-2 m)^3
= 16.387064 x 10^-6 m
= 16.387064 x 10^-6 m

But 1 fm = 10^-15 m
So 1 m = 1 x 10^15 fm

Therefore converting a cubic inch to femtometres,

1 in^3 = (16.387064 x 10^-6 m) x (10^15 fm per m)
=1.6387064 x 10^10 fm