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)

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)

nechirwan · Answer

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