A physical quantity is measured and the result is expressed as nu where u is the unit used and n is the numerical value. If the result is expressed in various units then
Let us take an example of mass, suppose if a body has a mass of 20Kg (in this 20 is the numerical value and Kg is the unit) so if we decrease the size of the unit, say Kg to gram (g) then the numerical value will be 20,000
∴ 20Kg = 20,000g
If the size of the unit Kg will increase from Kg to quintal, then the numerical value will be 0.2
∴ 20Kg = 0.2 quintal
From this example we can say that if the unit is increases then the numerical value is decreases and if the unit is decreases then the numerical value is increases.
∴ numerical value,
hence proved