Dimension of a physical quantity is a function that determines the number of times we need to alter the numerical value of physical quantity while passing from one system of units of measurement within the same class.

**Dimensional quantity:**

A dimensional quantity is one whose numerical value is changed upon transition from one system of units of measurement to another system of units of measurement within the same class.

Consider a physical quantity, Force and say in MKS system, the value of force is F = 9N = 9 kgms^{-2}.

We want to make a transition from MKS to CGS units of measurement.

While passing from MKS to CGS units of measurement,

The units of mass is decreased by a factor, M = 1000

The units of length is decreased by a factor, L = 100

The units of time is decreased by a factor, T = 1

We know the dimension of force is [F] = MLT^{-2}.

According to the definition of dimension, the numerical value of force in CGS unit will be

F = 9 x MLT^{-2}g_{m}C_{m}s^{-2}

= 9 x 1000 x100 x 1^{-2} gcms^{-2}

= 9 x 10^{5 }gcms^{-2}

So, in transition from MKS to CGS units- the numerical value of force is increased by a factor MLT^{-2}

And the unit of force is decreased by a factor MLT^{-2}.

So, force is a dimensional quantity with dimension [MLT^{-2}]