While we also buy some other articles in $kilogram$.

So we can understand that the mass of any article is measured in both $gram$ and $kilogram$ generally.

Similarly we have heard about the speed of the vehicles. The speed of vehicle is also measured in different unit system.

The speed of the vehicles is generally measured in $kmph$.

Sometimes, the speed is measured in $rpm$.

The numerical value of the speed and mass changes as the unit system changes. So we must have an idea of different unit system.

We need to also understand how any quantity can be converted from one unit system to another system.

Let’s first understand different unit systems.

There are generally three systems of unit measurement.

The $MKS$ system of unit measurement is further standardized as $SI$ system with some improvements.

In $SI$ system of unit measurement, the standard units are measured as,

The $CGS$ system of unit measurement is also known as Gaussian system.

In Gaussian system of unit measurement, the standard units are measured as,

In $FPS$ system of unit measurement, the standard units are measured as,

The units are convertible from one system to another system.

Now let’s discuss the conversion of unit from one system to another.

Magnitude of the physical quantity remains invariant in any system of unit but its numerical value changes.

Let’s consider a physical quantity $Q$

Now the quantity $Q$ can be represented in system of units $u_{1}$ and $u_{2}$.

Suppose the numerical value in $u_{1}$ system of unit be $n_{1}$ and $n_{2}$ be in $u_{2}$ system of unit.

Now consider the magnitude of the fundamental quantities be $M_{1}$, $L_{1}$, $T_{1}$ in $u_{1}$ system and $M_{2}$, $L_{2}$, $T_{2}$ in $u_{2}$ system.

The formula for quantity $Q$ in first system of unit can be written as,

And the formula for quantity $Q$ in second system of unit can be written as,

If the numerical value $n_{1}$ in first system is known then we can find numerical value $n_{2}$ in second system.

For instance, let we have to convert the acceleration due to gravity from MKS system to CGS system.

And for this we will put the values of $$[M],[L]&[T]$$ in the expression provided earlier.

So, the acceleration in the CGS system will be given by;

Revision

There are generally three systems of unit measurement.

Magnitude of the physical quantity remains invariant in any system of unit but its numerical value changes. The numerical value will depend upon the system of units.

If the numerical value $n_{1}$ in first system is known then we can find numerical value $n_{2}$ in second system.