if gain is a dimensional quantity(just a ratio), why it is expressed in decibels sometimes?

Answer 1

You mean 'dimensionless'.
It's expressed in dB to simplify a lot of calculations, especially gain through several stages. You don't have to multiply out the gain of each stage times all the others, just add up the dB gain of each stage and that's the total, end-to-end' gain of the system in db.

Doug

Answer 2

The decibel (dB) is a logarithmic unit of measurement that expresses the magnitude of a physical quantity (usually power) relative to a specified or implied reference level.

Its logarithmic nature allows very large or very small ratios to be represented by a convenient number, Being essentially a ratio, it is a dimensionless unit in A SIMILAR MANNER TO SCIENTIFIC NOTATION. Decibels are useful for a wide variety of measurements in acoustics, physics, electronics and other disciplines.

The number 1000 is represented as K ( kilo) and 1/1000 is represented as m ( milli ). These are not units and only tell the ratio of some quantity to one unit of the same quantity.

A kilo meter is written as 1 km, where k is a ratio and meter is a unit.