Though this question may seem related to Physics, I think that at the very root this is a mathematical question and so I have posted this on math.stackexchange.
Background: Initially I thought that the terms-unit and dimension, refer to the same thing.
Physical quantities are categorised into fundamental/basic physical quantities and derived physical quantities. A fundamental physical quantity cannot be broken down into simpler physical quantitities, cannot be obtained from other fundamental quantities and all the known physical quantities can be obtained using fundamental quantities. There was a line in my book which stated
Mass, length, time, thermodynamic temperature, electric current, amount of substance, luminous intensity are the seven fundamental quantities and are often called the seven dimensions of the world. Thus the dimension of mass is [M], that of length is [L] and so on. The dimensions of a derived physical quantity are the powers to which the units of the fundamental physical quantities have to be raised in order to represent that derived physical quantity completely.
This is very confusing and I am finding it difficult to understand the difference between the two terms-dimension and unit.
Question: What exactly is the difference between the meaning of the terms unit and dimension?
Best Answer
The difference is quite subtle and of little practical importance if done accordingly.
The difference is that a unit incorporates a property of scale while dimension doesn't. For example in the case of length it could be measured in meters, decimeters or kilometers, but nevertheless the dimension is length.
If you use unit-analysis instead of dimensional analysis you would have to take into account that different units of length only differs by a (dimensionless) constant.