- Only those physical quantities which have same dimensions can be added and subtracted. This is called principle of homogeneity of dimensions.
- Dimensions can be multiplied and cancelled like normal algebraic methods.
- In mathematical equations, quantities on both sides must always have same dimensions.
- Arguments of special functions like trigonometric, logarithmic and ratio of similar physical quantities are dimensionless.
- Equations are uncertain to the extent of dimensionless quantities.
Example Distance = Speed x Time. In Dimension terms, [L] = [LT-1] x [T]
Since, dimensions can be cancelled like algebra, dimension [T] gets cancelled and the equation becomes [L] = [L].