2:29

2:17

2:42

3:39

1:35

In dimensional analysis, a dimensionless quantity is a quantity to which no physical dimension is assigned. It is also known as a bare number or pure number or a quantity of dimension one and the corresponding unit of measurement in the SI is one unit and it is not explicitly shown. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Examples of quantities, to which dimensions are regularly assigned, are length, time, and speed, which are measured in dimensional units, such as metre, second and metre per second. This is considered to aid intuitive understanding. However, especially in mathematical physics, it is often more convenient to drop the assignment of explicit dimensions and express the quantities without dimensions, e.g., addressing the speed of light simply by the dimensionless number 1.

### History

### Pure numbers

### Ratios, proportions, and angles

### Buckingham {{pi}} theorem

### Dimensionless physical constants

### Other quantities produced by nondimensionalization