What is meant by dimensionless quantity?

A dimensionless quantity is a physical quantity that does not have any associated physical dimensions, such as mass, length, or time, and is expressed as a pure number. These quantities often result from dividing two measurements with the same units, so the units cancel out, leaving no units behind.

Key Features

• No Dimension: Cannot be described in terms of basic physical dimensions like length (L), mass (M), or time (T).
• Unitless or Special Unit: Usually has no unit, but sometimes uses special unit names like radians (for angles) or steradians.
• Examples: Common dimensionless quantities include strain (change in length/original length), coefficients of friction, relative density, and mathematical ratios and percentages.
• Physical Significance: Dimensionless quantities are important in science and engineering, as they simplify equations and reveal underlying relationships independent of the chosen unit system.

Thus, a dimensionless quantity is just a ratio or pure number with no physical units attached—its value remains the same regardless of the measurement system used.