Coefficient of runoff represents the fraction of rainfall that is converted into surface runoff. It is a dimensionless value ranging from 0 to 1. A coefficient of 0 indicates that all of the rainfall is infiltrated into the ground and there is no surface runoff, while a coefficient of 1 indicates that none of the rainfall is infiltrated and all of it becomes surface runoff.

Perfectly impervious areas are surfaces that do not allow any infiltration of water into the ground. These areas include paved surfaces, such as roads, sidewalks, and rooftops, where water cannot penetrate through. In such areas, the entire rainfall becomes surface runoff as there is no infiltration. Therefore, the coefficient of runoff for perfectly impervious areas is 1.0.

Let's understand this concept in more detail:

- Coefficient of runoff: It is a ratio of the volume of runoff to the volume of rainfall. It is expressed as a decimal between 0 and 1. A coefficient of 0 means no surface runoff, and a coefficient of 1 means all rainfall becomes surface runoff.

- Impervious areas: These are surfaces that do not allow water to infiltrate. They have a high runoff coefficient because water cannot penetrate through them. Examples of impervious areas include concrete pavements, roofs, and compacted soils.

- Perfectly impervious areas: These are surfaces that are completely impermeable and do not allow any water infiltration. They are typically man-made surfaces such as concrete or asphalt pavements. In these areas, water cannot soak into the ground, and therefore, all the rainfall becomes surface runoff.

- Coefficient of runoff for perfectly impervious areas: Since all the rainfall becomes surface runoff in perfectly impervious areas, the coefficient of runoff is equal to 1.0. This means that for every unit of rainfall, one unit of runoff is generated.

In summary, the coefficient of runoff for perfectly impervious areas is 1.0 because all the rainfall becomes surface runoff. This is due to the impermeable nature of these surfaces, which do not allow any water infiltration into the ground.