Question

In metric units, slope is usually expressed as a pure number?

Answer 1

Solution

Yes slope is usually expressed as a pure number. Slope is generally defined as amount of rise or vertical distance traversed per unit horizontal distance moved. It is the ratio of vertical distance to horizontal distance. Since in both numerator and denominator we have same dimensional quantity (i.e. length) their ratio is unitless.(Vertical Length / Horizontal Length = unitless number).

In coordinate system we denote vertical rise(or fall ) as y and horizontal as x. So slope can be denoted as :

For e.g. suppose a body moves in a path such that with every 5m horizontal distance covered its height falls by 10 m.