Question

The gradient of a road is its slope expressed as percent. What is the slope of a road with a $7\% $ gradient?

Answer 1

Hint: Here to do this question, first we should understand what is the meaning of percent. Its mean is divided by hundred. Here the slope is given in percentage and we have to find it in the fraction format because the value of slope is always a real number.

Complete step-by-step answer:
In the above question, first we should understand the meaning of slope.
The slope of a road or a line is an indication of its steepness. We express slope as gradient in the form of percentage.
“percent” means “out of $100$” or “per $100$” .Therefore, x% can be written as $\dfrac{x}{{100}}$.
Therefore, the slope of a road is given as a $7\% $ gradient.
Therefore, $7\% = \dfrac{7}{{100}}$
The slope is therefore: $m = \dfrac{7}{{100}}$.
Also, we can find slope by comparing the vertical change against the horizontal change., often expressed as $\dfrac{{rise}}{{run}}$.
Therefore, we can say that if the gradient is given as $7\% $, which means the same as $\dfrac{7}{{100}}$, it would mean a rise of only $7$units along a run of $100$.

Note: We can also find the slope using a graph. We just have to find the value of the tangent of a curve at that point. Also, if we know the value of angle which the tangent is making with the positive x-axis, we can find the value of slope using the relation $\tan \theta = m$, where $\theta $ is the angle of inclination and m is the value of slope.