### Percent notations

$1\%=\frac{1}{100}=0.01$

$100\%=\frac{100}{100}=1$

$25\%=\frac{25}{100}=\frac{1}{4}=0.25$

$x\%=\frac{x}{100}=0.01x$

With the following abbreviations the formulas for calculating percentages can be written clearly.

- G : Basic value
- p%: Percentage
- p : Percent number
- W : Percent value

$W=\frac{p\cdot G}{100}$

$p\%=\frac{W}{G}$

$p=\frac{100\cdot W}{G}$

$G=\frac{100\cdot W}{p}$

### Slope in percent

The indication of a slope or a gradient in percent indicates how much the altitude changes in relation to the horizontal distance. For example, 10% slope are reached per 100m horizontally 10m vertical. This corresponds to an angle of 5.7 °. The angle is given by arctan (p / 100).