The term "percent" (also written as "per cent") is derived from the Latin word "per centum", which means, "by the hundred". Indeed, a [b]percentage[/b] expresses a ratio, which is expressed as a fraction of 100. Mathematically speaking,[br][br][math] \large 1\%=\frac{1}{100},[/math][br][br]that is,[br][br][math] \large 1\%=0,01.[/math][br][br]Using this definition, we can convert percentages to decimal numbers, or vice versa.

Percent is a relative measure. Its importance is always tied to the situation. If the chocolate plate is divided into two, as in Figure 1, then both are quite satisfied. The amount of chocolate is the same for both, although one receives a uniform piece and the other two pieces from the edges. If one person takes their own 50% in the middle of the bed, the other feels that they have received a smaller portion (at least the writer's spouse complains about it regularly).

Percentages are often solved by a formula[br] [br][br][math]\Large p= \dfrac{b}{a} = \dfrac{b}{a}\cdot 100\%.[/math][br][br] [br]The letter [i]b[/i] of the formula refers to the same thing as [i]p[/i], but it is in units. The unit can be, for example, euros, meters, litres. The [i]a[/i] of the formula refers to the original, i.e. what is compared. It is often recognized by its verbal form, because it often has a word "from", "of", or "compared to" in front of it..[br] [br]Equation solving methods with the above formula can easily solve the missing information.

Convert 0,072 and [math]\frac{3}{4}[/math] into percentages.[br][br][b]Solution:[/b] To convert decimal numbers into percentages, we multiply by 100. This principally moves the decimal separator two steps to the right. Therefore,[br][br][math]\large 0,072=0,072\cdot100\%=7,2\%. [/math][br][br]To convert [math]\frac{3}{4}[/math] into a percentage, we first convert the fraction into a decimal number. That is, [math]\frac{3}{4} = 0.75[/math]. Finally, we multiply the decimal number by 100:[br][br][math]\large \frac{3}{4} = 0,75 = 0,75 \cdot 100 \% = 75 \% .[/math]

Convert 42,3% and 0,12% into decimal numbers.[br][br][b]Solution:[/b] To convert percentages into decimal numbers, we divide by 100. This principally moves the decimal separator two steps to the left, so[br][br][math] \large 42,3\% = \frac{42,3}{100} = 0,423 . [/math][br][br]Similarly,[br][br][math] \large 0,12\% = \frac{0,12}{100} = 0,0012 . [/math]