PerCent 2007-09-19 14:43:05 2007-09-20 10:23:24 Definition fraction percentage point per cent number base value per cent value % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions \usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here \theoremstyle{definition} \newtheorem*{thmplain}{Theorem} \PMlinkescapeword{mean} The \PMlinkescapetext{word} {\em per cent} may be in general interpreted to mean a `hundredth'. So e.g. 5 per cent is `5 hundredths', i.e. $\frac{5}{100}$. In practice, giving some number of per cents, one means so many hundredths of a quantity given in the same \PMlinkescapetext{sentence} or being clear from the context; for example, we can say that the illiteracy in the world is about 20 per cent -- meaning that 20/100 of the adults of the world cannot read. If we say that the interest (rate) of a loan is 8 per cent, it means that one must pay interest for the loan 8/100 of the amount of the loan in a year. If a percentage of a quantity has changed e.g. from 12\% to 15\%, we must not say that it has grown 3\% but that it has grown 3 {\em percentage points}.\\ \textbf{Determination of percentage} How many percent a number $a$ is of a second number $b$? The answer, the {\em per cent number} $p$, is obtained from \begin{align} p = \frac{a}{b}\cdot 100. \end{align} The number $b$ here is called the {\em base value} and $a$ the {\em per cent value}(?). Essentially, the procedure in (1) may be replaced by converting the ratio $\frac{a}{b}$ to hundredths, which can be done formally by multiplying this ratio by\, $1 = \frac{100}{100} = 100\%$: $$\frac{a}{b} = \frac{a}{b}\cdot 100\,\%.$$