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The word 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 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 percentage points.
Determination of percentage
How many percent a number $a$ is of a second number $b$ ? The answer, the per cent number $p$ , is obtained from
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(1) |
The number $b$ here is called the base value and $a$ the 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 $1 = \frac{100}{100} = 100\%$ : $$\frac{a}{b} = \frac{a}{b}\cdot 100\,\%.$$
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