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[parent] per cent (Definition)

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

$\displaystyle p = \frac{a}{b}\cdot 100.$ (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\%$:
$\displaystyle \frac{a}{b} = \frac{a}{b}\cdot 100\,\%.$



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"per cent" is owned by CWoo. [ full author list (2) | owner history (1) ]
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Other names:  percent
Also defines:  percentage point, per cent number, base value, per cent value

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Cross-references: ratio, percentage, clear, number, hundredth
There are 9 references to this entry.

This is version 4 of per cent, born on 2007-09-19, modified 2007-09-20.
Object id is 9947, canonical name is PerCent.
Accessed 1454 times total.

Classification:
AMS MSC00A69 (General :: General and miscellaneous specific topics :: General applied mathematics)
 97D99 (Mathematics education :: Education and instruction in mathematics :: Miscellaneous)

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