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# Percent

A percentage is a way of expressing a proportion or a fraction as a whole number. A number such as "45%", "45 percent" is actually shorthand for the fraction "45/100". The word percent is also written per cent.

One may thus say, for example,

45 percent of human beings...
and this is equivalent to saying either of
45 out of every 100 people...
0.45 of the human population...

A percentage may be a number larger than 100; for example, 200% is doubling.

The symbol for percent "%" is a stylised form of the two zeros. (In computing, other names for the character include: ITU-T: percent sign; mod; grapes. INTERCAL: double-oh-seven.)

Confusion from the use of percentages Because percentages are always relative to the quantity they affect, several common mistakes arise when using then.

### Changes

For example, an interest rate is given as a percentage like 10%. If this rises to 20%, it is incorrect to say "the interest rate has risen by 10%", because this actually means "risen by 10% of the original 10%", i.e. it is now 11%.

Instead, the expression "percentage points" is often used. So, in the previous example, one can say "the interest rate has increased by 10 percentage points".

### Cancellations

Another common error when using percentages is to imagine that percentage increases and decreases cancel. A 50% increase from 100 is 100 + 50 = 150. A 50% reduction from 150 is 150 - 75 = 75. In general, the net effect is (1+x)(1-x)=1-x2, or a net decrease proportional to the square of the percentage change.

Owners of dot com stocks came to understand that even if a stock has sunk 99%, it can nevertheless still sink another 99%. Also, if a stock rises by a large percentage, you're still broke if the stock subsequently drops 100%.

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