# Percent

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A percentage is a way of expressing a proportion, a ratio or a fraction as a whole number, by using 100 as the denominator. A number such as "45%" ("45 percent" or "45 per cent") is shorthand for the fraction 45/100 or 0.45.

As an illustration,

"45 percent of human beings..."

is equivalent to both of the following:

"45 out of every 100 people..."
"0.45 of the human population..."

The easiest way to think about percentages is to know that a "percent", represented by the symbol %, is simply a number equal to 1/100, or 0.01.

A percentage may be a number larger than 100; for example, 200% of a number refers to twice the number. In fact, this would be a 100% increase, while a 200% increase would give a number three times the original value. Thus one can see the relationship between percent increase and times increase.

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## Confusion from the use of percentages

Many confusions arise from the use of percentages, due to inconsistent usage or misunderstanding of basic arithmetic.

### Changes

Due to inconsistent usage, it is not always clear from the context what a percentage is relative to. When speaking of a "10% rise" or a "10% fall" in a quantity, the usual interpretation is that this is relative to the initial value of that quantity; for example, a 10% increase on an item initially priced at 200\$ is 20\$, giving a new price of 220\$; to many people, any other usage is incorrect.

In the case of interest rates, however, it is a common practice to use the percent change differently: suppose that an initial interest rate is given as a percentage like 10%. Suppose the interest rate rises to 20%. This could be described as a 100% increase, measuring the increase relative to the initial value of the interest rate. However, many people say in practice "The interest rate has risen by 10%," meaning 10% of 100% additional to the initial 10% (giving 20% in total), though it should mean according to the usual interpretation of percentages a 10% increase on the initial 10% (giving 11%).

To counter this confusion, the expression "percentage points" is often used. So, in the previous example, "The interest rate has increased by 10 percentage points" would be an unambiguous expression that the rate is now 20%. Often also, the term "basis points" is used, one basis point being one one hundredth of a percentage point. Thus, the interest rate above increased by 1000 basis points.

### Cancellations

A common error when using percentages is to imagine that a percentage increase is cancelled out when followed by the same percentage decrease. A 50% increase from 100 is 100 + 50, or 150. A 50% reduction from 150 is 150 - 75, or 75. In general, the net effect is:

(1 + x)(1 - x) = 1 - x2

i.e. 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% meaning it has a zero value.

## Word and symbol

In British English, percent is usually written as two words (per cent). In American English, percent is the most common variant. In the early part of the twentieth century, there was a dotted abbreviation form per cent., which came from the original Latin per centum. The concept of considering values as parts of a hundred is originally Greek.

The symbol for percent "%" is a stylised form of the two zeros. It evolved from a symbol similar except for a horizontal line instead of diagonal (c. 1650), which in turn evolved from a symbol representing "P cento" (c. 1425). Traditionally, the symbol follows the number to which it applies.

In Unicode, there is also an "ARABIC PERCENT SIGN" (U+066A), which has the circles replaced by square dots set on edge.

In computing, the percent character is also used for the mod operation in programming languages that derive their syntax from C. In the textual representation of URLs, a % immediately followed by a hexadecimal number denotes the code of a character that cannot be otherwise represented. Names for the percent sign include percent sign; mod; grapes in ITU-T, and the humorous double-oh-seven in INTERCAL.

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