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Encyclopedia > Percent

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. In mathematics, a fraction is a quotient of numbers, like 3⁄4, or more generally, an element of a quotient field. ... In algebra, a vulgar fraction consists of one integer divided by a non-zero integer. ...

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.


Confusion from the use of percentages

Many confusions arise from the use of percentages, due to inconsistent usage or misunderstanding of basic arithmetic. Arithmetic or arithmetics (from the Greek word αριθμός = number) in common usage is a branch of (or the forerunner of) mathematics which records elementary properties of certain operations on numerals, though in usage by professional mathematicians, it often is treated as synonym for number theory. ...


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%). An interest rate is the rental price of money. ...

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. Percentage points are the proper unit for the difference of two percentages. ... A basis point (bps) is one hundredth of a percentage point (0. ...


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. Dot-com (also dotcom or redundantly dot. ...

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. British English is a term primarily used by people outside of the UK to refer to the form of the English language spoken in the British Isles. ... American English or U.S. English is the form of the English language used mostly in the United States of America. ... (19th century - 20th century - 21st century - more centuries) Decades: 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s The 20th century lasted from 1901 to 2000 in the Gregorian calendar (often from (1900 to 1999 in common usage). ... Latin is the language originally spoken in the region around Rome called Latium. ...

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. Events June 23 - Claimant King Charles II of England, Scotland and Ireland arrives in Scotland, the only of the three Kingdoms that has accepted him as ruler. ... Events Foundation of the Katholieke Universiteit Leuven, Belgium Births Deaths March 17 - Ashikaga Yoshikazu, Ashikaga shogun July 21 - Manuel II Palaeologus, Byzantine Emperor Categories: 1425 ...

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. Originally, the word computing was synonymous with counting and calculating, and a computer was a person who computes. ... The word modulo is the Latin ablative of modulus. ... A programming language or computer language is a standardized communication technique for expressing instructions to a computer. ... The C Programming Language, Brian Kernighan and Dennis Ritchie, the original edition that served for many years as an informal specification of the language The C programming language is a standardized programming language developed in the early 1970s by Ken Thompson and Dennis Ritchie for use on the UNIX operating... A Uniform Resource Locator, URL (either pronounced as earl (IPA: [ɜː˞l]; SAMPA: [3:`l]) or spelled out), or Web address, is a standardized address for some resource (such as a document or image) on the Internet (or elsewhere). ... In mathematics and computer science, hexadecimal or simply hex is a numeral system with a radix or base of 16 usually written using the symbols 0–9 and A–F or a–f. ... The ITU Telecommunication Standardization Sector (ITU-T) coordinates standards for telecommunications on behalf of the International Telecommunication Union (ITU). ... INTERCAL is a programming language parody, the canonical esoteric programming language. ...

Related units

A permille or per mille is a tenth of a percent or one part per thousand. ... Parts per million (ppm) is a measure of concentration that is used where low levels of concentration are significant. ...

External links

  • Explains the history of the symbol (http://www.roma.unisa.edu.au/07305/symbols.htm)
  • Percentages calculator, practice, and word problems (http://www.algebra.com/calculators/algebra/percentage/)

  Results from FactBites:
Church of the Customer Blog (1778 words)
It assured worried citizens that 99 percent of its members were law-abiding citizens, thereby marginalizing the remaining "1 percent" as outlaws.
One Percenters organize and wear their patches as the proverbial finger raised toward society’s expectations of them.
Furthermore, the One Percenter clubs are organized around the idea of a community, and their unconventional lives and motorcycle lifestyles are reinforced by the strong-as-steel bonds with other members.
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