# Dictionary Definition

# User Contributed Dictionary

## English

### Alternative spellings

- per cent (UK)

### Etymology

Latin per centum, for every hundred.### Pronunciation

- IPA: //
- (US) SAMPA:/p3r.sEnt/

### Noun

#### Usage notes

- A percentage is often denoted by the character %.
- 50% denotes 50 percent''.

#### Translations

- Afrikaans: persent
- Chinese: 百分之
- Czech: procento
- Danish: procent
- Dutch: procent , percent
- Esperanto: procento, pocento, elcento
- Finnish: prosentti
- French: pour cent
- German: Prozent
- Greek: τοις εκατό (tois ekato), τα εκατό (ta ekato)
- Hebrew: אחוז
- Italian: per cento
- Icelandic: hundraðshluti , prósenta , hundraðstala
- Korean: 퍼센트 (peosenteu)
- Latin: per centum
- Polish: procent
- Portuguese: percento
- Romanian: procent , la sută
- Spanish: por ciento
- Swedish: procent

#### Derived terms

### See also

## French

### Verb

percent- Third-person plural present of percer.

# Extensive Definition

In mathematics, a percentage is
a way of expressing a number as a fraction of 100 (per cent
meaning "per hundred"). It is often denoted using the percent
sign, "%". For example, 45% (read as "forty-five percent") is
equal to 45 / 100, or 0.45.

Percentages are used to express how large one
quantity is relative to another quantity. The first quantity
usually represents a part of, or a change in, the second quantity,
which should be greater than zero. For example, an increase of
$ 0.15 on a price of $ 2.50 is an increase by a
fraction of 0.15 / 2.50 = 0.06. Expressed as a percentage, this is
therefore a 6% increase.

Although percentages are usually used to express
numbers between zero and one, any dimensionless
proportionality can be expressed as a percentage. For instance,
111% is 1.11 and −0.35% is −0.0035.

## Proportions

Percentages are correctly used to express
fractions of the total. For example, 25% means 25 / 100, or one
quarter, of some total.

Percentages larger than 100%, such as 101% and
110%, may be used as a literary paradox to express motivation
and exceeding of expectations. For example, "We expect you to give
110% [of your ability]"; however, there are cases when percentages
over 100 can be meant literally (such as "a family must earn at
least 125% over the poverty line to sponsor a spouse visa").

## Calculations

The fundamental concept to remember when
performing calculations with percentages is that the percent symbol
can be treated as being equivalent to the pure number constant
1/100=0.01. For example, 35% of 300 can be written as .

To find the percentage of a single unit in a
whole of N units, divide 100% by N. For instance, if you have 1250
apples, and you want to find out what percentage of these 1250
apples a single apple represents, provides the answer of
0.08%.

To calculate a percentage of a percentage,
convert both percentages to fractions of 100, or to decimals, and
multiply them. For example, 50% of 40% is: It is not correct to
divide by 100 and use the percent sign at the same time. (E.g. ,
not , which is actually .)

### An example problem

Whenever we talk about a percentage, it is
important to specify what it is relative to, i.e. what the total is
that corresponds to 100%. The following problem illustrates this
point.

- In a certain college 60% of all students are female, and 10% of all students are computer science majors. If 5% of female students are computer science majors, what percentage of computer science majors are female?

We are asked to compute the ratio of female computer science
majors to all computer science majors. We know that 60% of all
students are female, and among these 5% are computer science
majors, so we conclude that (60 / 100) × (5/100) = 3/100 or 3% of
all students are female computer science majors. Dividing this by
the 10% of all students that are computer science majors, we arrive
at the answer: 3% / 10% = 30 / 100 or 30% of all computer science
majors are female.

This example is closely related to the concept of
conditional
probability.

Here are other examples:

- What is 200% of 30?
- Answer: 200% × 30 = (200 / 100) × 30 = 60.

- What is 13% of 98?
- Answer: 13% × 98 = (13 / 100) × 98 = 12.74.

- 60% of all university students are male. There are 2400 male
students. How many students are in the university?
- Answer: 2400 = 60% × X, therefore X = (2400 / (60 / 100)) = 4000.

- There are 300 cats in the village, and 75 of them are black.
What is the percentage of black cats in that village?
- Answer: 75 = X% × 300 = (X / 100) × 300, so X = (75 / 300) × 100 = 25, and therefore X% = 25%.

- The number of students at the university increased to 4620,
compared to last year's 4125, an absolute increase of 495 students.
What is the percentual increase?
- Answer: 495 = X% × 4125 = (X / 100) × 4125, so X = (495 / 4125) × 100 = 12, and therefore X% = 12%.

## Percent increase and decrease

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, if an item is initially priced at $200
and the price rises 10% (an increase of $20), the new price will be
$220. Note that this final price is 110% of the initial price (100%
+ 10% = 110%).

Some other examples of percent changes:

- An increase of 100% in a quantity means that the final amount is 200% of the initial amount (100% of initial + 100% of initial = 200% of initial); in other words, the quantity has doubled.
- An increase of 800% means the final amount is 9 times the original (100% + 800% = 900% = 9 times as large).
- A decrease of 60% means the final amount is 40% of the original (100% − 60% = 40%).
- A decrease of 100% means the final amount is zero (100% − 100% = 0%).

In general, a change of x percent in a quantity
results in a final amount that is 100+x percent of the original
amount (equivalently, 1+0.01x times the original amount).

It is important to understand that percent
changes, as they have been discussed here, do not add in the usual
way. For example, if the 10% increase in price considered earlier
(on the $200 item, raising its price to $220) is followed by a 10%
decrease in the price (a decrease of $22), the final price will be
$198, not the original price of $200.

The reason for the apparent discrepancy is that
the two percent changes (+10% and −10%) are measured relative to
different quantities ($200 and $220, respectively), and thus do not
"cancel out".

In general, if an increase of x percent is
followed by a decrease of x percent, the final amount is
(1+0.01x)(1-0.01x)=1-(0.01x)^2 times the initial amount — thus the
net change is an overall decrease by x percent of x percent (the
square of the original percent change when expressed as a decimal
number).

Thus, in the above example, after an increase and
decrease of x=10 percent, the final amount, $198, was 10% of 10%,
or 1%, less than the initial amount of $200.

In the case of interest
rates, it is a common practice to state the percent change
differently. If an interest rate rises from 10% to 15%, for
example, it is typical to say, "The interest rate increased by 5%"
— rather than by 50%, which would be correct when measured as a
percentage of the initial rate (i.e., from 0.10 to 0.15 is an
increase of 50%). Such ambiguity can be avoided by using the term
"percentage
points". In the previous example, the interest rate "increased
by 5 percentage points" from 10% to 15%. If the rate then drops by
5 percentage points, it will return to the initial rate of 10%, as
expected.

## Word and symbol

In British
English, percent is usually written as two words (per cent,
although percentage and percentile are written as one word). In
American
English, percent is the most common variant (but cf. per mille
written as two words). In EU context the word is always spelled out
in one word percent, despite the fact that they usually prefer
British spelling, which may be an indication that the form is
becoming prevalent in British spelling as well. In the early part
of the twentieth
century, there was a dotted abbreviation form "per cent.", as
opposed to "per cent". The form "per cent." is still in use as a
part of the highly formal language found in certain documents like
commercial loan agreements (particularly those subject to, or
inspired by, common law), as well as in the Hansard transcripts
of British Parliamentary proceedings. While the term has been
attributed to Latin per centum,
this is a pseudo-Latin
construction and the term was likely originally adopted from
Italian
per cento or French
pour cent. The concept of considering values as parts of a hundred
is originally Greek. The
symbol
for percent (%) evolved from a symbol abbreviating the Italian
per cento.

Grammar and style guides often differ as to how
percentages are to be written. For instance, it is commonly
suggested that the word percent (or per cent) be spelled out in all
texts, as in "1 percent" and not "1%." Other guides prefer
the word to be written out in humanistic texts, but the symbol to
be used in scientific texts. Most guides agree that they always be
written with a numeral, as in "5 percent" and not "five
percent," the only exception being at the beginning of a sentence:
"Ninety percent of all writers hate style guides." Decimals are
also to be used instead of fractions, as in "3.5 percent
of the gain" and not "3 ½ percent of the gain." It is also
widely accepted to use the percent symbol (%) in tabular and
graphic material. Variations of practically all of these rules may
be encountered, including in this article; the only really fast
rule is to be consistent. It is important to know what method of
solving the problem you would use.

There is no consensus as to whether a space
should be included between the number and percent sign in English.
Style guides – such as the Chicago
Manual of Style – commonly prescribe to write the number and
percent sign without any space in between. The
International System of Units and the ISO 31-0
standard, on the other hand, require a space.

## Related units

- Percentage point
- Per mille (‰) 1 part in 1,000
- Basis point () 1 part in 10,000
- Per cent mille (pcm) 1 part in 100,000
- Parts per million (ppm)
- Parts per billion (ppb)
- Parts per trillion (ppt)
- Baker percentage
- Concentration
- Grade (slope)

## External links

## References

percent in Belarusian (Tarashkevitsa):
Адсотак

percent in Bulgarian: Процент

percent in Catalan: Percentatge

percent in Chuvash: Процент

percent in Czech: Procento

percent in Danish: Procent

percent in German: Prozent

percent in Estonian: Protsent

percent in Spanish: Porcentaje

percent in Esperanto: Procento

percent in Basque: Ehuneko

percent in French: Pourcentage

percent in Korean: 백분율

percent in Icelandic: Hundraðshluti

percent in Italian: Percentuale

percent in Hebrew: אחוז

percent in Latvian: Procents

percent in Lithuanian: Nuošimtis

percent in Hungarian: Százalék

percent in Dutch: Procent

percent in Japanese: パーセント

percent in Norwegian: Prosent

percent in Norwegian Nynorsk: Prosent

percent in Polish: Procent

percent in Portuguese: Percentagem

percent in Russian: Процент

percent in Simple English: Percent

percent in Slovak: Percento

percent in Slovenian: Odstotek

percent in Finnish: Prosentti

percent in Swedish: Procent

percent in Tamil: விழுக்காடு

percent in Telugu: శాతం

percent in Thai: อัตราร้อยละ

percent in Ukrainian: Відсоток

percent in Yiddish: פראצענט

percent in Chinese: 百分比