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In mathematics, a percentage is a way of expressing a number as a fraction of 100 (per cent meaning "per hundred"). Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and It is often denoted using the percent sign, "%". The percent sign ( %) is the symbol used to indicate a Percentage (that the preceding number is divided by one hundred 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. In Dimensional analysis, a dimensionless quantity (or more precisely a quantity with the dimensions of 1) is a Quantity without any Physical units This article is about proportionality the mathematical relation For instance, 111% is 1. 11 and −0. 35% is −0. 0035.

Contents

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. A paradox is a true statement or group of statements that leads to a Contradiction or a situation which defies intuition; or inversely 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 (35 / 100) × 300 = 105.

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, 100% / 1250 = (100 / 1250)% 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:

(50 / 100) × (40 / 100) = 0. 50 × 0. 40 = 0. 20 = 20 / 100 = 20%.

It is not correct to divide by 100 and use the percent sign at the same time. (E. g. 25% = 25 / 100 = 0. 25, not 25% / 100, which is actually (25 / 100) / 100 = 0. 0025. )

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. A ratio is an expression which compares quantities relative to each other 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. Conditional probability is the Probability of some event A, given the occurrence of some other event B.

Here are other examples:

  1. What is 200% of 30?
    Answer: 200% × 30 = (200 / 100) × 30 = 60.
  2. What is 13% of 98?
    Answer: 13% × 98 = (13 / 100) × 98 = 12. 74.
  3. 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.
  4. 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%.
  5. 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:

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. Interest is a fee paid on borrowed capital Assets lent include Money, Shares, Consumer goods through Hire purchase, major assets 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". Percentage points ( pp) are the unit for the arithmetic difference of two Percentages Consider the following hypothetical example in 1980 40 percent 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

Main article: Percent sign

In British English, percent is usually written as two words (per cent, although percentage and percentile are written as one word). The percent sign ( %) is the symbol used to indicate a Percentage (that the preceding number is divided by one hundred British English or UK English ( BrE, BE, en-GB) is the broad term used to distinguish the forms of the English language used in the In American English, percent is the most common variant (but cf. Phonology North American English regional phonology In many ways compared to English English, North American English is conservative in its Phonology. 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. The twentieth century of the Common Era began on ", 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. Hansard is the traditional name for the printed transcripts of Parliamentary debates in the Westminster system of Government. 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. Latin ( lingua Latīna, laˈtiːna is an Italic language, historically spoken in Latium and Ancient Rome. Dog Latin or mock-Latin refers to the creation of a Phrase or Jargon in imitation of Latin, often by directly translating English Italian ( or lingua italiana) is a Romance language spoken by about 63 million people as a First language, primarily in Italy. French ( français,) is a Romance language spoken around the world by 118 million people as a native language and by about 180 to 260 million people The concept of considering values as parts of a hundred is originally Greek. The term ancient Greece refers to the period of Greek history lasting from the Greek Dark Ages ca The symbol for percent (%) evolved from a symbol abbreviating the Italian per cento. The percent sign ( %) is the symbol used to indicate a Percentage (that the preceding number is divided by one hundred

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 Chicago Manual of Style (abbreviated in writing as CMS or CMOS or verbally as Chicago) is a Style guide for American English [1] The International System of Units and the ISO 31-0 standard, on the other hand, require a space. ISO 31-0 is the introductory part of international standard ISO 31 on quantities and units. [2][3]

Related units

External links

References

  1. ^ The Chicago Manual of Style. Percentage points ( pp) are the unit for the arithmetic difference of two Percentages Consider the following hypothetical example in 1980 40 percent A per mil or per mille (also spelled permil, per mill or promille) ( Latin, literally meaning 'for (every thousand' is a tenth A basis point (often denoted as bp or ‱ rarely permyriad) is a unit that is equal to 1/100th of a Percentage point. A per cent mille or pcm is one one-thousandth of a Percent. It can be thought of as a "milli-percent" "Parts-per" notation is used especially in Science and Engineering, to denote Ratios (relative proportions in measured quantities particularly "Parts-per" notation is used especially in Science and Engineering, to denote Ratios (relative proportions in measured quantities particularly "Parts-per" notation is used especially in Science and Engineering, to denote Ratios (relative proportions in measured quantities particularly Baker percentage, sometimes called formula percentage, is a way of indicating the proportion of ingredients when making Bread. In Chemistry, concentration is the measure of how much of a given substance there is mixed with another substance The grade (or gradient or pitch or slope) of any physical feature such as a Hill, Stream, Roof, railroad, or The Chicago Manual of Style (abbreviated in writing as CMS or CMOS or verbally as Chicago) is a Style guide for American English University of Chicago Press (2003). The University of Chicago Press is the largest University press in the United States Retrieved on 2007-01-05. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 1477 - Battle of Nancy: Charles the Bold is killed and Burgundy becomes part of France.
  2. ^ The International System of Units. International Bureau of Weights and Measures (2006). The International Bureau of Weights and Measures ( Bureau international des poids et mesures, in French) is an international Standards organization, one Retrieved on 2007-08-06. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 1538 - Bogotá, Colombia, is founded by Gonzalo Jiménez de Quesada.
  3. ^ Quantities and units – Part 0: General principles. ISO 31-0 is the introductory part of international standard ISO 31 on quantities and units. International Organization for Standardization (1999-12-22). Year 1999 ( MCMXCIX) was a Common year starting on Friday (link will display full 1999 Gregorian calendar) Events 1790 - The Turkish fortress of Izmail is stormed and captured by Suvorov and his Russian armies Retrieved on 2007-01-05. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 1477 - Battle of Nancy: Charles the Bold is killed and Burgundy becomes part of France.

Dictionary

percentage

-noun

  1. The amount, number or rate of something, regarded as part of a total of 100; a part of a whole.
  2. A share of the profits.
  3. (informal) Benefit or advantage.
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