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In mathematics, a percentage ( from Latin per centum “ by a hundred ” ) is a count or ratio expressed as a fraction of 100. It is often denoted using the percentage sign, “ % ”, [ 1 ] although the abbreviations “ percentage. “, “ percentage ” and sometimes “ personal computer ” are besides used. [ 2 ] A share is a dimensionless number ( pure number ) ; it has no unit of measurement of measurement .
Examples
For exemplar, 45 % ( read as “ fortyfive percentage ” ) is equal to the fraction 45/100, the ratio 45:55 ( or 45:100 when comparing to the total rather than the other dowry ), or 0.45. Percentages are often used to express a proportionate function of a total. ( similarly, one can besides express a phone number as a divide of 1000, using the term “ per mille “ or the symbol “ ‰ ”. )
case 1
If 50 % of the entire total of students in the class are male, that means that 50 out of every 100 students are male. If there are 500 students, then 250 of them are male .
example 2
An increase of $ 0.15 on a price of $ 2.50 is an increase by a divide of 0.15/2.50 = 0.06. Expressed as a percentage, this is a 6 % increase. While many percentage values are between 0 and 100, there is no mathematical restriction and percentages may take on other values. [ 3 ] For example, it is coarse to refer to 111 % or −35 %, specially for percentage changes and comparisons .
history
In Ancient Rome, long before the universe of the decimal arrangement, computations were often made in fractions in the multiples of 1/100. For example, Augustus levied a tax of 1/100 on goods sold at auction known as centesima rerum venalium. calculation with these fractions was equivalent to computing percentages. As denominations of money grew in the Middle Ages, computations with a denominator of 100 became increasingly standard, such that from the late fifteenth century to the early sixteenth hundred, it became common for arithmetical text to include such computations. many of these texts applied these methods to profit and loss, matter to rates, and the govern of Three. By the seventeenth hundred, it was standard to quote interest rates in hundredths. [ 4 ]
Percent augury
A percentage sign of the zodiac The term “ percentage ” is derived from the Latin per centum, meaning “ hundred ” or “ by the hundred ”. [ 5 ] [ 6 ] The sign for “ percentage ” evolved by gradual contraction of the italian condition per cento, meaning “ for a hundred ”. The “ per ” was much abbreviated as “ p. ” —eventually disappeared entirely. The “ cento ” was contracted to two circles separated by a horizontal line, from which the mod “ % ” symbol is derived. [ 7 ]
Calculations
The percentage measure is computed by multiplying the numeral value of the proportion by 100. For model, to find 50 apples as a percentage of 1250 apples, one first computes the proportion 50/1250 = 0.04, and then multiplies by 100 to obtain 4 %. The percentage value can besides be found by multiplying foremost alternatively of late, so in this case, the 50 would be multiplied by 100 to give 5,000, and this consequence would be divided by 1250 to give 4 %. To calculate a percentage of a percentage, convert both percentages to fractions of 100, or to decimals, and multiply them. For model, 50 % of 40 % is :

50
/
100
×
40
/
100
= 0.50 × 0.40 = 0.20 =
20
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/
100
= 20 % .
It is not correct to divide by 100 and use the percentage sign at the same clock time ; it would literally imply division by 10,000. For model, 25 % = 25/100 = 0.25, not 25 % /100, which actually is 25⁄100/100 = 0.0025. A term such as 100/100 % would besides be faulty, since it would be read as 1 percentage, even if the intent was to say 100 %. Whenever communicating about a share, it is authoritative to specify what it is relative to ( i.e., what is the full that corresponds to 100 % ). The postdate 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 proportion of female calculator skill majors to all calculator science majors. We know that 60 % of all students are female, and among these 5 % are calculator science majors, so we conclude that 60/100 × 5/100 = 3/100 or 3 % of all students are female computer skill majors. Dividing this by the 10 % of all students that are calculator science majors, we arrive at the answer : 3 % /10 % = 30/100 or 30 % of all computer skill majors are female. This case is closely related to the concept of conditional probability .
percentage increase and decrease
due to inconsistent custom, it is not constantly absolved from the context what a share is relative to. When talk of a “ 10 % raise ” 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 modern price will be $ 220. eminence that this final price is 110 % of the initial price ( 100 % + 10 % = 110 % ). Some other examples of percentage changes :
 An increase of 100% in a quantity means that the final amount is 200% of the initial amount (100% of initial + 100% of increase = 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 percentage in a measure results in a final measure that is 100 + x percentage of the original amount ( equivalently, ( 1 + 0.01 x ) times the original come ) .
Compounding percentages
percentage changes applied consecutive do not add up in the usual way. For example, if the 10 % increase in monetary value considered earlier ( on the $ 200 item, raising its price to $ 220 ) is followed by a 10 % decrease in the price ( a decrease of $ 22 ), then the concluding price will be $ 198— not the master price of $ 200. The cause for this apparent discrepancy is that the two percentage changes ( +10 % and −10 % ) are measured relative to different quantities ( $ 200 and $ 220, respectively ), and therefore do not “ cancel out ”. In general, if an increase of x percentage is followed by a decrease of x percentage, and the initial total was p, the final amount is p ( 1 + 0.01 x ) ( 1 − 0.01 x ) = p ( 1 − ( 0.01 x ) 2 ) ; hence the final change is an overall decrease by x percentage of x percentage ( the feather of the original percentage change when expressed as a decimal number ). thus, in the above exemplar, after an increase and decrease of x = 10 percentage, the concluding come, $ 198, was 10 % of 10 %, or 1 %, less than the initial sum of $ 200. The net change is the same for a decrease of x percentage, followed by an increase of x percentage ; the final sum is p ( 1 – 0.01 x ) ( 1 + 0.01 x ) = p ( 1 − ( 0.01 x ) 2 ). This can be expanded for a font where one does not have the lapp percentage change. If the initial sum p leads to a percentage change x, and the second percentage switch is y, then the final total is p ( 1 + 0.01 x ) ( 1 + 0.01 y ). To change the above case, after an increase of x = 10 percentage and decrease of y = −5 percentage, the final amount, $ 209, is 4.5 % more than the initial measure of $ 200. As shown above, percentage changes can be applied in any order and have the like impression. In the case of interest rates, a identical common but ambiguous way to say that an sake pace rose from 10 % per annum to 15 % per annum, for exercise, is to say that the interest rate increased by 5 %, which could theoretically mean that it increased from 10 % per annum to 10.05 % per annum. It is clearer to say that the interest rate increased by 5 share points ( pp ). The lapp confusion between the different concepts of percentage ( age ) and percentage points can potentially cause a major misinterpretation when journalists report about election results, for example, expressing both newly results and differences with earlier results as percentages. For case, if a party obtains 41 % of the vote and this is said to be a 2.5 % increase, does that mean the earlier solution was 40 % ( since 41 = 40 × ( 1 + 2.5/100 ) ) or 38.5 % ( since 41 = 38.5 + 2.5 ) ? In fiscal markets, it is common to refer to an increase of one percentage point ( e.g. from 3 % per annum to 4 % per annum ) as an addition of “ 100 basis points ” .
Word and symbol
In british English, percent is normally written as two words ( per cent ), although percentage and percentile are written as one word. [ 8 ] In american English, percent is the most coarse version [ 9 ] ( but per mille is written as two words ). In the early on twentieth hundred, there was a dot abbreviation shape “ per cent. “, as opposed to “ per cent “. The shape “ per cent. “ is still in use in the highly formal speech found in certain documents like commercial lend agreements ( particularly those subject to, or inspired by, common jurisprudence ), arsenic well as in the Hansard transcripts of british Parliamentary proceedings. The condition has been attributed to Latin per centum. [ 10 ] The concept of considering values as parts of a hundred is originally greek. [ citation needed ] The symbol for percentage ( % ) evolved from a symbol abbreviating the italian per cento. In some other languages, the form procent or prosent is used alternatively. Some languages use both a bible derived from percent and an formula in that lyric meaning the like thing, e.g. romanian procent and la sută ( therefore, 10% can be read or sometimes written ten for [each] hundred, similarly with the English one out of ten ). other abbreviations are rare, but sometimes seen. grammar and style guides much differ as to how percentages are to be written. For exemplify, it is normally suggested that the password percentage ( or per penny ) be spelled out in all textbook, as in “ 1 percentage ” and not “ 1 % ”. other guides prefer the word to be written out in humanist textbook, but the symbol to be used in scientific text. Most guides agree that they always be written with a numeral, as in “ 5 percentage ” and not “ five percentage ”, the alone exception being at the begin of a prison term : “ Ten percentage of all writers love style guides. ” Decimals are besides to be used alternatively of fractions, as in “ 3.5 percentage of the profit ” and not “ 3+1⁄2 percentage of the profit ”. however the titles of bonds issued by governments and other issuers use the fractional class, e.g. “ 3+1⁄2 % Unsecured Loan Stock 2032 Series 2 ”. ( When pastime rates are very low, the number 0 is included if the interest rate is less than 1 %, e.g. “ 0+3⁄4 % Treasury Stock ”, not “ 3⁄4 % Treasury Stock ”. ) It is besides wide accepted to use the percentage symbol ( % ) in tabular and graphic substantial. In line with common English rehearse, expressive style guides—such as The Chicago Manual of Style —generally state that the number and percentage augury are written without any space in between. [ 11 ] however, the International System of Units and the ISO 310 standard require a space. [ 12 ] [ 13 ]
other uses
The news “ share ” is frequently a misnomer in the context of sports statistics, when the referenced number is expressed as a decimal fraction symmetry, not a percentage : “ The Phoenix Suns ‘ Shaquille O’Neal led the NBA with a .609 field goal share ( FG % ) during the 2008–09 temper. ” ( O’Neal made 60.9 % of his shots, not 0.609 %. ) alike, the winning share of a team, the fraction of matches that the club has won, is besides normally expressed as a decimal proportion ; a team that has a .500 acquire share has won 50 % of their matches. The practice is credibly related to the like way that batting averages are quoted. As “ percentage ” it is used to describe the abruptness of the slope of a road or railway, recipe for which is 100 × rise/run which could besides be expressed as the tangent of the angle of tendency times 100. This is the proportion of distances a vehicle would advance vertically and horizontally, respectively, when going up or downhill, expressed in percentage. percentage is besides used to express composition of a concoction by mass percentage and mole percentage .
Related units
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visual image of 1 %, 1‰, 1‱, 1 pcm and 1 ppm as fractions of the large block