Percentage Equation if You Know the Discount

Number or ratio expressed equally a fraction of 100

A pie chart showing the per centum by web browser visiting Wikimedia sites (Apr 2009 to 2012)

In mathematics, a percentage (from Latin per centum "past a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percentage sign, "%",^[ane] although the abbreviations "per centum.", "pct" and sometimes "pc" are too used.^[2] A percentage is a dimensionless number (pure number); it has no unit.

Examples

For example, 45% (read equally "twoscore-v percent") is equal to the fraction 45 / 100 , the ratio 45:55 (or 45:100 when comparison to the total rather than the other portion), or 0.45. Percentages are oft used to limited a proportionate part of a total.

(Similarly, one tin can also limited a number every bit a fraction of grand, using the term "per mille" or the symbol "‰".)

Example i

If fifty% of the full number of students in the class are male, that means that 50 out of every 100 students are male. If in that location are 500 students, then 250 of them are male person.

Example two

An increment of $0.15 on a cost of $2.50 is an increase by a fraction of 0.15 / 2.50 = 0.06. Expressed as a percentage, this is a half dozen% increase.

While many percent values are between 0 and 100, there is no mathematical restriction and percentages may take on other values.^[3] For example, it is common to refer to 111% or −35%, particularly for percentage changes and comparisons.

History

In Ancient Rome, long before the existence of the decimal organisation, computations were often made in fractions in the multiples of 1 / 100 . For case, Augustus levied a revenue enhancement of ane / 100 on goods sold at sale known equally centesima rerum venalium. Computation with these fractions was equivalent to calculating percentages.

As denominations of money grew in the Middle Ages, computations with a denominator of 100 became increasingly standard, such that from the late 15th century to the early 16th century, it became common for arithmetics texts to include such computations. Many of these texts practical these methods to turn a profit and loss, interest rates, and the Rule of 3. Past the 17th century, it was standard to quote interest rates in hundredths.^[4]

Percent sign

The term "percent" is derived from the Latin per centum, pregnant "hundred" or "by the hundred".^[5] ^[half-dozen] The sign for "percent" evolved by gradual contraction of the Italian term per cento, pregnant "for a hundred". The "per" was often abbreviated as "p."—eventually disappeared entirely. The "cento" was contracted to ii circles separated by a horizontal line, from which the modernistic "%" symbol is derived.^[7]

Calculations

The per centum value is computed by multiplying the numeric value of the ratio by 100. For example, to find 50 apples every bit a pct of 1250 apples, one first computes the ratio l / 1250 = 0.04, and then multiplies past 100 to obtain four%. The percent value can besides exist found by multiplying first instead of later, so in this case, the 50 would be multiplied by 100 to give v,000, and this result would exist divided by 1250 to give four%.

To calculate a percent of a percent, convert both percentages to fractions of 100, or to decimals, and multiply them. For instance, 50% of 40% is:

fifty / 100 \times 40 / 100 = 0.50 \times 0.40 = 0.xx = 20 / 100 = 20%.

Information technology is not correct to split up by 100 and use the pct sign at the same time; it would literally imply division by 10,000. For example, 25% = 25 / 100 = 0.25, not 25% / 100 , which really is 25⁄100 / 100 = 0.0025. A term such every bit 100 / 100 % would as well be incorrect, since it would be read as 1 pct, even if the intent was to say 100%.

Whenever communicating nigh a percent, it is important to specify what information technology is relative to (i.eastward., what is the full that corresponds to 100%). The post-obit trouble illustrates this indicate.

In a certain higher threescore% of all students are female, and 10% of all students are figurer science majors. If five% of female person students are informatics majors, what percentage of reckoner science majors are female?

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

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

Percentage 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 "x% rise" or a "10% autumn" 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 x% (an increase of $20), the new price will be $220. Note that this final price is 110% of the initial toll (100% + 10% = 110%).

Some other examples of percent changes:

An increment of 100% in a quantity means that the final corporeality is 200% of the initial amount (100% of initial + 100% of increment = 200% of initial). In other words, the quantity has doubled.
An increase of 800% ways the concluding 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% = forty%).
A decrease of 100% ways the final amount is zippo (100% – 100% = 0%).

In general, a alter of $ten$ percent in a quantity results in a final amount that is 100 + $x$ percent of the original amount (equivalently, (one + 0.01 $x$ ) times the original corporeality).

Compounding percentages

Percentage changes applied sequentially do not add upwards in the usual fashion. For example, if the ten% increase in cost considered before (on the $200 item, raising its toll to $220) is followed by a x% decrease in the price (a subtract of $22), and then the final price will be $198—not the original price of $200. The reason for this apparent discrepancy is that the 2 percent changes (+ten% and −10%) are measured relative to different quantities ($200 and $220, respectively), and thus do not "cancel out".

In full general, if an increment of $10$ percent is followed by a subtract of $ten$ percentage, and the initial corporeality was $p$ , the final corporeality is $p$ (1 + 0.01 $x$ )(1 − 0.01 $x$ ) = $p$ (1 − (0.01 $x$ )²); hence the net change is an overall decrease by $x$ percent of $ten$ percent (the foursquare of the original pct change when expressed every bit a decimal number). Thus, in the in a higher place example, after an increase and decrease of $x$ = ten percentage, the concluding corporeality, $198, was 10% of x%, or 1%, less than the initial amount of $200. The net change is the same for a decrease of $x$ percent, followed past an increase of $10$ per centum; the concluding amount is $p$ (1 - 0.01 $ten$ )(1 + 0.01 $x$ ) = $p$ (1 − (0.01 $x$ )ⁱⁱ).

This tin be expanded for a case where one does non take the same percent change. If the initial amount $p$ leads to a percent change $10$ , and the 2nd pct change is $y$ , then the final amount is $p$ (1 + 0.01 $x$ )(i + 0.01 $y$ ). To change the above example, afterwards an increase of $x$ = ten percent and decrease of $y$ = −5 percent, the final amount, $209, is 4.5% more than the initial amount of $200.

As shown above, pct changes can exist applied in any order and have the aforementioned result.

In the case of interest rates, a very common but cryptic way to say that an interest rate rose from 10% per annum to 15% per annum, for example, is to say that the interest rate increased by five%, which could theoretically hateful that it increased from 10% per annum to 10.05% per annum. It is clearer to say that the interest rate increased past 5 percentage points (pp). The same confusion between the dissimilar concepts of percent(age) and percentage points tin potentially cause a major misunderstanding when journalists written report well-nigh ballot results, for example, expressing both new results and differences with earlier results equally percentages. For example, if a party obtains 41% of the vote and this is said to be a ii.5% increase, does that hateful the earlier result was xl% (since 41 = forty × (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) every bit an increase of "100 basis points".

Word and symbol

In British English, percent is usually written as two words (per cent), although per centum and percentile are written as one word.^[8] In American English language, percent is the most common variant^[9] (but per mille is written equally two words).

In the early 20th century, at that place was a dotted abridgement form "per cent.", every bit opposed to "per cent". The form "per cent." is still in use in the highly formal language establish in sure documents like commercial loan agreements (particularly those subject to, or inspired by, common law), likewise equally in the Hansard transcripts of British Parliamentary proceedings. The term has been attributed to Latin pct.^[10] The concept of considering values as parts of a hundred is originally Greek.^{[ citation needed ]} The symbol for percent (%) evolved from a symbol abbreviating the Italian per cento. In some other languages, the form procent or prosent is used instead. Some languages employ both a word derived from percent and an expression in that language significant the same thing, e.g. Romanian procent and la sută (thus, 10% can be read or sometimes written 10 for [each] hundred, similarly with the English 1 out of ten). Other abbreviations are rarer, just sometimes seen.

Grammar and way guides frequently differ equally to how percentages are to be written. For instance, information technology is commonly suggested that the word pct (or per cent) be spelled out in all texts, as in "1 percent" and not "1%". Other guides adopt the word to be written out in humanistic texts, only the symbol to be used in scientific texts. Most guides concur that they always be written with a numeral, as in "5 percent" and non "5 percent", the just exception beingness at the start of a sentence: "Ten percent of all writers beloved fashion guides." Decimals are also to be used instead of fractions, every bit in "three.v percent of the gain" and non "3+ 1⁄2 percent of the gain". However the titles of bonds issued by governments and other issuers apply the fractional grade, e.thousand. "3+ one⁄2 % Unsecured Loan Stock 2032 Series two". (When interest rates are very low, the number 0 is included if the interest charge per unit is less than 1%, eastward.g. "0+ 3⁄four % Treasury Stock", not " 3⁄4 % Treasury Stock".) Information technology is likewise widely accepted to apply the per centum symbol (%) in tabular and graphic fabric.

In line with mutual English practice, style guides—such as The Chicago Manual of Way—generally state that the number and percent sign are written without any space in betwixt.^[11] Even so, the International System of Units and the ISO 31-0 standard require a space.^[12] ^[13]

Other uses

The word "percentage" is often a misnomer in the context of sports statistics, when the referenced number is expressed every bit a decimal proportion, not a percentage: "The Phoenix Suns' Shaquille O'Neal led the NBA with a .609 field goal percentage (FG%) during the 2008–09 flavour." (O'Neal made 60.9% of his shots, not 0.609%.) Likewise, the winning percentage of a team, the fraction of matches that the club has won, is too usually expressed as a decimal proportion; a team that has a .500 winning percentage has won 50% of their matches. The practice is probably related to the like way that batting averages are quoted.

As "percent" it is used to describe the steepness of the slope of a road or railway, formula for which is 100 × rise / run which could also exist expressed every bit the tangent of the angle of inclination times 100. This is the ratio of distances a vehicle would advance vertically and horizontally, respectively, when going upwardly- or downhill, expressed in per centum.

Percentage is too used to express composition of a mixture past mass percent and mole percent.

Visualisation of 1%, ane‰, 1‱, ane pcm and 1 ppm as fractions of the large block (larger version)

Percentage point difference of 1 function in 100
Per mille (‰) 1 part in i,000
Footing point (bp) difference of ane part in 10,000
Permyriad (‱) 1 office in ten,000
Per cent mille (pcm) 1 part in 100,000
Grade (gradient)
Centiturn

Applied applications

Baker percentage
Volume percent

See besides

1000 pct
Relative change and divergence
Percent difference
Percentage change
Parts-per notation
Per-unit system
Percent point function

References

^ "Introduction to Percents". www.mathsisfun.com . Retrieved 28 August 2020.
^ Dakers, Marion (7 Jan 2015). "Eurozone Officially Falls into Deflation, Piling Force per unit area on ECB." The Telegraph. Retrieved 27 Dec 2019.
^ Bennett, Jeffrey; Briggs, William (2005), Using and Agreement Mathematics / A Quantitative Reasoning Arroyo (third ed.), Pearson Addison Wesley, p. 134, ISBN0-321-22773-5
^ Smith, D.E. (1958) [1951]. History of Mathematics. Vol. 2. Courier Dover Publications. pp. 247–249. ISBN0-486-20430-8.
^ American Heritage Dictionary of the English Language, 3rd ed. (1992) Houghton Mifflin
^ "Definition of PERCENT". world wide web.merriam-webster.com . Retrieved 28 August 2020.
^ Smith p. 250
^ Brians, Paul. "Per centum/per cent". Common Errors in English Usage. Washington State University. Retrieved 22 Nov 2010.
^ "Per centum (per cent)". Oxford Dictionaries. Retrieved 22 November 2010.
^ "Percent". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)
^ "The Chicago Transmission of Style". University of Chicago Press. 2003. Retrieved 5 January 2007.
^ "The International System of Units" (PDF). International Bureau of Weights and Measures. 2006. Retrieved 6 August 2007.
^ "ISO 31-0 — Quantities and units – Part 0: General principles". International Organization for Standardization. 22 December 1999. Retrieved 5 Jan 2007.

Look upward pct in Wiktionary, the gratuitous dictionary.

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Source: https://en.wikipedia.org/wiki/Percentage