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Chapter 4 - percentage

In mathematics, a percentage (from Latin per centum "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%",[1][2] although the abbreviations "pct.", "pct" and sometimes "pc" are also used.[3] A percentage is a dimensionless number (pure number); it has no unit of measurement.

Examples

For example, 45% (read as "forty-five percent") is equal to the fraction 45/100, the ratio 45:55 (or 45:100 when comparing to the total rather than the other portion), or 0.45. Percentages are often used to express a proportionate part of a total.

(Similarly, one can also express a number as a fraction of 1000, using the term "per mille" or the symbol "‰".)

A pie chart showing the percentage by web browser visiting Wikimedia sites (April 2009 to 2012)

Example 1

If 50% of the total number 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 fraction 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.[4] For example, it is common to refer to 111% or −35%, especially for percent changes and comparisons

In Ancient Rome, long before the existence of the decimal system, 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. Computation 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 15th century to the early 16th century, it became common for arithmetic texts to include such computations. Many of these texts applied these methods to profit and loss, interest rates, and the Rule of Three. By the 17th century, it was standard to quote interest rates in hundredths.

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.[9] In American English, percent is the most common variant[10] (but per mille is written as two words).

In the early 20th century, there was a dotted abbreviation form "per cent.", as opposed to "per cent". The form "per cent." is still in use in 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. The term has been attributed to Latin per centum.[11] 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. In some other languages, the form procent or prosent is used instead. Some languages use both a word derived from percent and an expression in that language meaning the same thing, e.g. Romanian procent and la sută (thus, 10% can be read or sometimes written ten for [each] hundred, similarly with the English one out of ten). Other abbreviations are rarer, but sometimes seen.

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: "Ten percent of all writers love style guides." Decimals are also to be used instead of fractions, as in "3.5 percent of the gain" and not "3+1⁄2 percent of the gain". However the titles of bonds issued by governments and other issuers use the fractional form, e.g. "3+1⁄2% Unsecured Loan Stock 2032 Series 2". (When interest 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 also widely accepted to use the percent symbol (%) in tabular and graphic material.

In line with common English practice, style guides—such as The Chicago Manual of Style—generally state that the number and percent sign are written without any space in between.[12] However, the International System of Units and the ISO 31-0 standard require a space.[13][14]