388 percentage

Pentagram

into two parts of ratio equal to the golden mean, and

point Bdivides length AC in the same manner. This, of

course, happens on all sides of the star. Also, the

lengths AF, DF, AE, and DE are all equal, making

AFDE a rhombus.

If the distance from Ato Dis 1, then:

The distance of the center of the pentagram to

point C is and to the point Eis

. The height of the pentagram is

.

percentage A number that represents a fraction of

100 is called a percentage. For example, 5 percent,

written 5%, is the fraction , and 125 percent is the

fraction . The term percent comes from the Latin

phrase per centum, meaning “by the hundred.” It is said

that the Roman Emperor Augustus (63

B

.

C

.

E

.–14

C

.

E

.)

levied a tax of one part per 100 on the proceeds of

all goods sold at auctions and markets. Since then it

has been popular to represent all taxes in terms of

percentages.

Any fraction can be converted to a percentage by

multiplying by 100. For example, the fraction is

interpreted as “four-fifths of 100” and so is written:

×100 = = 80 percent. Decimals can also be

represented as percentages by multiplying by 100:

0.327, for example, as a percentage equals 0.327 ×100

= 32.7 percent.

To convert a percentage back to a fraction or a deci-

mal, divide by 100 and omit the percentage sign. For

example, 85 percent represents “85 parts of 100” and so

is the fraction 85/100 or, equivalently, the decimal 0.85.

One hundred percent of a quantity is 100/100 of it,

that is, all of it. For example, if 23 students are

enrolled in a dance and all 23 appear on a particular

day, then 100 percent of the class is present. If only 20

appear, then only the fraction 20/23 ≈0.87 of the class

is present, that is, 87 percent.

A percentage value larger than 100 percent repre-

sents a quantity larger than the original whole. For

example, if the Boys Soccer Group sold 1,850 choco-

late bars in 2002, and 1,998 chocolate bars in 2003,

then the number of bars sold in 2003 compared

with the number sold the previous year is = 1.08

or 108 percent. One would call this an 8 percent

increase in chocolate bar sales. In general, if a quan-

tity changes from value ato value b, then the percent-

age increase of the value is given by the formula:

×100 percent.

It is said that the symbol % for percentage likely

evolved from shorthand notations used by 15th-century

Italian clerks for the term per cento. Such abbreviations

included: per 100, P 00 and Pc°, with the c in the final

expression eventually being replaced with a diagonal

line. A 1425 manuscript shows the symbol % in use.

The term permillage is used for parts per thousand

with accompanying symbol: o/oo. For example, a

quantity expressed as 543 o/oo represents 543 parts

per thousand, or the fraction 543/1,000.

percentage error If the

ERROR

or uncertainty in a

measurement of a quantity is expressed as a

PERCENT

-

(b– a)

––

a

1998

––

1850

400

––

5

4

––

5

4

––

5

125

––

100

5

––

100