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Chapter 7—Percents

7-1 Introducing Percents

What does percent mean?  One clue is the fact that centum is the Latin word for hundred. So when we say "20 percent," we mean 20 per 100, or 20 out of a hundred.

How much is 25 cents? There's that word again—centum. Twenty-five cents is 25 parts of a hundred cents (a hundred cents is, of course, equal to one dollar).

 Definitions Values expressed as a percentage are being expressed in "parts  per hundred."  Notation for Percents

Percents (parts per 100) are most  often marked with a  percent sign  %.

 For example, if 40 out of a hundred cars are colored white, you can say that 40 percent (written as 40%) of cars are painted white.More Examples 6% = six out of a hundred 87% = 87 out of a hundred Definitions Values that are expressed in percent are labeled with the percent sign, %.

Here are a few everyday examples of  expressing parts-per-hundred with the percent sign: Percentages are part of everyday living.

Examples:

Express the following amounts as a percentage

 1.  30 items out of 100 Ans: 30% 2. 85 items out of 100Ans: 85% 3.  Two items out of a hundred. Ans: 2%

Percents can also be expressed as fractions -- a percentage value placed over 100.

For example, 12% can  be  expressed as 12/100

30 items out of 100 can be expressed as the ratio, 30/100
85 items out of 100 can be expressed as the ratio, 85/100
Two items out of a hundred can be expressed as the ratio, 2/100
92 parts per hundred can be shown  as 92/100

So, writing a percentage as a ratio (fraction) is a simple matter of showing the number of  items over 100

 Procedure Any percentage  value can be rewritten as a ratio by placing that value over 100

Percents can be expresses in decimal form -- a percentage value times 0.01.

For example, 12% can  be  expressed as 12 x 0.01

30 items out of 100 can be expressed as 30 x 0.01
85 items out of 100 can be expressed as 85 x 0.01
Two items out of a hundred can be expressed as 2 x 0.01
92 parts per hundred can be shown  as 92 x 0.01

Examples & Exercises

 Percent Notation These Examples & Exercises help you master the  three basic forms of notation for percentages.

Adjusting Fraction and Decimal Values to % Notation

Most arithmetic operations with percentages are best done using the fraction or decimal forms. Generally speaking, the procedure goes like this:

1. Convert the % notation to fraction or decimal form
2. Complete the desired math operations using the fraction or decimal forms
3. Rewrite the results with % notation
 Note It isn't unusual to display values in one form of notation, but do some math with them in a different form ... and then convert the results back to the customary display notation.

Examples & Exercises

 Percent Notation Use these Examples & Exercises to check your understanding  and build your confidence when converting fraction and decimal  notation back to % notation.

Thinking Mathematically

You have seen how you can rewrite some value divided by 100 directly to % notation. Very generally speaking, this is given by:

 n = n% 100

But what if need to  rewrite a fraction with % notation, but the denominator isn't 100? Simply this: Adjust the fraction so that the denominator is 100.

Example:

Problem: Rewrite 15/50 with % notation.

Solution: Multiply both the numerator and denominator by a value that forces the denominator to 100. That value would be 2 in this example:

 15 x 2 = 30 =30 50 2 100

15/50 = 30%

 Important It is necessary to multiply the numerator and denominator by the same exact value. This leaves the actual value of the ratio intact.

Examples & Exercises

 Fraction to % Notation Use these Examples & Exercises to check your understanding  of how to convert any fraction to the equivalent % notation.

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