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 againcentum. Twenty-five cents is 25 parts of a hundred cents (a hundred cents is, of course, equal to one dollar).
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. |
- 6% = six out of a hundred
- 87% = 87 out of a hundred
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.
Express the following amounts as a percentage
|1. 30 items out of 100 |
|2. 85 items out of 100 |
|3. Two items out of a hundred. |
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
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
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:
- Convert the % notation to fraction or decimal form
- Complete the desired math operations using the fraction or decimal forms
- Rewrite the results with % notation
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
Use these Examples & Exercises to check your understanding and build your confidence when converting fraction and decimal notation back to % notation.
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.