PERCENTAGE

The expression of a part to a whole in terms of hundredths is known as percentage. The term percent comes from the Latin word centum, meaning "hundred." The word "percent" can loosely be defined as: divided by one hundred. The whole of something, therefore,  is always 100 percent, 100%, or 100 hundredths.

The square shown below is divided into 100 total small squares: 25 of these squares are colored are shade of grey.

The grey colored part of the whole square can be described in several different ways. It can be described as a common fraction: 25/100 -or- 1/4; as a decimal fraction .25; or as a percentage 25%. Similarly, each of the 100 small squares may be described as 1/100, as 0.01, or as 1% of the whole. The whole square is clearly 100% because it is divided into 100 equal parts. It would still be 100%, however, even if it were divided into only four parts, and the colored areas would still constitute 25% of the whole square. Anything can represent a whole: a glass of milk, a football field, 30 children, or an entire population of people.

Computing Percentage

Percentage is closely related to decimal and common fractions. In fact, percentages can be easily changed into both decimal and common fractions, and vice versa. A decimal is changed to a percent by moving the decimal point two places to the right and adding the percentage sign - the equivalent of multiplying by 100. For example, .08 equals 8%. The same procedure is used when there are more than two numbers to the right of the decimal point. For example, .045 becomes 4.5%.

A percent is changed to a decimal fraction by dropping the percent sign and moving the decimal point two places to the left - equivalent to dividing by 100 (the meaning of percent). For example, 80% becomes .80 -or- .8 ; and 6 & 1/2 % becomes 0.065.

To change a common fraction to a percent, it is first changed to a decimal with two decimal places (hundredths), and then the decimal is converted into a percent (per the above). For example, 3/4 = .75 = 75%. To change percent to a common fraction, it is first changed to a decimal. The decimal is then changed to a common fraction and the fraction is reduced to its lowest terms. For example, 25% = .25 = 25/100 = 1/4.

To find a percent of a number, the percent is changed to a decimal and the decimal is multiplied by the number. For example, 25% of 45 is solved by the computation 0.25 x 45 = 11.25.

Technically, in the problem above, the .25 is the rate (the percent), the 45 is the base (the original total quantity, and the 11.25 is the percentage (the answer to the percent problem). The basic equation is:

Rate (percent as a decimal) * Base (original total amount) = Percentage (answer)

Rate * Base = Percentage

... where the asterisk symbol "*" indicates multiplication.


A common percentage problem is when a purchase is made at a store on an item that is discounted at a percent rate.  For example, you enter a store and discover that a TV set that normally sells for $350 is "on sale" for 25% off. You are interested in determining the cost of the TV "on sale" ... the amount you must pay.

Method 1:  Since the discount is 25% you need to find 25% of $350. You convert 25% into a decimal, .25, and then multiply this times 350: .25 x 350 = $87.50. The $87.50 is the percentage ... the amount of discount. To find the actual cost of the TV, you subtract this amount from the normal cost of the TV: 350 - 87.50 = $262.50. This is the current price/cost of the TV.

Method 2: Since the discount is 25% ... that means that the sale price is 75% of the total (100% the full cost minus the 25% discount being allowed is 75%). Finding 75% of $350, you convert the 75% into a decimal and multiply time the 350: .75 x 350 = $262.50. The sale price of the TV is $262.50.


Finding a Percent (What Percent?)

A type of problem which frequently arises is one in which a percent needs to be found. Basically, you have two given numbers ... and want to know how one (as a percent) compares to the other.

A common problem of this type is found in test grading in a school environment. Often test grades are expressed as a percent of correct answers. When tests do not consist of 100 questions, it is necessary to find what percent of the total number of questions were answered correctly. The solution to this problem is a simple division or ratio problem - in which you divide the part by the whole amount.

For example, if a test consists of 25 questions and 21 of the questions were answered correctly, the percentage of correct answers is 84%. This answer is found by first creating a common fraction. The fraction in this problem 21/25 is then changed to a decimal by dividing 21 by 25. The decimal .84 is then changed to the percentage 84%.

Percent = (Numeric Part that is to be compared / Total Amount) * 100


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