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Percent

PERCENTS GREATER THAN 100

WARNING: There are two prerequisites for learning about percents: knowledge of decimals and fractions.
There is a series of questions listed below. In order for you to continue, you should answer yes to all of them. If you are unsure of any of these points, click on the appropriate question for a review.

Can you muliply and divide a decimal by 100? Can you reduce a fraction to lowest terms?
Can you add decimals together? Can you add fractions?
Can you subtract decimals? Can you subtract fractions?
Can you multiply decimals? Can you multiply fractions?
Can you divide decimals? Can you divide fractions?
Can you change a decimal
into a fraction?
Can you change a fraction
into a decimal?
Can you change an improper fraction
into a mixed fraction?
Can you change a mixed fraction
into an improper fraction?




INTRODUCTION TO PERCENTS GREATER THAN 100

So far all of the percents we have seen were less than 100. (percents < 100)
But there is no law that says percents can't be greater than 100 (at least not in most states)
On this page we'll explore percents greater than 100 (percents > 100)

Remember the rectangle diagram from our first page? Well here it is again. Only now it brought its identical twin brother.

In the diagram below you will see two rectangles. Each of these rectangles is identical. Consider only one of them to be the base. It is important for you to remember that we did not double the base, we just printed it twice.


The idea of a percent larger than 100 means we're going to have the entirety of one of the rectangles (100%) plus a portion of the second one.

In this second diagram you'll again see the first rectangle and in the second rectangle 90 of the squares are white and 10 of them are colored red.



Imagine if you will that we are interested in the entire first rectangle (100% of the rectangle) plus only the white squares in its duplicate (90% of the rectangle).
Altogether we care about 190% of the rectangle.

What will soon become clear is that whenever we are taking a percent of a base:





PERCENTS, DECIMALS, & FRACTIONS

Starting with a percent

First of all percents greater than 100 are treated just like any other percent

You still are going to change them into fractions by placing them over a denominator of 100.

To change a percent into a decimal you will still drop the "%" sign and move the decimal point two places to the left.

The only change will be the fraction will now be an improper fraction which you'll change into a mixed fraction, and the decimal will no longer have "0" as its whole number part.

Below you'll see a few examples of changing percents into fractions and decimals

Starting with a fraction


If we started with a mixed fraction we could separate its whole number and fraction parts, then change the fraction part into a decimal by dividing the numerator by the denominator.
Then simply add the whole number part to the decimal.

Now we have two different ways to change our fraction to a percent.
We could multiply its equivalent decimal by 100 (move the decimal point two places to the right)
or
We could change the improper form of the fraction into a ratio of some number over 100. (i.e. a/b = ?/100). To solve this problem multiply the fraction by 100 (i.e. ? = 100 * a/b). That number will be our percent.

Below you'll sere a few examples of changing a fraction into a decimal and a percent.

Starting with a decimal

To change the decimal into a fraction, first separate the whole number and decimal parts (just as you did above). Change the decimal part into a fraction by putting its corresponding whole number over the appropriate power of ten (If the decimal has one decimal place, put it over 10 ; if it has two decimal places, put it over 100, if it has three decimal places, put it over 1000, etc.).
Now reduce this fraction to lowest terms. Once you're finished reintroduce the whole number part to complete your mixed fraction

To change the decimal to a percent, multiply it by 100 (move the decimal two places to the right)

Below you'll see a few examples of changing a decimal into a fraction and a percent.