Calculating percentages is useful in all academic fields, but also in everyday life such as calculating a tip for a waiter or waitress or calculating sales or income tax. There are a few ways to calculate a percentage.
100% or More
Percentages always represent a portion of something out of a hundred, where one hundred represents the whole or entirety. Therefore, there is no measurement for percentage, and a percentage can only make sense when there are established parameters for what is the whole and how much one-hundredth is of the whole. Percentages are easier to understand when individual units are defined. For example, three individual people out of a group of one hundred people is three percent of the group or 3/100. The entire group of people or the whole would be represented as one hundred percent or 100/100. Increasing the number value of the percent increases the portion of the whole. That is, 20% is a smaller portion than 50% and 75%. And 100% represents the entire portion or whole. However, not all circ*mstances perfectly present units of a whole that are easily divided into hundredths. Some fractions are less obvious such as 33/50. However, this fraction is still a percentage.
 |
Percentages and Fractions
All percentages are really fractions with the unseen denominator of 100. Additionally, all fractions are percentages or can be represented as a percent. As previously mentioned, even fractions like 33/50 without the denominator of 100 are still percentages and can still be represented out of 100. That is, the denominator 50 is half of 100, so 50 multiplied by 2 is equal to 100. Additionally, the numerator 33 must also be multiplied by 2. Therefore, 33/50 is equal to 66/100 or 66%. However, it isn't always necessary to convert fractions without the denominator of 100 into fractions with the denominator of 100. The fraction 33/50 can be converted into a decimal before being converted into a percentage.
Percentages and Decimals
Decimals are easily converted into percentages because both decimals and percentages are based on the exponent of 10. The denominator of 100 in a fraction can be divided into tenths. In decimals, each movement of the decimal point to the left or right increases or decreases the value of the number by exponents of 10. For example, 0.01 is one-hundredth of a whole because the 1 is positioned in the one-hundredth place. Whereas 0.10 is equal to one-tenth, 1/10, or ten out of a hundred (10/100), because the one is positioned in the tenth place. Therefore, 1.00 represents the whole or 100/100.
Therefore, a decimal can easily be converted into a percentage by simply moving the decimal point over to the right two spaces. For example, 0.3678 becomes 36.78%. As previously mentioned, fractions without denominators of 100 can be converted into decimals to make it easier to convert them into percentages. That is, instead of converting 33/50 into 66/100, the fraction can be inputted into a calculator to convert it into a percent. For example, 33 divided by 50 is equal to 0.66, which can then be converted into a percentage by moving the decimal over to the right two spaces, which gives you 66%.
To unlock this lesson you must be a Study.com Member.
Create your account
Overall, percentages are necessary fractional representations of parts of a whole. A percentage is a ratio, fraction, or portion of a whole which is represented as 100. The word percent comes from the Latin phrase per centum which means "by the hundred" or per one hundred. Percentages can be represented with a numerical value followed by the percent symbol (%). There are three main ways of writing a percentage besides writing it out using words. For example, eighty-seven percent can be represented as 87%.
Percentages can also be represented as fractions of decimals. 87% is equal to 87/100 or 0.87. To convert fractions into percentages, the fraction must be converted so that the denominator is equal to 100, and then the numerator would represent the percent. Additionally, the numerator of the fraction can be divided by the denominator to convert it into a decimal. To convert a decimal into a percentage, the decimal point simply has to be moved over to the right two spaces.
To unlock this lesson you must be a Study.com Member.
Create your account
Video Transcript
What Is a Percent?
Picture a big pizza with your favorite toppings on it. Now, I like pepperoni, so mine has lots of pepperoni slices. Now picture the pizza being sliced into fourths, then eights, then sixteenths. Yum! My stomach's rumbling - is yours? Picture holding a slice of pizza in your hand, and you're holding a percentage of the pizza. So, a percentage, or percent, is a part of a whole. The word has its roots in the Latin language, from the phrase 'per centum,' which literally means 'per hundred.'
What Does It Mean?
We can think of a hundred as a whole, or all of something. A hundred percent of a pizza is the whole pizza. Half a pizza would be 50 percent, or half of a hundred percent. The percentage tells you how much of the whole you have.
If we divided our pizza into 100 little slices, then each slice would represent 1 percent of the pizza. This is another way to visualize percentages. You can take a whole of something and divide it into 100 little pieces and then figure out how many little pieces are in the portion you are interested in. If I wanted a quarter of the pizza, I would see that it would require 25 little slices out of 100, or 25 percent of the pizza.
It is definitely possible to have a percentage that represents more than a whole or more than a hundred of something. What if you had a friend with a very good appetite, and he happened to eat 2 whole pizzas? Let's visualize this. If we divided each pizza into our little 100 slices, how many slices did he eat? Yes, he would have eaten 200 little slices. That sounds like a lot, but your friend has a big appetite, and he's won several eating contests because of it. Anyway, if he ate 200 little slices, then he would have eaten 200 percent of one pizza.
We know that a hundred percent is a whole of something. Percents less than a hundred mean that they are less than a whole. Percents more than a hundred mean that they include a whole of something plus more of the something.
Writing Percentages
There are three ways to write our percentages. We can use the mathematical percentage symbol, or we can write it in either decimal or fraction form. Let's take a look at how we can write 50 percent. Using the percentage symbol, it will look like 50%. The percentage symbol looks like two little zeroes with a slash separating them.
In decimal form, 50 percent is 0.50. In decimal form, 1 is the same as a 100%. In fraction form, 50 percent is 1/2. 1 in this form also means a 100%. If you divide 1 by 2, you will see that you get the decimal form of the fraction, 0.50.
Let's try writing 25 percent in the three different forms. Using the symbol, it's 25%. In decimal form, it is 0.25, and in fraction form, it is 1/4. Can you guess what 1 divided by 4 equals?
Uses
Now that we know how to write percentages, let's talk about where in the real world you will encounter them. The first that I'm sure you are familiar with is in school, when the teacher hands back a graded test. What do you normally see in red? Yes, you see your grade or your test score. Most times, you will either see the percentage symbol or the fraction form. If you did really well on your test, you might see a score of 97% or 97/100 if there were 100 questions and you got 97 of them right.
Another place that you will see percentages is when you go shopping, either at a physical store or online. Many stores will have sales or special discounts that'll save you money. You might see your favorite shirt on sale for a 20% discount. Or, you might even see your favorite shoes on sale for 80% off. Which discount, the 20% or the 80%, will save you more money? That's right, the 80%, because that sale or discount means you only pay 20% of the cost of the shoes, where you would have to pay 80% of the cost of the shirt. The higher the percentage discount, the more you save.
Lesson Summary
To review, percentage literally means 'per hundred;' you can also think of it as part of a whole. 100% is a whole of something. If you had more than a hundred, then you have more than a whole. You have a whole plus something more. If you had less than a hundred, then you only have a piece of the whole. The three ways to write your percentage are with the percentage symbol (%), in decimal form and in fraction form.
Learning Outcomes
After this lesson, you will be able to:
- Define percentage
- Explain what it means to have 100% of something or more or less than 100% of something
- Understand the three ways to write percentages
- Identify real-world examples of when you would find percentages
To unlock this lesson you must be a Study.com Member.
Create your account
