How Do You Change Fractions To Decimals

Lesson iv: Converting Percentages, Decimals, and Fractions

/en/percents/percentages-in-real-life/content/

Converting fractions, decimals, and percents

When we talk, nosotros often utilise different words to limited the aforementioned thing. For instance, nosotros could depict the same car as tiny or little or small. All of these words mean the car is not big. Fractions, decimals, and percents are like the words tiny, little, and pocket-sized. They're all merely different ways of expressing parts of a whole.

screenshot of 1/2

In this image, each measuring cup has the aforementioned amount of juice in it. Just nosotros've expressed this amount in three means: as a fraction, as a pct, and every bit a decimal. Since they're expressing the aforementioned amount, we know that 1/ii, l%, and 0.5 are equal to each other. Whatsoever time we encounter i/ii, we'll know information technology can also hateful l% or 0.5.

Sometimes it's useful to convert i kind of number into some other. For example, information technology's much easier to add 1/4 and 0.v if yous turn 0.5 into a fraction. Learning how to convert fractions, decimals, and percents will also help you equally you learn more advanced math.

Fractions and decimals

Every fraction can besides be written as a decimal, and vice versa. You may non practice this very often, but converting decimals and fractions can help you in math. For example, it'due south easier to decrease 1/half-dozen from 0.52 if you plough 1/6 into a decimal first.

Converting a fraction into a decimal

Allow'due south convert a fraction into a decimal. We'll be using a math skill you've already learned: long division. To refresh your retentiveness on this skill, you can review our Long Division lesson.

Click through the slideshow to learn how to convert a fraction into a decimal.

Let's see how nosotros can convert 1/iv into a decimal.
To convert a fraction into a decimal, we'll just dissever the numerator...
To convert a fraction to a decimal, we'll merely carve up the numerator...by the denominator.
In our case, we'll split up 1 by iv.
1 divided by 4 equals 0.
To proceed dividing, nosotros'll add a decimal betoken and a zero after the 1.
Nosotros'll also add a decimal point later the 0 on top.
At present we tin can carve up 10 by 4.
x divided by 4 equals 2.
Now nosotros'll multiply iv by 2.
4 times ii equals 8. So we'll subtract 8 from ten.
10 minus 8 equals 2.
Since ii is greater than 0, nosotros're not finished dividing yet. We'll add another 0 later the decimal signal and bring it downward.
At present we'll divide 20 by 4.
xx divided by 4 equals 5.
Now we'll multiply. four times 5 equals twenty.
When nosotros subtract 20 from 20, we get 0. The 0 ways we're done dividing.
1 divided by four equals 0.25.
And so 1/four is equal to 0.25.

Try This!

Convert each of these fractions into a decimal.

Converting a decimal into a fraction

At present we'll practise it in reverse. Permit's convert a decimal into a fraction.

Click through the slideshow to see how to convert a decimal into a fraction.

We're going to rewrite 0.85 as a fraction. To convert a decimal into a fraction, we'll apply place values.
In decimals, the number immediately to the right of the decimal point is in the tenths place.
The identify to the right of the tenths place is the hundredths identify.
To convert a decimal, first we'll bank check the place value of the last number to the right.
In 0.85, v is in the hundredths place.
This means our decimal is equal to 85 hundredths. 85 hundredths can also be written equally 85/100.
Now nosotros have our fraction. But it's always a good idea to reduce fractions when we tin can—it makes them easier to read.
To reduce, we need to discover the largest number that will go evenly into both 85 and 100.
5 is the largest number that goes evenly into 85 and 100. And then we'll divide both parts of our fraction by 5.
Start nosotros'll dissever the numerator. 85 divided by v equals 17.
Now nosotros'll divide the denominator. 100 divided by 5 equals 20. This ways 85/100 can exist reduced to 17/20.
So 0.85 is equal to 17/20.

Reducing a fraction may seem unnecessary when you're converting a decimal. Merely it's important if you're going to use the fraction in a math problem. If you're adding two fractions, you may even demand to reduce or change both fractions so they have a common denominator.

Endeavour This!

Convert these decimals into fractions. Be certain to reduce each fraction to its simplest form!

Percents and decimals

Knowing how to catechumen percents and decimals will help you calculate things like sales tax and discounts. To larn how, check out our Percentages in Real Life lesson.

Converting a percent into a decimal

Converting a percent into a decimal is surprisingly easy. Information technology only takes a few simple steps.

Click through the slideshow to learn how to convert a percent into a decimal.

We're going to convert 17% into a decimal.
First, nosotros'll have the percent sign...
First, nosotros'll have the percent sign...and turn it into a decimal point.
Next, nosotros'll movement the decimal point ii spaces to the left.
At present nosotros'll motility the decimal point ii spaces to the left.
We've converted our per centum to a decimal. 17% is equal to 0.17.
Let'south look at another example. This time we'll turn 78% into a decimal.
First, nosotros'll replace the percentage sign with a decimal point.
So we'll move the decimal point two spaces to the left.
Then nosotros'll motion the decimal signal two spaces to the left.
78% is equal to 0.78.
Let's look at another example. This time we'll plough eight% into a decimal.
First, we'll supercede the percent sign with a decimal point.
Then, nosotros'll move the decimal point ii spaces to the left.
Then, we'll move the decimal point two spaces to the left.
Notice there is an extra space next to the 8. Nosotros can't just leave an open infinite with nada in information technology. Since zero equals zip, we'll replace the space with zero.
Notice there is an extra space next to the 8. We can't just leave an open up infinite with zero in it. Since zero equals cypher, we'll replace the infinite with zilch.
viii% is equal to .08

Why does this work?

Converting percents into decimals is so piece of cake that you may experience like you've missed something. Only don't worry—it really is that simple! Here's why the method we showed you works.

When we turn a percentage into a decimal, we're really doing two steps. First, nosotros convert our percent into a fraction. Since all percents are out of 100, we but put the per centum over 100, like this:

78% = 78/100

In the second step, we catechumen 78/100 into a decimal. You lot already know this means we'll divide the numerator by the denominator, like this:

78 ÷ 100 = 0.78

So why didn't we testify you lot these steps in the slideshow? Considering you can get the reply without them. You know that all percents are out of 100, and so yous tin can skip making the pct into a fraction. You have to split the per centum by 100 to get a decimal, only at that place's a quick fashion to do that. Only motility the decimal point two spaces to the left! This manner, you tin get the same answer with just one easy stride.

Try This!

Convert these percents into decimals.

Converting a decimal into a percent

Now we'll reverse what you just learned. Let's convert a decimal into a pct.

Click through the slideshow to see how to catechumen a decimal into a percent.

We're going to convert 0.45 into a per centum.
We'll reverse what we did in the last section. This fourth dimension, we'll move the decimal point two places to the correct.
Nosotros'll reverse what we did in the last section. This time, we'll motility the decimal point ii places to the correct.
Now we'll replace the decimal point with a percent sign.
We've finished converting our decimal into a pct. 0.45 is equal to 45%.
Let's try some other example. This fourth dimension our decimal has three numbers to the right of the decimal point.
But nosotros're however going to move the decimal betoken two spaces to the right.
Merely we're yet going to move the decimal indicate two spaces to the right.
We nonetheless have a number to the right of the decimal bespeak. The number isn't a 0, and then we can't drop it.
Instead, nosotros'll keep the decimal point and add a per centum sign at the end of the number.
So 0.635 is equal to 63.5%.

Endeavour This!

Summate these decimals as percents.

Percents and fractions

Knowing how to write percents as fractions and vice versa can help yous in your everyday life. For example, let's say yous earned a form of 80% on a test. Yous can catechumen 80% into a fraction to find out how many of your answers were correct. When your teacher grades the exam, she may practise the opposite. If a student got 8 out of 10 questions correct, the teacher can convert eight/10 to a percent to give the student a grade.

Converting a percent into a fraction

When you're converting a percentage into a fraction, it helps to remember that percents are ever out of 100. You can practise with percents in our Introduction to Percentages lesson.

Click through the slideshow to learn how to convert a per centum into a fraction.

Nosotros're going to convert xxx% into a fraction.
In Introduction to Percents, you learned that all percents are out of 100. In fact, that'due south what the word percent means.
So any percent is equal to itself over 100. In our example, 30% is equal to 30/100.
Now nosotros've converted 30% into a fraction, merely nosotros still demand to reduce it.
10 is the largest number that goes evenly into 30 and 100. So we tin can divide both parts of the fraction past 10.
We'll divide the numerator of the fraction first. xxx divided by ten equals 3.
Now we'll separate the denominator. 100 divided by x equals 10.
And so xxx% is equal to 3/10.

Endeavor This!

Write these percentages equally fractions. Make sure to reduce each fraction to its simplest form.

Converting a fraction into a percent

Converting a fraction uses two of the skills you but learned: writing a fraction as a decimal, and writing a decimal equally a percent. Allow'due south see how we can utilize these skills to convert a fraction into a percent.

Click through the slideshow to learn how to catechumen a fraction into a percent.

Let's convert iii/half dozen into a percent.
Only like when we converted a fraction into a decimal, we'll divide the numerator by the denominator.
3 divided past half dozen equals 0.5.
We've turned our fraction into a decimal.
Now nosotros'll turn the decimal into a percent by moving the decimal indicate 2 spaces to the correct.
At present we'll turn the decimal into a percent past moving the decimal betoken 2 spaces to the right.
We'll also change the decimal indicate into a percent sign. 0.fifty is equal to 50%.
So 3/6 is equal to 50%.