Write 1/4 As A Decimal

Lesson 4: Converting Percentages, Decimals, and Fractions

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Converting fractions, decimals, and percents

When we talk, nosotros often use different words to express the same thing. For example, nosotros could describe the same car as tiny or picayune or small-scale. All of these words mean the automobile is non big. Fractions, decimals, and percents are like the words tiny, little, and small. They're all just unlike ways of expressing parts of a whole.

screenshot of 1/2

In this prototype, each measuring cup has the same amount of juice in it. But we've expressed this amount in iii means: as a fraction, as a pct, and as a decimal. Since they're expressing the same amount, we know that 1/two, 50%, and 0.5 are equal to each other. Any time we see 1/2, we'll know it can also mean 50% or 0.five.

Sometimes it's useful to convert one kind of number into another. For instance, it's much easier to add ane/4 and 0.5 if you plow 0.v into a fraction. Learning how to convert fractions, decimals, and percents will also help you equally y'all learn more than advanced math.

Fractions and decimals

Every fraction can also be written equally a decimal, and vice versa. Yous may not do this very often, merely converting decimals and fractions can help yous in math. For instance, it'southward easier to decrease one/half-dozen from 0.52 if you plow 1/vi into a decimal first.

Converting a fraction into a decimal

Let's convert a fraction into a decimal. We'll be using a math skill you've already learned: long partitioning. To refresh your memory on this skill, y'all can review our Long Segmentation lesson.

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

Let's see how we can catechumen 1/4 into a decimal.
To convert a fraction into a decimal, we'll just split up the numerator...
To convert a fraction to a decimal, nosotros'll just dissever the numerator...past the denominator.
In our example, nosotros'll divide i past 4.
i divided by iv equals 0.
To proceed dividing, we'll add a decimal point and a goose egg subsequently the one.
We'll too add a decimal signal after the 0 on acme.
Now we can divide 10 past 4.
ten divided by 4 equals 2.
At present nosotros'll multiply iv by two.
iv times 2 equals 8. And so nosotros'll subtract 8 from x.
10 minus 8 equals 2.
Since 2 is greater than 0, we're not finished dividing however. We'll add another 0 after the decimal point and bring information technology down.
At present we'll divide 20 past 4.
twenty divided past 4 equals 5.
Now we'll multiply. 4 times 5 equals twenty.
When we decrease 20 from 20, we become 0. The 0 ways we're washed dividing.
ane divided by 4 equals 0.25.
And so 1/4 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 do it in opposite. Let's convert a decimal into a fraction.

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

Nosotros're going to rewrite 0.85 as a fraction. To convert a decimal into a fraction, we'll use 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 identify is the hundredths place.
To catechumen a decimal, starting time we'll cheque the place value of the concluding number to the correct.
In 0.85, five is in the hundredths identify.
This means our decimal is equal to 85 hundredths. 85 hundredths can also be written every bit 85/100.
At present we take our fraction. But it'due south always a good idea to reduce fractions when we can—information technology makes them easier to read.
To reduce, we need to observe 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 so nosotros'll divide both parts of our fraction past 5.
First we'll divide the numerator. 85 divided by 5 equals 17.
Now nosotros'll divide the denominator. 100 divided by v equals 20. This means 85/100 can be reduced to 17/20.
So 0.85 is equal to 17/20.

Reducing a fraction may seem unnecessary when you lot're converting a decimal. But it's important if you're going to use the fraction in a math trouble. If you're adding two fractions, you may fifty-fifty need to reduce or change both fractions and then they have a common denominator.

Try This!

Convert these decimals into fractions. Be sure to reduce each fraction to its simplest course!

Percents and decimals

Knowing how to catechumen percents and decimals volition assistance you calculate things like sales taxation and discounts. To larn how, check out our Percentages in Existent Life lesson.

Converting a percent into a decimal

Converting a percent into a decimal is surprisingly piece of cake. It 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.
Get-go, we'll take the percent sign...
Offset, nosotros'll take the pct sign...and turn it into a decimal point.
Next, nosotros'll movement the decimal point two spaces to the left.
Now we'll move the decimal bespeak two spaces to the left.
We've converted our percent to a decimal. 17% is equal to 0.17.
Let's wait at another example. This time we'll plow 78% into a decimal.
First, we'll supplant the percent sign with a decimal point.
Then we'll motion the decimal signal two spaces to the left.
Then we'll move the decimal point two spaces to the left.
78% is equal to 0.78.
Allow's await at another case. This time nosotros'll turn 8% into a decimal.
Commencement, we'll replace the per centum sign with a decimal point.
And then, we'll move the decimal indicate ii spaces to the left.
And then, nosotros'll move the decimal point two spaces to the left.
Notice there is an extra space next to the 8. We can't but leave an open up space with zero in it. Since zero equals nothing, we'll replace the space with zero.
Find there is an actress infinite next to the eight. We can't only exit an open up infinite with cypher in it. Since zero equals nothing, we'll supplant the space with goose egg.
8% is equal to .08

Why does this work?

Converting percents into decimals is and then like shooting fish in a barrel that y'all may feel similar you've missed something. Just don't worry—it actually is that simple! Hither's why the method we showed y'all works.

When we plough a percent into a decimal, we're actually doing 2 steps. Showtime, we convert our percent into a fraction. Since all percents are out of 100, we only put the percent over 100, like this:

78% = 78/100

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

78 ÷ 100 = 0.78

So why didn't nosotros evidence you lot these steps in the slideshow? Considering yous can get the answer without them. You know that all percents are out of 100, so you can skip making the pct into a fraction. You have to dissever the percent by 100 to go a decimal, but there's a quick mode to do that. Just move the decimal signal two spaces to the left! This fashion, yous can get the same reply with but one piece of cake pace.

Try This!

Convert these percents into decimals.

Converting a decimal into a percent

At present we'll contrary what y'all simply learned. Allow'southward convert a decimal into a percent.

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

We're going to convert 0.45 into a percent.
We'll opposite what we did in the last department. This time, we'll move the decimal point two places to the right.
Nosotros'll reverse what we did in the last department. This time, we'll motion the decimal point two places to the right.
Now we'll supersede the decimal point with a percent sign.
We've finished converting our decimal into a per centum. 0.45 is equal to 45%.
Let's try another example. This time our decimal has iii numbers to the right of the decimal point.
But we're still going to move the decimal signal two spaces to the right.
Simply nosotros're still going to move the decimal point ii spaces to the correct.
We nevertheless have a number to the correct of the decimal point. The number isn't a 0, so nosotros tin can't drop information technology.
Instead, nosotros'll keep the decimal bespeak and add together a pct sign at the end of the number.
So 0.635 is equal to 63.5%.

Effort This!

Calculate these decimals as percents.

Percents and fractions

Knowing how to write percents as fractions and vice versa can help you in your everyday life. For case, let'south say yous earned a form of lxxx% on a test. Yous tin can convert 80% into a fraction to detect out how many of your answers were correct. When your teacher grades the test, she may do the reverse. If a student got 8 out of 10 questions right, the instructor tin catechumen 8/10 to a pct to give the student a course.

Converting a percent into a fraction

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

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

We're going to catechumen 30% into a fraction.
In Introduction to Percents, you learned that all percents are out of 100. In fact, that'southward what the word percent means.
Then whatever percent is equal to itself over 100. In our example, 30% is equal to xxx/100.
Now we've converted thirty% into a fraction, but we all the same demand to reduce it.
10 is the largest number that goes evenly into 30 and 100. So we tin divide both parts of the fraction by 10.
We'll separate the numerator of the fraction get-go. 30 divided by 10 equals three.
Now we'll divide the denominator. 100 divided by 10 equals 10.
And so 30% is equal to 3/ten.

Effort This!

Write these percentages as 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 just learned: writing a fraction as a decimal, and writing a decimal equally a percent. Let'south run into how nosotros can use these skills to convert a fraction into a percent.

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

Let'due south convert 3/6 into a percent.
But like when nosotros converted a fraction into a decimal, we'll divide the numerator past the denominator.
3 divided by 6 equals 0.five.
We've turned our fraction into a decimal.
At present we'll turn the decimal into a per centum by moving the decimal point ii spaces to the right.
Now we'll turn the decimal into a per centum past moving the decimal signal two spaces to the right.
Nosotros'll besides modify the decimal bespeak into a percent sign. 0.50 is equal to l%.
So three/half dozen is equal to 50%.