Convert 1/2 To A Decimal

Lesson 4: Converting Percentages, Decimals, and Fractions

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Converting fractions, decimals, and percents

When we talk, nosotros ofttimes use unlike words to express the same thing. For case, we could depict the same motorcar equally tiny or little or small. All of these words mean the machine is non big. Fractions, decimals, and percents are like the words tiny, little, and small-scale. They're all but unlike means of expressing parts of a whole.

screenshot of 1/2

In this image, each measuring loving cup has the same amount of juice in it. Simply nosotros've expressed this corporeality in three ways: as a fraction, as a percentage, and equally a decimal. Since they're expressing the same corporeality, we know that i/2, 50%, and 0.5 are equal to each other. Any fourth dimension we see ane/ii, nosotros'll know information technology can likewise hateful 50% or 0.5.

Sometimes information technology'southward useful to convert one kind of number into another. For example, it'southward much easier to add 1/4 and 0.5 if you turn 0.5 into a fraction. Learning how to convert fractions, decimals, and percents will besides help yous as yous learn more advanced math.

Fractions and decimals

Every fraction can also be written as a decimal, and vice versa. You may not do this very often, merely converting decimals and fractions can aid you in math. For example, it's easier to subtract 1/6 from 0.52 if you turn i/vi into a decimal first.

Converting a fraction into a decimal

Let'south convert a fraction into a decimal. We'll exist using a math skill you've already learned: long partition. To refresh your retentivity on this skill, yous can review our Long Division lesson.

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

Permit'south see how nosotros can convert 1/4 into a decimal.
To convert a fraction into a decimal, we'll just divide the numerator...
To convert a fraction to a decimal, nosotros'll but separate the numerator...by the denominator.
In our example, we'll split up one by 4.
one divided by four equals 0.
To keep dividing, nosotros'll add a decimal betoken and a nix after the 1.
We'll also add a decimal point later on the 0 on top.
Now we can divide 10 by 4.
10 divided by four equals 2.
Now nosotros'll multiply 4 by two.
4 times 2 equals 8. So we'll subtract 8 from ten.
10 minus 8 equals 2.
Since ii is greater than 0, we're not finished dividing yet. We'll add another 0 subsequently the decimal bespeak and bring it down.
At present we'll split xx by 4.
20 divided by iv equals 5.
Now we'll multiply. 4 times 5 equals 20.
When we subtract xx from twenty, we become 0. The 0 means we're washed dividing.
1 divided by 4 equals 0.25.
Then 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 nosotros'll do it in reverse. Let's convert a decimal into a fraction.

Click through the slideshow to come across how to catechumen a decimal into a fraction.

We're going to rewrite 0.85 as a fraction. To catechumen a decimal into a fraction, nosotros'll use place values.
In decimals, the number immediately to the correct of the decimal indicate is in the tenths identify.
The identify to the right of the tenths place is the hundredths place.
To convert a decimal, first we'll bank check the place value of the last number to the correct.
In 0.85, 5 is in the hundredths place.
This ways our decimal is equal to 85 hundredths. 85 hundredths can also be written equally 85/100.
Now we have our fraction. But it's always a good thought to reduce fractions when we can—information technology makes them easier to read.
To reduce, nosotros need to notice the largest number that will get evenly into both 85 and 100.
v is the largest number that goes evenly into 85 and 100. So we'll split both parts of our fraction by 5.
First nosotros'll divide the numerator. 85 divided by v equals 17.
At present we'll split the denominator. 100 divided by 5 equals 20. This means 85/100 can be reduced to 17/twenty.
So 0.85 is equal to 17/20.

Reducing a fraction may seem unnecessary when you're converting a decimal. Simply information technology'south important if you're going to use the fraction in a math problem. If you're adding ii fractions, you may fifty-fifty need to reduce or modify both fractions and then they accept a mutual denominator.

Try This!

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

Percents and decimals

Knowing how to convert percents and decimals volition help you calculate things like sales tax and discounts. To learn how, cheque out our Percentages in Real Life lesson.

Converting a per centum into a decimal

Converting a pct into a decimal is surprisingly easy. It only takes a few simple steps.

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

We're going to catechumen 17% into a decimal.
Showtime, we'll accept the pct sign...
Kickoff, we'll take the pct sign...and turn it into a decimal point.
Side by side, we'll move the decimal betoken two spaces to the left.
Now we'll move the decimal point ii spaces to the left.
We've converted our percent to a decimal. 17% is equal to 0.17.
Let's wait at another instance. This time we'll plough 78% into a decimal.
Commencement, nosotros'll replace the pct sign with a decimal betoken.
So we'll move the decimal point 2 spaces to the left.
Then we'll motion the decimal point two spaces to the left.
78% is equal to 0.78.
Permit's await at another example. This fourth dimension we'll turn eight% into a decimal.
Kickoff, nosotros'll replace the percent sign with a decimal point.
Then, we'll move the decimal bespeak two spaces to the left.
And then, we'll move the decimal betoken two spaces to the left.
Notice there is an extra space adjacent to the viii. We can't merely leave an open up space with nothing in it. Since zippo equals nothing, we'll supplant the space with zero.
Find in that location is an extra space next to the 8. We tin can't just leave an open up space with nothing in information technology. Since zero equals aught, we'll supervene upon the infinite with zero.
eight% is equal to .08

Why does this work?

Converting percents into decimals is then like shooting fish in a barrel that you may feel similar you've missed something. But don't worry—it actually is that simple! Here'due south why the method we showed you works.

When we turn a percentage into a decimal, nosotros're actually doing two steps. First, we convert our percent into a fraction. Since all percents are out of 100, we just 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 divide the numerator past the denominator, like this:

78 ÷ 100 = 0.78

And so why didn't we prove you these steps in the slideshow? Because you can get the answer without them. Yous know that all percents are out of 100, so you can skip making the percent into a fraction. You take to dissever the percentage by 100 to get a decimal, but there's a quick fashion to do that. Just motility the decimal point two spaces to the left! This way, you can get the same answer with only 1 like shooting fish in a barrel step.

Try This!

Convert these percents into decimals.

Converting a decimal into a percent

Now we'll opposite what you just learned. Let's convert a decimal into a percentage.

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 reverse what we did in the last department. This time, we'll move the decimal bespeak two places to the right.
Nosotros'll contrary what we did in the terminal section. This time, nosotros'll move the decimal point two places to the correct.
Now nosotros'll replace the decimal point with a percent sign.
We've finished converting our decimal into a percent. 0.45 is equal to 45%.
Allow'south try another instance. This fourth dimension our decimal has three numbers to the right of the decimal point.
But we're nevertheless going to move the decimal point two spaces to the right.
Just we're still going to movement the decimal signal two spaces to the right.
Nosotros notwithstanding have a number to the right of the decimal signal. The number isn't a 0, so we can't drop it.
Instead, we'll proceed the decimal indicate and add a percent sign at the end of the number.
And then 0.635 is equal to 63.5%.

Attempt This!

Calculate these decimals as percents.

Percents and fractions

Knowing how to write percents as fractions and vice versa tin assist you in your everyday life. For example, let'southward say you earned a grade of 80% on a test. You can catechumen 80% into a fraction to find out how many of your answers were correct. When your instructor grades the test, she may practice the reverse. If a student got viii out of 10 questions right, the teacher can catechumen viii/10 to a percent to give the student a class.

Converting a percent into a fraction

When you're converting a per centum into a fraction, it helps to remember that percents are always out of 100. You tin practice with percents in our Introduction to Percentages lesson.

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

Nosotros're going to convert thirty% into a fraction.
In Introduction to Percents, you learned that all percents are out of 100. In fact, that'southward what the discussion percent means.
Then 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, just we still need to reduce it.
ten is the largest number that goes evenly into 30 and 100. And then we can divide both parts of the fraction past ten.
We'll carve up the numerator of the fraction first. 30 divided by 10 equals three.
At present we'll split the denominator. 100 divided by 10 equals x.
And then 30% is equal to 3/10.

Try This!

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

Converting a fraction into a percentage

Converting a fraction uses two of the skills you just learned: writing a fraction as a decimal, and writing a decimal every bit a percentage. Allow'southward come across how nosotros can use these skills to catechumen a fraction into a percent.

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

Let's convert iii/half-dozen into a percent.
Simply like when we converted a fraction into a decimal, we'll separate the numerator by the denominator.
iii divided by 6 equals 0.5.
We've turned our fraction into a decimal.
Now we'll plough the decimal into a percent by moving the decimal point two spaces to the correct.
Now we'll plough the decimal into a per centum past moving the decimal point two spaces to the right.
Nosotros'll also change the decimal indicate into a percent sign. 0.50 is equal to 50%.
So 3/half-dozen is equal to l%.