0.17 Percent As A Decimal

Lesson 5: Converting Percentages, Decimals, and Fractions

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Converting fractions, decimals, and percents

When we talk, we often employ unlike words to express the aforementioned affair. For instance, nosotros could describe the same car as tiny or little or modest. All of these words mean the car is not large. Fractions, decimals, and percents are similar the words tiny, little, and small-scale. They're all just different ways of expressing parts of a whole.

screenshot of 1/2

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

Sometimes information technology's useful to catechumen one kind of number into another. For example, information technology'southward much easier to add 1/4 and 0.v if you turn 0.5 into a fraction. Learning how to convert fractions, decimals, and percents will likewise help you lot as you lot learn more advanced math.

Fractions and decimals

Every fraction can also exist written as a decimal, and vice versa. You lot may not practise this very often, but converting decimals and fractions tin help yous in math. For example, it's easier to subtract ane/6 from 0.52 if you turn 1/half-dozen into a decimal starting time.

Converting a fraction into a decimal

Let's catechumen a fraction into a decimal. Nosotros'll be using a math skill you've already learned: long division. To refresh your memory on this skill, you lot can review our Long Sectionalization lesson.

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

Let's run into how we can convert 1/four into a decimal.
To convert a fraction into a decimal, we'll simply dissever the numerator...
To convert a fraction to a decimal, we'll just divide the numerator...by the denominator.
In our case, we'll dissever i by 4.
1 divided by four equals 0.
To keep dividing, we'll add a decimal point and a nix after the 1.
We'll also add a decimal bespeak after the 0 on summit.
Now we can divide 10 by 4.
10 divided by 4 equals two.
Now we'll multiply 4 by 2.
4 times ii equals 8. So we'll subtract 8 from 10.
x minus eight equals 2.
Since two is greater than 0, we're non finished dividing however. We'll add another 0 after the decimal point and bring it down.
Now nosotros'll divide 20 by 4.
twenty divided by 4 equals 5.
Now nosotros'll multiply. 4 times 5 equals 20.
When we subtract 20 from 20, we go 0. The 0 means we're done dividing.
1 divided by four equals 0.25.
And so one/4 is equal to 0.25.

Endeavour This!

Convert each of these fractions into a decimal.

Converting a decimal into a fraction

Now nosotros'll do it in contrary. Permit's catechumen 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 utilize place values.
In decimals, the number immediately to the right of the decimal signal is in the tenths place.
The place to the right of the tenths identify is the hundredths place.
To catechumen a decimal, outset nosotros'll check the place value of the last number to the right.
In 0.85, five is in the hundredths place.
This means our decimal is equal to 85 hundredths. 85 hundredths can besides be written as 85/100.
At present we have our fraction. But it's always a practiced idea to reduce fractions when we can—it makes them easier to read.
To reduce, we demand to detect the largest number that will become evenly into both 85 and 100.
5 is the largest number that goes evenly into 85 and 100. So we'll divide both parts of our fraction by v.
Kickoff nosotros'll divide the numerator. 85 divided by v equals 17.
At present we'll carve up the denominator. 100 divided by five equals 20. This ways 85/100 tin can exist reduced to 17/20.
So 0.85 is equal to 17/xx.

Reducing a fraction may seem unnecessary when you're converting a decimal. But it'south of import if you're going to utilise the fraction in a math trouble. If you're calculation two fractions, you lot may even need to reduce or change both fractions and then they have a mutual denominator.

Endeavour This!

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

Percents and decimals

Knowing how to convert percents and decimals volition help y'all calculate things similar sales tax and discounts. To learn how, check out our Percentages in Existent Life lesson.

Converting a percent into a decimal

Converting a percent into a decimal is surprisingly easy. It just takes a few unproblematic steps.

Click through the slideshow to learn how to catechumen a pct into a decimal.

We're going to convert 17% into a decimal.
First, we'll accept the percentage sign...
Beginning, we'll take the percent sign...and turn it into a decimal point.
Next, we'll move the decimal signal two spaces to the left.
Now we'll move the decimal betoken ii spaces to the left.
Nosotros've converted our percent to a decimal. 17% is equal to 0.17.
Let'due south look at another instance. This time nosotros'll plow 78% into a decimal.
First, nosotros'll replace the per centum sign with a decimal point.
And so we'll move the decimal point ii spaces to the left.
Then we'll motility the decimal signal ii spaces to the left.
78% is equal to 0.78.
Let'south look at another example. This time we'll turn 8% into a decimal.
First, we'll supervene upon the percent sign with a decimal indicate.
So, nosotros'll move the decimal betoken two spaces to the left.
Then, we'll motility the decimal point ii spaces to the left.
Discover there is an extra infinite next to the 8. We can't just exit an open space with nothing in it. Since goose egg equals zip, nosotros'll replace the space with aught.
Notice there is an extra space adjacent to the eight. We can't merely exit an open infinite with cipher in it. Since zero equals nothing, we'll replace the space with nothing.
8% is equal to .08

Why does this work?

Converting percents into decimals is and then easy that you may experience like you've missed something. Just don't worry—it actually is that elementary! Here'south why the method we showed you works.

When we turn a pct into a decimal, we're actually doing two steps. First, nosotros convert our percent into a fraction. Since all percents are out of 100, we just put the percent over 100, similar this:

78% = 78/100

In the 2nd step, we convert 78/100 into a decimal. You already know this ways nosotros'll divide the numerator past the denominator, similar this:

78 ÷ 100 = 0.78

So why didn't nosotros show you these steps in the slideshow? Because you tin can get the answer without them. Y'all know that all percents are out of 100, so you tin can skip making the percent into a fraction. You have to divide the percentage by 100 to get a decimal, but there's a quick style to do that. Only motion the decimal point 2 spaces to the left! This way, you lot tin can get the same answer with just 1 easy step.

Try This!

Convert these percents into decimals.

Converting a decimal into a pct

Now we'll contrary what yous only learned. Permit's convert a decimal into a percent.

Click through the slideshow to see 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 section. This time, nosotros'll motility the decimal point ii places to the right.
Nosotros'll reverse what we did in the terminal section. This time, nosotros'll move the decimal indicate 2 places to the right.
Now we'll replace the decimal point with a percent sign.
Nosotros've finished converting our decimal into a pct. 0.45 is equal to 45%.
Let'south attempt some other example. This time our decimal has three numbers to the right of the decimal point.
Only nosotros're nonetheless going to motion the decimal bespeak two spaces to the correct.
Simply nosotros're still going to move the decimal betoken 2 spaces to the right.
We however accept a number to the right of the decimal signal. The number isn't a 0, so we can't drop information technology.
Instead, we'll continue the decimal indicate and add a percent sign at the end of the number.
So 0.635 is equal to 63.v%.

Endeavour 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 instance, let'south say you earned a course of 80% on a examination. You can convert fourscore% into a fraction to find out how many of your answers were right. When your instructor grades the test, she may practise the contrary. If a student got 8 out of 10 questions right, the instructor tin can convert 8/10 to a per centum to requite the student a class.

Converting a percent into a fraction

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

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

We're going to catechumen 30% into a fraction.
In Introduction to Percents, y'all learned that all percents are out of 100. In fact, that'south what the word percent ways.
So any percent is equal to itself over 100. In our example, thirty% is equal to 30/100.
Now we've converted 30% into a fraction, merely we still need 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 by ten.
We'll divide the numerator of the fraction offset. 30 divided past 10 equals 3.
Now nosotros'll split the denominator. 100 divided by 10 equals 10.
Then 30% is equal to iii/ten.

Attempt This!

Write these percentages every bit fractions. Brand sure to reduce each fraction to its simplest form.

Converting a fraction into a percent

Converting a fraction uses 2 of the skills you just learned: writing a fraction as a decimal, and writing a decimal as a pct. Let's see how we tin employ these skills to convert a fraction into a per centum.

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

Let's convert 3/vi into a percent.
Just like when we converted a fraction into a decimal, nosotros'll separate the numerator past the denominator.
3 divided past six equals 0.five.
We've turned our fraction into a decimal.
Now we'll turn the decimal into a per centum by moving the decimal signal two spaces to the right.
Now we'll turn the decimal into a pct by moving the decimal betoken two spaces to the right.
We'll also change the decimal point into a percent sign. 0.50 is equal to 50%.
So 3/6 is equal to l%.

Try This!

Convert these fractions into percents.