Converting Between Percentages, Decimals, and Fractions

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Fraction to decimal to percentage conversion

We tend to use a variety of synonyms and antonyms when attempting to convey the same meaning in conversation. Different adjectives can be used to describe the same car, for instance: These descriptions collectively indicate that the vehicle in question is not particularly spacious. Tiny, little, and small are how fractions, decimals, and percentages are measured. All of these are just different ways of articulating individual pieces of a larger whole.

All of the cups in this picture contain the same volume of juice. However, we have provided this sum in three different notations: a fraction, a percentage, and a decimal. For the simple reason that they both have the same numerical value, we can deduce that 1/2 , 50% , and 0.5 are on an even playing field The moment we observe 1/2 when we realize it also means 50% or 0.5

Converting from one numerical format to another can come in handy at times. When adding, for instance, it's a lot 1/4 and 0.5 Turning the corner 0.5 with a fractional representation Converting between fractions, decimals, and percents is a skill that will serve you well in your pursuit of higher mathematics.

Calculating with fractions and decimals

It is possible to express any fraction as a decimal, and any decimal as a fraction. Even if you don't do it often, converting between decimals and fractions is a useful skill to have. Subtracting is a good illustration. 1/6 from 0.52 Upon reflection, if 1/6 decimal form first

Methods for Changing Fractions into Decimals

Okay, let's do the math and turn that fraction into a decimal. The math skill we'll be using is long division, which you should already be familiar with. You can review our Long Division tutorial if you need a refresher on the topic.

Explore the slides to see how to turn a fraction into a decimal.

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  How can we make this transformation? 1/4 converted to decimal form

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  Simply dividing the numerator will allow us to convert the fraction to a decimal.

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  If we divide the numerator by ten, the result will be a decimal. relative to the smallest common factor

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  For this example, let's say we want to 1 by 4

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  1 divided by 4 equals

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  Putting a decimal point and a 0 after the will allow us to continue dividing. 1

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  The number will have a decimal point added after it. on top

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  It's time to split up. 10 by 4

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  10 divided by 4 equals 2

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  Let's go ahead and multiply now. 4 by 2

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  4 times 2 equals 8 We'll use subtraction instead. 8 from 10

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  10 minus 8 equals 2

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  Since 2 exceeds in size or importance We haven't completed our divisions yet Another will be added the digits after the decimal point and round it off

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  We'll break up into our respective groups now. 20 by 4

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  20 divided by 4 equals 5

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  We're about to multiply now. 4 times 5 equals 20

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  By deducting 20 from 20 , we get The that the division is complete

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  1 divided by 4 equals 0.25

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  So 1/4 proportionally equal to 0.25

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The following fractions need to be converted to decimals.

The process of transforming a decimal into a fraction

Now let's go backwards through that process. How about we turn this decimal into a fraction?

To learn how to change a decimal to a fraction, just click through the slideshow below.

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  We are planning on rewriting the entire thing. 0.85 as a percentage Using place values, we can change a decimal to a fraction.

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  After a decimal point, the digits to the right represent the tenths of that number.

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  The hundredths place is the spot directly after the tenths place.

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  First, we look at the rightmost digit of the decimal and make sure it has the correct place value.

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  In 0.85 , 5 has a decimal place value of 100

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  Consequently, our decimal is equivalent to 85 hundredths A hundred and eighty-fiveth of a second can also be expressed as 85/100

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  We have arrived at our fraction Still, whenever possible, we should round off fractions to make them simpler to read.

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  In order to condense, we must locate the greatest number that divides equally into each 85 and 100

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  5 is the greatest integer divisible by 85 and 100 To simplify this fraction, we will divide both parts by 5

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  The numerator will be divided first. 85 divided by 5 equals 17

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  Let's break down the denominator now. 100 divided by 5 equals 20 This means 85/100 reduces to 17/20

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  So 0.85 compares to 17/20

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Bringing a fraction down to a decimal may seem like an unnecessary step. But if you're going to use the fraction in a calculation, you need to know this. It's possible that you'll need to adjust one or both fractions to get a common denominator before you can add them.

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Please fractionize these decimals. Make sure that every fraction is written in its simplest form.

Decimals and percentages

The ability to convert between percent and decimal form is useful for figuring out pricing and other discounts. Check out our article on the application of percentages to learn more.

Fractionalizing a percentage

It's surprisingly simple to convert a percentage to a decimal. Some basic steps are all that is required.

To see how to turn a percentage into a decimal, just click through the slideshow below.

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  The group is making the switch. 17% to the tenths place

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  We'll start with the percent sign to get a sense of the scale.

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  So, let's start with the percent sign. and make a decimal out of it

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  To continue, let's shift the decimal point to the left by two places.

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  The decimal point will be shifted to the left by two places now.

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  As a result, we have expressed our percentage as a decimal. 17% corresponds to 0.17

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  What about we take a look at a different illustration We'll be making a 180-degree turn this time. 78% converting it to decimal form

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  To start, we'll swap the percent sign for a decimal point.

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  As a result, we'll shift the decimal point to the left by two places.

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  The decimal point will then be shifted to the left by two places.

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  78% corresponds to 0.78

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  Here's a different case to consider. Let's try a 180 this time. 8% to the tenths place

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  We'll start by switching the percent sign for a decimal point.

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  The decimal point will then be shifted to the left by two places.

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  Following this, we'll shift the decimal point to the left by two places.

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  See the blank space after the 8? We cannot abandon a vacant lot. We'll just put a 0 there in place of the space because 0 means "nothing."

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  You may have noticed the blank space after the 8. We can't just abandon that empty room. Therefore, we will substitute a 0 for the void.

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  8% the same as 08

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Exactly why is this effective, anyway?

You might feel like you're missing out on something because converting percentages into decimals is so simple. No need to worry, though; it's really that easy The following is why the technique we demonstrated yields positive results.

A percentage can be converted to a decimal by performing two operations: At the outset, we must divide our percentage by 100 to get a fraction. Given that all percentages are invalid 100 Simply increased the percentage by one 100 as in:

78% = 78/100

Specifically, in Step 2, we will be converting 78/100 decimal form The obvious solution is to divide the numerator by the denominator, as shown:

78 ÷ 100 = 0 78

In that case, why didn't we include these directions in the slideshow? As a result of not needing their help to find the solution All percentages are a complete and utter farce, as you well 100 Consequently, you can forego converting the percentage to a fraction To get the percentage, divide by 100 to convert a fraction to a decimal, but there's a simple trick for doing so To do this, you must only shift the decimal point to the left by two places. In this way, the same result can be attained with minimal effort.

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Round these percentages off to the nearest decimal

Putting a decimal number into percentage form

We are going to teach you the opposite of what you just learned. So, let's figure out how to turn that decimal into a percentage.

The slideshow below will show you how to change a decimal to a percentage.

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  We're making the switch 0.45 in terms of a percentage

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  Our previous discussion will be turned on its head. Now we'll round up to the nearest whole number plus two places.

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  We're going to do the opposite of the previous discussion. The decimal point will be shifted to the right by two places this time.

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  The decimal point will be replaced by a percent sign.

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  As a result of our efforts, our decimal fraction is now expressed as a percentage. 0.45 equates to 45%

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  So, let's try this out with another illustration. For this instance, our decimal has three digits to the right of the decimal point.

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  The decimal point will still be shifted right by two places, though.

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  Still, we'll be shifting that decimal point rightward by two places.

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  There is still a digit after the decimal point. That can't be a thus we must not abandon it

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  Instead, we'll add a percent sign after the number we're working with and keep the decimal point.

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  So 0.635 corresponds to 63.5%

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Change these fractions to percentages.

Formulas for calculating percentages and fractions

The ability to convert percentages to fractions and vice versa is an important skill. Say, for instance, you got an 80% on a test. Change is possible. 80% into a fraction in order to determine the percentage of correct responses Your teacher may use the inverse criterion when grading your exam. A student who answers 8 out of 10 questions correctly allows the teacher to convert 8/10 grade (usually expressed as a percentage) out of 100

Fractionalizing a percentage

If you need to convert a percentage to a fraction, keep in mind that percents are always larger than the fraction they are being converted to. 100 Our Introduction to Percentages unit provides practice with percentages.

To see how to turn a percentage into a fraction, just click through the slideshow below.

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  We're making the switch 30% to a decimal form

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  All percentages are incorrect, as you learned in the first chapter, 100 In fact, that is exactly what the symbol "%" denotes.

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  This means that any percentage is always equal to 100 percent plus 100 As demonstrated by our example, 30% equivalent to 30/100

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  We've finally come around 30% into a fraction, but we must still bring it down to a smaller form

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  10 is the greatest integer divisible by 30 and 100 Since this is the case, we can split the fraction in two and divide each half by 10

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  First, we'll split the fraction's numerator. 30 divided by 10 equals 3

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  So, let's break down the denominator now. 100 divided by 10 equals 10

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  So 30% in proportion to 3/10

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Convert these percentages into fractions. Please simplify all fractions to their lowest terms.

Putting a fraction into percentage form

You'll need to apply what you've learned about writing fractions as decimals and percentages to convert a fraction. Let's put these abilities to use by figuring out how to transform a fraction into a percentage.

You can find out how to do the conversion from a fraction to a percentage by clicking through the slideshow below.

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  Okay, let's change over 3/6 transform into a percentage

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  To divide the numerator by the denominator, as we did when turning the fraction into a decimal.

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  3 divided by 6 equals 0.5

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  The fraction we were working with has been converted to a decimal.

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  Here, we'll convert the decimal to a percentage by shifting the decimal point to the right by two places.

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  By shifting the decimal point to the right by two places, we can convert the number to a percentage.

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  Finally, we'll convert the decimal to a percentage sign. 0.50 in proportion to 50%

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  So 3/6 in proportion to 50%

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Perform the percentage conversion on these fractions.