How Do You Know if Fractions Are Equal to Each Other

Wondering how to convert decimals to fractions? Or how to convert fractions to decimals? It'southward easier than you lot think! Keep reading to come across the steps for decimal to fraction conversions (including why you demand to follow different steps if you have a repeating decimal), steps for fraction to decimal conversions, a handy chart with common decimal/fraction conversions, and tips for apace estimating conversions.

How to Convert Decimals to Fractions

How practice you convert a decimal to a fraction? Any decimal, even complicated-looking ones, can exist converted to a fraction; yous just need to follow a few steps. Below we explain how to convert both terminating decimals and repeating decimals to fractions.

Converting a Terminating Decimal to a Fraction

A terminating decimal is any decimal that has a finite other of digits. In other words, information technology has an end. Examples include .5, .234, .864721, etc. Terminating decimals are the nearly common decimals you'll run into and, fortunately, they are also the easiest to convert to fractions.

Footstep i

Write the decimal divided by one.

For case, say yous're given the decimal .55.Your start step is to write out the decimal and so it looks like ${.55}/{1}$.

Step 2

Adjacent, you desire to multiply both the top and lesser of your new fraction by 10 for every digit to the left of the decimal point.

In our case, .55 has two digits later the decimal point, then nosotros'll want to multiply the entire fraction past ten 10 10, or 100. Multiplying the fraction by ${100}/{100}$ gives us ${55}/{100}$.

Footstep 3

The terminal step is reducing the fraction to its simplest form. The simplest form of the fraction is when the top and lesser of the fraction are the smallest whole numbers they can exist. For instance, the fraction ${3}/{9}$ isn't in its simplest form considering information technology tin can still exist reduced downward to ⅓ by dividing both the top and lesser of the fraction by 3.

The fraction ${55}/{100}$ can be reduced by dividing both the elevation and bottom of the fraction by 5, giving u.s.a. ${11}/{20}$. eleven is a prime and can't be divided any more, and so we know this is the fraction in its simplest form.

The decimal .55 is equal to the fraction ${eleven}/{20}$.

Example

Convert .108 to a fraction.

After putting the decimal over 1, nosotros terminate up with ${.108}/{1}$.

Since .108 has three digits later the decimal place, we need to multiply the entire fraction by 10 10 10 x x, or grand. This gives usa ${108}/{1000}$.

Now nosotros need to simplify. Since 108 and grand are both fifty-fifty numbers, we know we can split both past 2. This gives u.s.a. ${54}/{500}$. These are still even numbers, so we tin divide by ii again to become ${27}/{250}$. 27 isn't a factor of 250, and then the fraction tin't be reduced any more.

The final answer is ${27}/{250}$.

Converting a Repeating Decimal to a Fraction

A repeating decimal is one that has no end. Since yous can't keep writing or typing the decimal out forever, they are ofttimes written as a string of digits rounded off (.666666667) or with a bar in a higher place the repeating digit(s) $\ov {(.6)}$.

For our instance, we'll convert .6667 to a fraction.

The decimal .6667 is equal to $\ov {(.6)}$, .666666667, .667, etc. They're all merely different ways to show that the decimal is actually a string of 6's that goes on forever.

Step 1

Let ten equal the repeating decimal you're trying to convert, and identify the repeating digit(s).

So x=.6667

vi is the repeating digit, and the end of the decimal has been rounded up.

Step 2

Multiply by whatever value of 10 you need to get the repeating digit(s) on the left side of the decimal.

For .6667, we know that 6 is the repeating digit. We want that half dozen on the left side of the decimal, which ways moving the decimal place over one spot. So nosotros multiply both sides of the equation past (10 10 1) or ten.

10x = 6.667

Note: You but desire 1 "set" of repeating digit(s) on the left side of the decimal. In this example, with 6 as the repeating digit, you only want one 6 on the left of the decimal. If the decimal was 0.58585858, you'd merely want one prepare of "58" on the left side. If it helps, you tin can picture all repeating decimals with the infinity bar over them, so .6667 would be$\ov {(.6)}$.

Footstep 3

Next nosotros want to get an equation where the repeating digit is simply to the correct of the decimal.

Looking at x = .6667, we tin can run into that the repeating digit (6) is already just to the correct of the decimal, and so we don't need to practise any multiplication. Nosotros'll keep this equation as x = .6667

Pace 4

Now we need to solve for x using our two equations, x = .667 and 10x = 6.667.

10x - x =6.667-.667

9x = half-dozen

ten = ${six}/{9}$

10 = ⅔

Instance

Catechumen 1.0363636 to a fraction.

This question is a bit trickier, but we'll be doing the same steps that we did higher up.

First, make the decimal equal to x, and determine the repeating digit(s). 10 = 1.0363636 and the repeating digits are 3 and 6

Next, go the repeating digits on the left side of the decimal (once more, you only want one set up of repeating digits on the left). This involves moving the decimal three places to the right, so both sides need to be multiplied past (10 x 3) or thou.

1000x = 1036.363636

Now get the repeating digits to the correct of the decimal. Looking at the equation ten = 1.0363636, y'all tin can see that there currently is a zero between the decimal and the repeating digits. The decimal needs to exist moved over ane space, so both sides need to exist multiplied by 10 x 1.

10x = 10.363636

Now use the 2 equations, 1000x = 1036.363636 and 10x = 10.363636, to solve for ten.

1000x - 10x = 1036.363636 - 10.363636

990x = 1026

x = ${1026}/{990}$

Since the numerator is larger than the denominator, this is known equally an irregular fraction. Sometimes you tin can exit the fraction as an irregular fraction, or y'all may be asked to catechumen it to a regular fraction. You can do this by subtracting 990/990 from the fraction and making information technology a 1 that'll become side by side to the fraction.

${1026}/{990}$ - ${990}/{990}$ = 1 ${36}/{990}$

x = ane ${36}/{990}$

${36}/{990}$ tin be simplified by dividing it past 18.

x = 1 ${two}/{55}$

How to Convert Fractions to Decimals

The easiest mode to convert a fraction to a decimal is only to utilize your calculator. The line between the numerator and denominator acts as a segmentation line, so ${7}/{29}$ equals 7 divided by 29 or .241.

If you don't accept access to a estimator though, you can nonetheless convert fractions to decimals by using long division or getting the denominator to equal a multiple of 10. We explicate both these methods in this section.

Long Division Method

Catechumen ${3}/{viii}$ to a decimal.

Here is what ${3}/{viii}$ looks similar worked out with long sectionalization.

⅜ converted to a decimal is .375

Denominator every bit a Value of 10 Method

Convert ${iii}/{8}$ to a decimal.

Step 1

Nosotros desire the denominator, in this case viii, to equal a value of 10. We can practice this by multiplying the fraction by 125, giving united states of america ${375}/{1000}$.

Step two

Adjacent we desire to get the denominator to equal 1 so we tin get rid of the fraction. We'll do this by dividing each office of the fraction by 1000, which means moving the decimal over iii places to the left.

This gives us ${.375}/{1}$ or just .375, which is our reply.

Note that this method just works for a fraction with a denominator that can easily be multiplied to be a value of ten. Nonetheless, there is a trick yous can use to estimate the value of fractions you can't convert using this method. Check out the example below.

Instance

Convert ⅔ to a decimal.

There is no number you tin can multiply iii past to make it an exact multiple of 10, only you can get close.

By multiplying ⅔ past ${333}/{333}$, we get ${666}/{999}$.

999 is very close to yard, so let'south human activity like it actually is one thousand, separate each function of the fraction by 1000, and move the decimal place of 666 three places to the left, giving us .666

The verbal decimal conversion of ⅔ is the repeating decimal .6666667, simply .666 gets us very close.

So whenever you lot have a fraction whose denominator tin't hands be multiplied to a value of 10 (this will happen to all fractions that catechumen to repeating decimals), just get the denominator as shut to a multiple of 10 as possible for a shut estimate.

Common Decimal to Fraction Conversions

Below is a nautical chart with mutual decimal to fraction conversions. Y'all don't need to memorize these, but knowing at least some of them off the top of your head will arrive easy to do some mutual conversions. If you're trying to catechumen a decimal or fraction and don't have a calculator, y'all can also see which value in this chart the number is closest to so y'all can make an educated estimate of the conversion.

Decimal	Fraction
0.03125	${i}/{32}$
0.0625	${i}/{16}$
0.one	${1}/{x}$
0.1111	${ane}/{9}$
0.125	${1}/{viii}$
0.16667	${1}/{vi}$
0.2	${i}/{5}$
0.2222	${2}/{ix}$
0.25	${one}/{4}$
0.3	${iii}/{x}$
0.3333	${1}/{3}$
0.375	${3}/{8}$
0.4	${2}/{v}$
0.4444	${4}/{9}$
0.5	${1}/{two}$
0.5555	${5}/{nine}$
0.half dozen	${3}/{5}$
0.625	${5}/{8}$
0.6666	${2}/{iii}$
0.7	${7}/{10}$
0.75	${three}/{4}$
0.7777	${7}/{9}$
0.8	${4}/{v}$
0.8333	${5}/{6}$
0.875	${vii}/{viii}$
0.8888	${8}/{9}$
0.9	${9}/{10}$

Summary: How to Make a Decimal Into a Fraction

If you're trying to convert a decimal to fraction, starting time you need to determine if it's a terminal decimal (i with an end) or a repeating decimal (one with a digit or digit that repeats to infinity). Once you lot've done that, you tin follow a few steps for the decimal to fraction conversion and for writing decimals every bit fractions.

If you're trying to catechumen a fraction to decimal, the easiest fashion is merely to use your calculator. If yous don't accept ane handy, you tin utilise long sectionalization or get the denominator equal to a multiple of 10, then move the decimal place of the numerator over.

For quick estimates of decimal to fraction conversions (or vice versa), you lot can await at our chart of common conversions and see which is closest to your figure to get a ballpark idea of its conversion value.

What'due south Side by side?

Want to know the fastest and easiest ways to catechumen betwixt Fahrenheit and Celsius? Nosotros've got yous covered! Cheque out our guide to the all-time ways to catechumen Celsius to Fahrenheit (or vice versa).

Are you learning nigh logarithms and natural logs in math class?Nosotros have a guide on all the natural log rules you need to know.

Did you know that h2o has a very special density? Check out our guide to acquire what the density of h2o is and how the density tin change.

Have friends who also need help with test prep? Share this article!

Near the Author

Christine graduated from Michigan State University with degrees in Environmental Biological science and Geography and received her Master'south from Duke University. In high schoolhouse she scored in the 99th percentile on the SAT and was named a National Merit Finalist. She has taught English and biology in several countries.

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Source: https://blog.prepscholar.com/convert-decimal-to-fraction

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