How Do You Know Which Decimals Are Smaller and Larger

Wondering how to convert decimals to fractions? Or how to convert fractions to decimals? It's easier than y'all call up! Keep reading to see the steps for decimal to fraction conversions (including why you need to follow different steps if you have a repeating decimal), steps for fraction to decimal conversions, a handy chart with mutual decimal/fraction conversions, and tips for apace estimating conversions.

How to Convert Decimals to Fractions

How do you lot catechumen a decimal to a fraction? Whatsoever decimal, even complicated-looking ones, can be converted to a fraction; you but 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 whatsoever decimal that has a finite other of digits. In other words, it has an cease. Examples include .five, .234, .864721, etc. Terminating decimals are the most mutual decimals you'll see and, fortunately, they are also the easiest to convert to fractions.

Step i

Write the decimal divided by one.

For example, say yous're given the decimal .55.Your first footstep is to write out the decimal so it looks like ${.55}/{ane}$.

Step 2

Next, you want to multiply both the superlative and bottom of your new fraction by 10 for every digit to the left of the decimal point.

In our example, .55 has two digits subsequently the decimal signal, so we'll want to multiply the unabridged fraction past 10 x 10, or 100. Multiplying the fraction by ${100}/{100}$ gives us ${55}/{100}$.

Stride 3

The terminal step is reducing the fraction to its simplest grade. The simplest course of the fraction is when the meridian and bottom of the fraction are the smallest whole numbers they tin can be. For example, the fraction ${3}/{9}$ isn't in its simplest form because it tin can still exist reduced downward to ⅓ by dividing both the top and bottom of the fraction by 3.

The fraction ${55}/{100}$ tin can exist reduced by dividing both the meridian and bottom of the fraction by 5, giving us ${11}/{20}$. xi is a prime and can't exist divided whatever more than, so we know this is the fraction in its simplest form.

The decimal .55 is equal to the fraction ${11}/{20}$.

Example

Catechumen .108 to a fraction.

After putting the decimal over 1, nosotros finish upward with ${.108}/{one}$.

Since .108 has three digits later the decimal place, nosotros need to multiply the entire fraction by ten x 10 ten ten, or 1000. This gives u.s. ${108}/{1000}$.

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

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

Converting a Repeating Decimal to a Fraction

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

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

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

Step 1

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

So x=.6667

six is the repeating digit, and the stop of the decimal has been rounded up.

Step two

Multiply past any value of ten 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. Nosotros want that six on the left side of the decimal, which means moving the decimal identify over 1 spot. So we multiply both sides of the equation by (10 x ane) or x.

10x = half dozen.667

Note: You only want one "set" of repeating digit(southward) on the left side of the decimal. In this example, with six as the repeating digit, you merely want one half-dozen on the left of the decimal. If the decimal was 0.58585858, you lot'd just desire i set of "58" on the left side. If information technology helps, yous can picture all repeating decimals with the infinity bar over them, then .6667 would be$\ov {(.six)}$.

Step 3

Next nosotros desire to get an equation where the repeating digit is just to the right of the decimal.

Looking at ten = .6667, we can see that the repeating digit (half dozen) is already merely to the right of the decimal, so we don't need to practise any multiplication. We'll go on this equation every bit x = .6667

Footstep 4

At present we demand to solve for x using our two equations, x = .667 and 10x = 6.667.

10x - ten =6.667-.667

9x = 6

x = ${six}/{nine}$

10 = ⅔

Case

Convert 1.0363636 to a fraction.

This question is a bit trickier, simply we'll exist doing the same steps that we did to a higher place.

Kickoff, make the decimal equal to x, and determine the repeating digit(s). x = ane.0363636 and the repeating digits are 3 and 6

Next, get the repeating digits on the left side of the decimal (again, you only want one prepare of repeating digits on the left). This involves moving the decimal 3 places to the right, so both sides need to be multiplied by (ten x 3) or 1000.

1000x = 1036.363636

Now get the repeating digits to the right of the decimal. Looking at the equation x = 1.0363636, you can see that there currently is a zero between the decimal and the repeating digits. The decimal needs to be moved over one space, and so both sides need to exist multiplied past 10 x one.

10x = ten.363636

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

1000x - 10x = 1036.363636 - x.363636

990x = 1026

x = ${1026}/{990}$

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

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

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

${36}/{990}$ can be simplified by dividing it by xviii.

x = 1 ${2}/{55}$

How to Convert Fractions to Decimals

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

If you don't accept access to a estimator though, y'all tin can still convert fractions to decimals by using long sectionalisation or getting the denominator to equal a multiple of x. Nosotros explain both these methods in this section.

Long Division Method

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

Here is what ${3}/{eight}$ looks like worked out with long partition.

⅜ converted to a decimal is .375

Denominator equally a Value of 10 Method

Convert ${3}/{8}$ to a decimal.

Step 1

We want the denominator, in this instance 8, to equal a value of x. We can do this by multiplying the fraction past 125, giving united states of america ${375}/{chiliad}$.

Step ii

Side by side we want to get the denominator to equal one so nosotros tin become rid of the fraction. We'll do this by dividing each function of the fraction past chiliad, which means moving the decimal over iii places to the left.

This gives us ${.375}/{1}$ or but .375, which is our answer.

Note that this method only works for a fraction with a denominator that can hands be multiplied to be a value of 10. However, there is a fob you can use to estimate the value of fractions yous tin't convert using this method. Bank check out the case below.

Case

Convert ⅔ to a decimal.

At that place is no number yous tin multiply three by to make information technology an verbal multiple of 10, simply y'all tin get close.

Past multiplying ⅔ by ${333}/{333}$, we get ${666}/{999}$.

999 is very close to 1000, so let's deed like it actually is chiliad, separate each part of the fraction by 1000, and movement the decimal place of 666 three places to the left, giving us .666

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

And so whenever you have a fraction whose denominator can't easily be multiplied to a value of 10 (this will happen to all fractions that convert to repeating decimals), simply get the denominator as close to a multiple of 10 as possible for a shut guess.

Mutual Decimal to Fraction Conversions

Below is a chart with mutual decimal to fraction conversions. You don't need to memorize these, simply knowing at least some of them off the top of your head will arrive piece of cake to do some common conversions. If you lot're trying to convert a decimal or fraction and don't accept a computer, you tin also see which value in this chart the number is closest to and then you lot can brand an educated estimate of the conversion.

Decimal	Fraction
0.03125	${1}/{32}$
0.0625	${1}/{16}$
0.1	${1}/{x}$
0.1111	${1}/{ix}$
0.125	${one}/{viii}$
0.16667	${1}/{half dozen}$
0.2	${ane}/{v}$
0.2222	${two}/{9}$
0.25	${1}/{4}$
0.three	${3}/{ten}$
0.3333	${one}/{3}$
0.375	${3}/{8}$
0.four	${2}/{five}$
0.4444	${4}/{nine}$
0.five	${1}/{two}$
0.5555	${5}/{9}$
0.6	${3}/{5}$
0.625	${5}/{8}$
0.6666	${2}/{3}$
0.7	${7}/{ten}$
0.75	${three}/{four}$
0.7777	${7}/{9}$
0.8	${4}/{five}$
0.8333	${5}/{half dozen}$
0.875	${7}/{8}$
0.8888	${viii}/{nine}$
0.9	${9}/{ten}$

Summary: How to Make a Decimal Into a Fraction

If you lot're trying to convert a decimal to fraction, first you demand to determine if it's a terminal decimal (1 with an stop) or a repeating decimal (one with a digit or digit that repeats to infinity). Once you lot've done that, you can follow a few steps for the decimal to fraction conversion and for writing decimals as fractions.

If y'all're trying to convert a fraction to decimal, the easiest way is just to use your calculator. If y'all don't take i handy, y'all can use long division or go the denominator equal to a multiple of ten, then move the decimal place of the numerator over.

For quick estimates of decimal to fraction conversions (or vice versa), you can look at our nautical chart of mutual conversions and run across which is closest to your effigy to get a ballpark idea of its conversion value.

What's Next?

Want to know the fastest and easiest ways to convert between Fahrenheit and Celsius? We've got you covered! Check out our guide to the best ways to convert Celsius to Fahrenheit (or vice versa).

Are you learning about logarithms and natural logs in math class?We have a guide on all the natural log rules you demand to know.

Did you know that water has a very special density? Check out our guide to learn what the density of water is and how the density can alter.

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

About the Author

Christine graduated from Michigan State University with degrees in Environmental Biology and Geography and received her Master'south from Duke University. In high school 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.

obrienmantion1944.blogspot.com

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

Share this post