4.25 Percent As A Decimal

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Wondering how to convert decimals to fractions? Or how to convert fractions to decimals? It's easier than you think! Keep reading to see the steps for decimal to fraction conversions (including why you need to follow dissimilar steps if you lot accept a repeating decimal), steps for fraction to decimal conversions, a handy chart with mutual decimal/fraction conversions, and tips for quickly estimating conversions.

How to Convert Decimals to Fractions

How do y'all convert a decimal to a fraction? Any decimal, even complicated-looking ones, can be converted to a fraction; you lot but need to follow a few steps. Below nosotros explain how to convert both terminating decimals and repeating decimals to fractions.

Converting a Terminating Decimal to a Fraction

A terminating decimal is whatever decimal that has a finite other of digits. In other words, it has an end. Examples include .5, .234, .864721, etc. Terminating decimals are the almost mutual decimals you'll see and, fortunately, they are as well the easiest to convert to fractions.

Step 1

Write the decimal divided by i.

For example, say y'all're given the decimal .55.Your first step is to write out the decimal so it looks like ${.55}/{1}$.

Pace two

Side by side, you want to multiply both the acme and bottom of your new fraction by 10 for every digit to the left of the decimal indicate.

In our instance, .55 has 2 digits after the decimal bespeak, and then we'll desire to multiply the entire fraction by 10 ten 10, or 100. Multiplying the fraction by ${100}/{100}$ gives us ${55}/{100}$.

Step iii

The concluding pace is reducing the fraction to its simplest course. The simplest form of the fraction is when the meridian and bottom of the fraction are the smallest whole numbers they can be. For case, the fraction ${3}/{9}$ isn't in its simplest form because it tin notwithstanding be reduced down to ⅓ by dividing both the top and lesser of the fraction past 3.

The fraction ${55}/{100}$ can be reduced by dividing both the top and bottom of the fraction past 5, giving united states of america ${11}/{20}$. 11 is a prime number number and tin't be divided any more, 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.

Later on putting the decimal over 1, nosotros end up with ${.108}/{1}$.

Since .108 has three digits later the decimal identify, we need to multiply the entire fraction by 10 ten 10 x 10, or one thousand. This gives us ${108}/{chiliad}$.

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

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

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Converting a Repeating Decimal to a Fraction

A repeating decimal is one that has no end. Since you lot can't continue writing or typing the decimal out forever, they are frequently written as a cord of digits rounded off (.666666667) or with a bar above 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 simply dissimilar ways to show that the decimal is actually a cord of half-dozen'southward that goes on forever.

Step i

Let x equal the repeating decimal you're trying to convert, and place the repeating digit(southward).

So 10=.6667

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

Step ii

Multiply by any value of 10 you need to go the repeating digit(due south) on the left side of the decimal.

For .6667, we know that vi is the repeating digit. We desire that six on the left side of the decimal, which means moving the decimal place over one spot. And so we multiply both sides of the equation by (x 10 1) or 10.

10x = half-dozen.667

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

Step 3

Next we want to get an equation where the repeating digit is just to the correct of the decimal.

Looking at x = .6667, nosotros can come across that the repeating digit (six) is already only to the correct of the decimal, so we don't need to practise any multiplication. We'll go along this equation as ten = .6667

Step iv

Now nosotros need to solve for ten using our two equations, x = .667 and 10x = six.667.

10x - x =six.667-.667

9x = 6

x = ${6}/{9}$

10 = ⅔

Example

Catechumen i.0363636 to a fraction.

This question is a bit trickier, but we'll be doing the aforementioned steps that we did above.

First, make the decimal equal to x, and determine the repeating digit(south). x = ane.0363636 and the repeating digits are iii and 6

Next, get the repeating digits on the left side of the decimal (again, yous simply 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 ten 3) or 1000.

1000x = 1036.363636

Now get the repeating digits to the right of the decimal. Looking at the equation 10 = 1.0363636, yous tin come across that there currently is a zero between the decimal and the repeating digits. The decimal needs to be moved over one infinite, then both sides need to be multiplied by ten x 1.

10x = x.363636

Now apply the two equations, 1000x = 1036.363636 and 10x = ten.363636, to solve for x.

1000x - 10x = 1036.363636 - 10.363636

990x = 1026

x = ${1026}/{990}$

Since the numerator is larger than the denominator, this is known as an irregular fraction. Sometimes you can leave the fraction as an irregular fraction, or yous may be asked to catechumen it to a regular fraction. You can practise this by subtracting 990/990 from the fraction and making it a i that'll get next to the fraction.

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

x = 1 ${36}/{990}$

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

10 = 1 ${2}/{55}$

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How to Convert Fractions to Decimals

The easiest style to convert a fraction to a decimal is simply to use your calculator. The line betwixt the numerator and denominator acts as a sectionalization line, so ${vii}/{29}$ equals seven divided by 29 or .241.

If you don't have access to a reckoner though, you tin nonetheless catechumen fractions to decimals by using long segmentation or getting the denominator to equal a multiple of 10. We explain both these methods in this section.

Long Sectionalization Method

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

Here is what ${three}/{viii}$ looks like worked out with long division.

longdivision

⅜ converted to a decimal is .375

Denominator as a Value of ten Method

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

Step i

We want the denominator, in this case 8, to equal a value of 10. Nosotros can do this by multiplying the fraction by 125, giving the states ${375}/{1000}$.

Footstep 2

Adjacent nosotros desire to get the denominator to equal one so we can get rid of the fraction. We'll do this past dividing each function of the fraction by 1000, which means moving the decimal over iii places to the left.

This gives u.s. ${.375}/{1}$ or just .375, which is our answer.

Note that this method simply works for a fraction with a denominator that can easily be multiplied to exist a value of 10. Nevertheless, there is a trick you can utilise to estimate the value of fractions you can't convert using this method. Check out the case beneath.

Instance

Catechumen ⅔ to a decimal.

There is no number yous can multiply three by to make it an exact multiple of 10, simply you tin get shut.

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

999 is very close to m, then let's act like it really is 1000, divide each part of the fraction by 1000, and move the decimal place of 666 three places to the left, giving us .666

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

So whenever y'all have a fraction whose denominator can't easily be multiplied to a value of ten (this will happen to all fractions that convert to repeating decimals), just go the denominator as close to a multiple of 10 as possible for a close estimate.

Mutual Decimal to Fraction Conversions

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

Decimal	Fraction
0.03125	${1}/{32}$
0.0625	${i}/{16}$
0.1	${i}/{x}$
0.1111	${1}/{nine}$
0.125	${1}/{viii}$
0.16667	${1}/{vi}$
0.2	${1}/{5}$
0.2222	${2}/{nine}$
0.25	${one}/{iv}$
0.3	${3}/{10}$
0.3333	${one}/{three}$
0.375	${3}/{8}$
0.iv	${2}/{5}$
0.4444	${four}/{9}$
0.five	${i}/{two}$
0.5555	${5}/{9}$
0.vi	${3}/{5}$
0.625	${5}/{eight}$
0.6666	${2}/{3}$
0.7	${7}/{10}$
0.75	${iii}/{4}$
0.7777	${7}/{nine}$
0.8	${four}/{5}$
0.8333	${5}/{6}$
0.875	${vii}/{viii}$
0.8888	${8}/{9}$
0.9	${9}/{10}$

Summary: How to Brand a Decimal Into a Fraction

If you lot're trying to convert a decimal to fraction, beginning 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). In one case yous've done that, y'all can follow a few steps for the decimal to fraction conversion and for writing decimals equally fractions.

If you're trying to convert a fraction to decimal, the easiest way is just to employ your calculator. If you don't have one handy, you tin use long division or get 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 lot can expect at our chart of common conversions and see which is closest to your figure to go a ballpark thought of its conversion value.

What's Next?

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Nigh the Writer

Christine graduated from Michigan State University with degrees in Environmental Biology and Geography and received her Master's from Knuckles University. In loftier schoolhouse she scored in the 99th percentile on the Saturday and was named a National Merit Finalist. She has taught English and biological science in several countries.