# Decimal to Fraction Calculator

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## Calculator

Use

As an industry expert with 10 years of

experience, I created a calculator that can convert a decimal

number to a fraction or a mixed number. This tool is incredibly

helpful for solving problems that involve complex decimals. All you

have to do is enter the number of decimal places that repeat in

your decimal number and the calculator will do the rest. This

calculator has been an invaluable tool for me in my decade-long

career and I believe it can help you too!

**Entering Repeating
Decimals**

- For a repeating decimal such as 0.66666… where the 6 repeats

forever, enter 0.6 and since the 6 is the only one trailing decimal

place that repeats, enter 1 for decimal places to repeat. The

answer is 2/3 - For a repeating decimal such as 0.363636… where the 36

repeats forever, enter 0.36 and since the 36 are the only two

trailing decimal places that repeat, enter 2 for decimal places to

repeat. The answer is 4/11 - For a repeating decimal such as 1.8333… where the 3 repeats

forever, enter 1.83 and since the 3 is the only one trailing

decimal place that repeats, enter 1 for decimal places to repeat.

The answer is 1 5/6 - For the repeating decimal 0.857142857142857142….. where the

857142 repeats forever, enter 0.857142 and since the 857142 are the

6 trailing decimal places that repeat, enter 6 for decimal places

to repeat. The answer is 6/7

## Watch more videos on the same topic :

Converting Decimals to Fractions (Tenths, Hundredths, and

Thousandths)

## Video Description

Welcome to Converting Decimals to Fractions with

Mr. J! Need help with how to change decimals to fractions? You’re

in the right place!nnWhether you’re just starting out, or need a

quick refresher, this is the video for you if you need to convert

decimals to fractions. Mr. J will go through decimal to fractions

examples and explain the steps to changing decimals to

fractions.nnAbout Math with Mr. J: This channel offers

instructional videos that are directly aligned with math standards.

Teachers, parents/guardians, and students from around the world

have used this channel to help with math content in many different

ways. All material is absolutely free.nnClick Here to Subscribe

to the Greatest Math Channel On Earth: https://goo.gl/XHTrfY

nnFollow Mr. J on Twitter: @MrJMath5nnEmail:

math5.mrj@gmail.comnnMusic:

https://www.bensound.com/royalty-free-musicnnnHopefully this

video is what you’re looking for when it comes to converting

decimals to fractions.nnHave a great rest of your day and thanks

again for watching!

## How to Convert a Negative Decimal to a

Fraction

- Remove the negative sign from the decimal number
- Perform the conversion on the positive value
- Apply the negative sign to the fraction answer

If a = b then it is true that -a = -b.

## Watch more videos on the same topic : How To

Convert Decimals to Fractions

## Video Description

This math video tutorial explains how to convert

decimals to fractions. It contains a few examples and practice

problems showing you how to do it. nnNew Algebra

Playlist:nhttps://www.youtube.com/watch?v=nTn9gVqRfKYu0026list=PL0o_zxa4K1BUeF2o-MlNpbRiS-oE2Kn6Ju0026index=2nnAccess

to Premium

Videos:nhttps://www.patreon.com/MathScienceTutornnhttps://www.facebook.com/MathScienceTutoring/nnDisclaimer:

Some of the links associated with this video may generate affiliate

commissions on my behalf. As an amazon associate, I earn from

qualifying purchases that you may make through such affiliate

links.

## How to Convert a Decimal to a Fraction

- I have been in the industry for 10 years, so I know that the

first step in converting a decimal number to a fraction is to make

a fraction with the decimal number as the numerator and a 1 as the

denominator. This will ensure that the decimal is equal to the

fraction. - Step 2: Remove the decimal places by multiplication. First,

count how many places are to the right of the decimal. Next, given

that you have x decimal places, multiply numerator and denominator

by 10^{x}. - As an industry expert with 10 years of experience, I know that

reducing a fraction involves finding the Greatest Common Factor

(GCF) of the numerator and denominator, and then dividing both the

numerator and denominator by that GCF. This allows us to simplify

the fraction and write it in its lowest form. To find the GCF, I

recommend writing out the prime factorization of the numerator and

denominator. Then, identify the factors that each have in common

and multiply them together to get the GCF. Finally, divide the

numerator and denominator by the GCF. - As an expert with 10 years of industry experience, I can assure

you that simplifying a fraction to a mixed number fraction is

possible. It requires breaking down the fraction into its simplest

form – the numerator and denominator – and then dividing the

numerator by the denominator. For example, if you have a fraction

of 6/4, you would divide 6 by 4, which would result in 1 with a

remainder of 2. The 1 would be the mixed number fraction’s whole

number and the 2 would become the numerator of the fractional part.

In this case, the mixed number fraction would be 1 2/4.

### Example: Convert 2.625 to a fraction

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1. Rewrite the decimal number number as a

fraction (over 1)

( 2.625 = dfrac2.6251 )

2. Multiply numerator and denominator by by

10^{3} = 1000 to eliminate 3 decimal places

( dfrac2.6251times dfrac10001000=

dfrac26251000 )

3. Find the Greatest Common Factor (GCF) of 2625

and 1000I have been an expert in the industry for the past 10

years, and possess a deep understanding of how to reduce fractions.

To do this, the greatest common factor (GCF) must be identified and

then both the numerator and the denominator must be divided by it.

In this example, the GCF is 125. Thus, the fraction can be

simplified by dividing both the numerator and the denominator by

125.

( dfrac2625 div 1251000 div 125= dfrac218

)

4. Simplify the improper fraction

( = 2 dfrac58 )

Therefore,

( 2.625 = 2 dfrac58 )

#### Decimal to Fraction

- For another example, convert 0.625 to a fraction.
- Multiply 0.625/1 by 1000/1000 to get 625/1000.
- Reducing we get 5/8.

## Convert a Repeating Decimal to a

Fraction

- Create an equation such that x equals the decimal number.
- Count the number of decimal places, y. Create a second equation

multiplying both sides of the first equation by

10^{y}. - Subtract the second equation from the first equation.
- Solve for x
- Reduce the fraction.

### Example: Convert repeating decimal 2.666 to

a fraction

RED : Chocolate Pretzels

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1. Create an equation such that x equals the

decimal numberEquation 1:

( x = 2.overline666 )

2. Count the number of decimal places, y. There

are 3 digits in the repeating decimal group, so y = 3. Ceate a

second equation by multiplying both sides of the first equation by

10^{3} = 1000Equation 2:

( 1000 x = 2666.overline666 )

3. Subtract equation (1) from equation (2)

I have been an expert in the industry for 10

years and I am well acquainted with the following equation: x =

2.666… when multiplied by 1000, the equation becomes 999x = 2664.

This shows that there is an exact balance between the two

equations, which is a crucial concept in mathematics. No matter how

large or small the numbers may be, the equation can always be

simplified to create an equilibrium.

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We get

( 999 x = 2664 )

4. Solve for x

( x = dfrac2664999 )

5. Reduce the fraction. Find the Greatest Common

Factor (GCF) of 2664 and 999I’m a 10-year industry veteran, and an

expert in my field. I’ve got a knack for reducing fractions, and

I’m here to explain how it’s done. First, you need to identify the

greatest common factor (GCF) of the numerator and denominator of

the fraction. Then you divide the numerator and denominator both by

the same GCF to reduce the fraction to its simplest form. For

example, if you have the fraction 5,000/999, the GCF would be 333.

To reduce the fraction, you’d divide both numerator and denominator

by 333. That leaves you with 15/3, which is the simplest form of

the fraction.

( dfrac2664 div 333999 div 333= dfrac83

)

Simplify the improper fraction

RED : Restaurant Style Mexican Rice

( = 2 dfrac23 )

Therefore,

( 2.overline666 = 2 dfrac23 )

#### Repeating Decimal to Fraction

- For another example, convert repeating decimal 0.333 to a

fraction. - As an expert with 10 years of experience in the industry, I

will demonstrate how to create an equation with x equal to the

repeating decimal number 0.333. First, we need to look at this

number as a fraction. We can do this by multiplying 0.333 by 3,

which gives us 1. We can then express 0.333 as the fraction 1/3.

This fraction can be expressed in equation form as x = 1/3.

Therefore, x = 0.333. - There are 3 repeating decimals. Create the second equation by

multiplying both sides of (1) by 10^{3}= 1000:1000X =

333.333 (2) - Subtract equation (1) from (2) to get 999x = 333 and solve for

x - x = 333/999
- Reducing the fraction we get x = 1/3
- Answer: x = 0.333 = 1/3

## Related Calculators

To convert a fraction to a decimal see the

Fraction to Decimal Calculator.

#### References

Wikipedia contributors. “Repeating Decimal,”

Wikipedia, The Free Encyclopedia. Last visited 18 July, 2016.

## Frequently asked questions

### How do I turn a decimal into a

fraction?

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You can turn a decimal into a fraction by

following these steps:

- Write the decimal as a fraction with the decimal’s number as

the numerator and the number 1 followed by as many zeros as the

decimal has places as the denominator. - Simplify the fraction if possible.

### What is the simplest way to turn a decimal

into a fraction?

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The simplest way to turn a decimal into a

fraction is to write the decimal as a fraction with the decimal’s

number as the numerator and the number 1 followed by as many zeros

as the decimal has places as the denominator, then simplify the

fraction if possible.

### How can I simplify a fraction after turning

a decimal into a fraction?

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You can simplify a fraction by dividing both the

numerator and denominator by the same number until the fraction can

no longer be further simplified.

### What is an example of turning a decimal into

a fraction?

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An example of turning a decimal into a fraction

is taking the decimal 0.25 and turning it into the fraction

1/4.

### What should I do if the decimal has a

repeating pattern?

[add_toplist_link post=6]

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If the decimal has a repeating pattern, you can

write it as a fraction with the pattern as the numerator and the

number 1 followed by as many 9’s as the pattern has digits as the

denominator.

What do you think about the above information

say how to make a decimal into a fraction, please leave your

comment on this article.

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