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

How to Convert a Negative Decimal to a
Fraction

1. Remove the negative sign from the decimal number
2. Perform the conversion on the positive value
3. Apply the negative sign to the fraction answer

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

How to Convert a Decimal to a Fraction

1. 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.
2. 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.
3. 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.
4. 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
10³ = 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

1. Create an equation such that x equals the decimal number.
2. Count the number of decimal places, y. Create a second equation
   multiplying both sides of the first equation by
   10^y.
3. Subtract the second equation from the first equation.
4. Solve for x
5. 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
10³ = 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 10³ = 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.

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