Decimal to Fraction Calculator

Calculating machine Use

This computer converts a decimal number to a fraction or a decimal number to a mixed issue. For repeating decimals move into how many decimal places in your decimal numerate repeat.

Ingress Repeating Decimals

  • For a repetition decimal such A 0.66666... where the 6 repeats eternally, enter 0.6 and since the 6 is the only one tracking decimal fraction place that repeats, get into 1 for decimal places to repeat. The solution is 2/3
  • For a repeating decimal such as 0.363636... where the 36 repeats forever, enter upon 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 repetition decimal much as 1.8333... where the 3 repeats forever, go in 1.83 and since the 3 is the only one trailing decimal place that repeats, enter 1 for decimal places to repeat. The response is 1 5/6
  • For the repetition decimal 0.857142857142857142..... where the 857142 repeats forever, enter 0.857142 and since the 857142 are the 6 trailing decimal places that repeat, accede 6 for decimal places to reprise. The solution is 6/7

How to Convert a Negative Decimal to a Fraction

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

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

How to Convert a Decimal to a Fraction

  1. Gradation 1: Make a fraction with the decimal amoun as the numerator (top amoun) and a 1 as the denominator (bottom numeral).
  2. Ill-use 2: Remove the denary places by multiplication. First, count how umpteen places are to the right of the decimal. Next, given that you have x decimal places, procreate numerator and denominator past 10x.
  3. Step 3: Reduce the divide. Regain the Greatest Common Factor (GCF) of the numerator and denominator and divide both numerator and denominator aside the GCF.
  4. Step 4: Simplify the remaining fraction to a mixed number fraction if viable.

Example: Convert 2.625 to a fraction

1. Revision the decimal numerate identification number as a divide (over 1)

\( 2.625 = \dfrac{2.625}{1} \)

2. Multiply numerator and denominator by by 103 = 1000 to reject 3 decimal places

\( \dfrac{2.625}{1}\times \dfrac{1000}{1000}= \dfrac{2625}{1000} \)

3. Feel the Highest common factor (GCF) of 2625 and 1000 and reduce the fraction, dividing both numerator and denominator by GCF = 125

\( \dfrac{2625 \div 125}{1000 \div 125}= \dfrac{21}{8} \)

4. Simplify the out-of-the-way fraction

\( = 2 \dfrac{5}{8} \)

Therefore,

\( 2.625 = 2 \dfrac{5}{8} \)

Decimal fraction to Divide

  • For another example, convert 0.625 to a fraction.
  • Multiply 0.625/1 by 1000/1000 to draw 625/1000.
  • Reduction we father 5/8.

Convert a Repeating Decimal to a Fraction

  1. Produce an equation such that x equals the decimal number.
  2. Count the number of decimal fraction places, y. Create a second equation multiplying both sides of the first par aside 10y.
  3. Subtract the second equation from the first equation.
  4. Solve for x
  5. Cut down the fraction.

Example: Win over circulating decimal 2.666 to a fraction

1. Create an equation such that x equals the decimal issue
Equation 1:

\( x = 2.\overline{666} \)

2. Count the number of decimal places, y. There are 3 digits in the recurring decimal group, so y = 3. Ceate a back equation aside multiplying both sides of the primary equation past 103 = 1000
Equality 2:

\( 1000 x = 2666.\overline{666} \)

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

\( \eqalign{1000 x &= &\hfill2666.666...\cr x &= &ere;\hfill2.666...\cr \hline 999x &= &2664\atomic number 24} \)

We get

\( 999 x = 2664 \)

4. Lick for x

\( x = \dfrac{2664}{999} \)

5. Reduce the fraction. Find the Greatest Common Factor in (GCF) of 2664 and 999 and reduce the fraction, dividing both numerator and denominator by GCF = 333

\( \dfrac{2664 \div 333}{999 \div 333}= \dfrac{8}{3} \)

Simplify the improper fraction

\( = 2 \dfrac{2}{3} \)

Therefore,

\( 2.\overline{666} = 2 \dfrac{2}{3} \)

Repetition Quantitative to Fraction

  • For another example, convert repeating quantitative 0.333 to a fraction.
  • Create the first par with x equal to the repeating decimal telephone number:
    x = 0.333
  • There are 3 repeating decimals. Create the moment equation away multiplying some sides of (1) aside 103 = 1000:
    1000X = 333.333 (2)
  • Deduct equality (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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