Decimal to Fraction Calculator (2024)

Calculator Use

This calculator converts a decimal number to a fraction or a decimal number to a mixed number. For repeating decimals enter how many decimal places in your decimal number repeat.

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. Step 1: Make a fraction with the decimal number as the numerator (top number) and a 1 as the denominator (bottom number).
  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 10x.
  3. Step 3: Reduce the fraction. Find the Greatest Common Factor (GCF) of the numerator and denominator and divide both numerator and denominator by the GCF.
  4. Step 4: Simplify the remaining fraction to a mixed number fraction if possible.

Example: Convert 2.625 to a fraction

1. Rewrite the decimal number number as a fraction (over 1)

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

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

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

3. Find the Greatest 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 improper fraction

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

Therefore,

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

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 10y.
  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

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

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

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 = 1000
Equation 2:

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

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

\( \eqalign{1000 x &= &\hfill2666.666...\cr x &= &\hfill2.666...\cr \hline 999x &= &2664\cr} \)

We get

\( 999 x = 2664 \)

4. Solve for x

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

5. Reduce the fraction. Find the Greatest Common Factor (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,

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

Repeating Decimal to Fraction

  • For another example, convert repeating decimal 0.333 to a fraction.
  • Create the first equation with x equal to the repeating decimal number:
    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.

Decimal to Fraction Calculator (2024)

FAQs

How to convert decimals to fractions? ›

Decimals can be written in fraction form. To convert a decimal to a fraction, place the decimal number over its place value. For example, in 0.6, the six is in the tenths place, so we place 6 over 10 to create the equivalent fraction, 6/10. If needed, simplify the fraction.

What is 2.8 as a fraction? ›

Answer and Explanation:

2.8 as a fraction is 2 4/5. When you say 2.8 out loud, you hear: ''2 and 8 tenths''. This can also be written as a mixed number of 2 8/10. So 8/10 is your basic fraction, but it's always important to reduce a fraction to its simplest form.

How to write a repeating decimal as a fraction? ›

To start, set the decimal equal to a variable. Multiply the decimal by 10 and subtract the original decimal from it. Finally, divide both sides by 9 to obtain the fractional form of the decimal. For example, 0.7 repeating would be 7/9, and 1.2 repeating would be 11/9.

How convert numbers into decimal fraction? ›

This means that all fractions can be converted into decimals by dividing the numerator by the denominator. For example, the fraction 45 represents “4 out of 5,” or 4 divided by 5. This fraction can be converted into a decimal by dividing 4 by 5.

Is .75 as a fraction? ›

Answer: 0.75 can be expressed as 3/4 in the form of a fraction.

Is 0.75 a decimal fraction? ›

Answer: 0.75 as a fraction is 3/4.

How to convert 0.33333 into a fraction? ›

Answer: 0.33333 as a fraction is 1/3.

What is 0.5 as a fraction? ›

Answer: 0.5 as a fraction is written as 1/2.

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