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Decimal to Fraction Calculator

Convert Decimal to Fraction


Answer:
\[ 1.625 = 1 \frac{5}{8} \]Showing the work

Rewrite the decimal number as a fraction with 1 in the denominator\[ 1.625 = \frac{1.625}{1} \]Multiplying by 1 to eliminate 3 decimal places, we multiply top and bottom by 103 = 1000\[ \frac{1.625}{1}\times \frac{1000}{1000}= \frac{1625}{1000} \]Find the Greatest Common Factor (GCF) of 1625 and 1000, if it exists, and reduce our fraction by dividing both numerator and denominator by it, GCF = 125,\[ \frac{1625 \div 125}{1000 \div 125}= \frac{13}{8} \]Simplifying the improper fraction,\[ = 1 \frac{5}{8} \]In conclusion,\[ 1.625 = 1 \frac{5}{8} \]

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Calculator Use

This calculator converts a decimal number to a fraction.

How many decimal places repeat? If you are converting a repeating decimal to a fraction, enter the number of decimal places that repeat.

For a repeating decimal such as 2.33333.... you can enter 2.3 and Trailing decimal places to repeat = 1.

Convert a Decimal to a Fraction

  1. Make a fraction with the decimal number as the numerator (top number) and a 1 as the denominator (bottom number).
  2. Remove the decimal places by multiplication: Count how many places are to the right of the decimal. If you have x decimal places then multiply numerator and denominator by 10x.
  3. Reduce the fraction: Find the Greatest Common Factor (GCF) of the numerator and denominator and reduce the fraction by dividing both numerator and denominator by the GCF.
  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:

\( x = 2.\overline{666}\tag{1} \)

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:

\( 1000 x = 2666.\overline{666}\tag{2} \)

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.



 

Cite this content, page or calculator as:

Furey, Edward "Decimal to Fraction Calculator"; from http://www.calculatorsoup.com - Online Calculator Resource.

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