Decimal to Fraction Calculator

\[ 1.625 = 1 \frac<5> \]Showing the work Rewrite the decimal number as a fraction with 1 in the denominator\[ 1.625 = \frac \]Multiply to remove 3 decimal places. Here, you multiply top and bottom by 10 3 = 1000\[ \frac\times \frac= \frac \]Find the Greatest Common Factor (GCF) of 1625 and 1000, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 125,\[ \frac= \frac \]Simplify the improper fraction,\[ = 1 \frac<5> \]In conclusion,\[ 1.625 = 1 \frac<5> \]

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Calculator Use

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

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.

How to Convert a Decimal to a Fraction

Step 1: Make a fraction with the decimal number as the numerator (top number) and a 1 as the denominator (bottom number).
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 .
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.
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)

\( 2.625 = \dfrac<2.625> \)

2. Multiply numerator and denominator by by 10 3 = 1000 to eliminate 3 decimal places

\( \dfrac<2.625>\times \dfrac= \dfrac \)

3. Find the Greatest Common Factor (GCF) of 2625 and 1000 and reduce the fraction, dividing both numerator and denominator by GCF = 125

\( \dfrac<2625 \div 125>= \dfrac \) \( 2.625 = 2 \dfrac<5> \)

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

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 10 3 = 1000
Equation 2:

\( 1000 x = 2666.\overline <666>\)

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

\( 999 x = 2664 \)

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

\( \dfrac<2664 \div 333>= \dfrac \) \( 2.\overline <666>= 2 \dfrac \)

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 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.