Unlock the Power of Fractions with our Decimal to Fraction Calculator

Utilize our snazzy calculator and watch as decimal numbers morph into fractions or mixed numbers with ease! This amazing tool sees decimal numbers tremble in fear, cowering before its power of conversion. Simply input a decimal number, and voila! The calculator does the rest.

How to Enter Repeating Decimals

With repeating decimals, specify the number of decimal places that repeat. For instance, if you have 0.6666..., enter 0.6 and enter 1 for decimal places that repeat. You'll discover that the answer is 2/3. If you're working with 0.363636..., enter 0.36 and enter 2 for decimal places that repeat to reveal that the answer is 4/11. For a repeating decimal like 1.8333... containing 1 repeating decimal place, enter 1.83 and specify that 1 decimal place repeats to receive a fraction of 1 5/6. Lastly, for the repeating decimal of 0.857142857..., enter 0.857142 and choose 6 decimal places that repeat to get the solution of 6/7.

Converting Negative Decimals to Fractions

Convert the positive version of the decimal, then attach a negative sign to the resulting answer. For example, if you have -0.6, convert 0.6 to a fraction, which is 3/5, then tack on the negative sign to obtain -3/5.

Converting Decimals to Fractions

Follow these simple steps to convert your decimal to a fraction: first, utilize the decimal number as the numerator (top number) and a 1 as the denominator (bottom number) to make a fraction. Next, multiply both the numerator and denominator by 10 to the number of decimal places you have. Afterward, find the Greatest Common Factor (GCF) of the numerator and denominator and divide both by the GCF. Lastly, simplify the remaining fraction to a mixed number fraction if necessary, and voila!

Example: Converting 2.625 to a Fraction

1. Express the decimal as a fraction (over 1)

\( 2.625 = \dfrac \)

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

\( \dfrac\times \dfrac= \dfrac \)

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

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

4. Simplify the improper fraction using our handy calculator if needed.

Decimal to Fraction Conversion

Let us consider an example of conversion of 2.625 to a fraction. This can be written as 2 and 5/8. In order to convert 0.625 to a fraction, multiply it by 1000/1000 to get 625/1000. By reducing we get 5/8.

Conversion of Repeating Decimal to a Fraction

To convert a repeating decimal to a fraction, create an equation wherein x equals the decimal number. Count the number of decimal places, y, and create a second equation by multiplying both sides of the first equation by 10y. Subtract the second equation from the first equation and solve for x. Finally, reduce the fraction.

Example of converting 2.666 to a fraction:

1. Create an equation, x = 2.666666...

2. Count the number of repeating digits which is 3, and create a second equation by multiplying both sides of the first equation by 10^3 = 1000, so 1000x = 2666.666...

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

1000x - x = 2666.666... - 2.666666...

999x = 2664

4. Solve for x:

x = 2664/999

5. Reduce the fraction:

2664/999 = (8 x 333)/(3 x 333) = 8/3

Therefore, 2.666666... = 2 2/3.

Example of converting 0.333 to a fraction:

Create the first equation by equating x to the repeating decimal number, i.e., x = 0.333. There are three repeating decimals in this case. The second equation is obtained by multiplying both sides of the first equation by 10^3 = 1000, which gives 1000x = 333.333. By subtracting equation (1) from (2), we get 999x = 333, and solving for x gives x = 1/3. Thus, x = 0.333 = 1/3.

Related Calculators

To convert a fraction to a decimal, make use of the Fraction to Decimal Calculator.

References

Wikipedia contributors. "Repeating Decimal," Wikipedia, The Free Encyclopedia. Last visited 18 July, 2016.