## 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

- 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 10x.
- 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)

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

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

4. Simplify the improper fraction

Therefore,

#### 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 10y.
- 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:

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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:

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

We get

4. Solve for x

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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

Simplify the improper fraction

Therefore,

#### 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.