# "Effortlessly Convert Decimals to Fractions with Our Handy Calculator"

Get ready to convert decimal numbers with ease! This remarkable tool can seamlessly transform any decimal number into a fraction or a mixed number. To ensure accuracy when converting repeating decimals, simply enter the number of decimal places that repeat.

**Converting Repeating Decimals**

Take the repeating decimal 0.66666..., for example. If you want to convert it to a fraction, enter 0.6 and indicate 1 for the repeating decimal places. You will then get the answer 2/3. Another example is the repeating decimal 0.363636.... To convert it to a fraction, enter 0.36 and indicate 2 repeating decimal places. You will get the answer 4/11. For a repeating decimal like 1.8333..., enter 1.83 and indicate 1 repeating decimal place. You will get the answer 1 5/6. Lastly, to convert the repeating decimal 0.857142857142857142.... to a fraction, enter 0.857142 and indicate 6 repeating decimal places. You will get the answer 6/7.

## Converting Negative Decimals to Fractions

Don't be afraid to convert negative decimals! Simply remove the negative sign first, convert the positive value to a fraction, and then reapply the negative sign to the answer. Remember, if a = b, then it is true that -a = -b.

## Converting Decimals to Fractions

It's as easy as 1-2-3! Start by making a fraction with the decimal number as the numerator and 1 as the denominator. Then, remove the decimal places by multiplying both the numerator and denominator by 10 to the power of the number of decimal places. After that, reduce the fraction by finding the Greatest Common Factor (GCF) of the numerator and denominator, and divide both by the GCF. Finally, simplify the remaining fraction to a mixed number fraction if possible.

### Example: Convert 2.625 to a Fraction

1. Rewrite 2.625 as a fraction:

\( 2.625 = \dfrac \)

### 2. Multiply numerator and denominator by 10^3 = 1000 to eliminate the decimal places:

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

### 3. Find the GCF of 2625 and 1000 and reduce the fraction by dividing both numerator and denominator by the GCF = 125:

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

### 4. Simplify the improper fraction:

Simplify the improper fraction

With this calculator, anyone can convert decimal numbers to fractions and mixed numbers with ease!

Hence,

\( 2.625 = 2 \dfrac \)

Decimal to fraction conversion is an essential operation in many mathematical calculations. Consider an example where we need to convert 0.625 to a fraction. To convert this decimal to a fraction, we need to multiply 0.625 by 1000/1000, which results in 625/1000. Reducing this fraction gets 5/8.

## Convert a Repeating Decimal to a Fraction

Converting repeating decimals to fractions might seem like a challenging task, but it can be simplified by following a few steps. First, create an equation where x equals the repeating decimal number. Next, count the number of decimal places and label it as y. Finally, create another equation by multiplying both sides of the first equation with 10y. Subtract this equation from the first equation and solve for x, followed by the reduction of the fraction.

### Example: Convert repeating decimal 2.666 to a fraction

Let's consider an example to understand the conversion of a repeating decimal to a fraction. We need to convert 2.666 to a fraction. We create an equation so that x equals the decimal number:

- Equation 1: \( x = 2.\overline\)
- Upon counting, we observe that there are 3 digits in the repeating decimal group; therefore, y = 3. We can now create a second equation by multiplying both sides of the first equation by 1000:
- Equation 2: \( 1000 x = 2666.\overline\)
- Subtract Equation (1) from Equation (2) to get:

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

Solving for x gets us x = 2664/999, which upon reducing the fraction by using the Greatest Common Factor (GCF) 333, we get 8/3.

### Another Example: Convert repeating decimal 0.333 to a fraction

Let's consider another example of the conversion of a repeating decimal to a fraction. We need to convert repeating decimal 0.333 to a fraction. We create the first equation with x equal to the repeating decimal number:

- Equation 1: \( x = 0.333\)
- Three decimals repeat in this case, so y = 3. We can now create the second equation by multiplying both sides of the first equation by 1000:
- Equation 2: \( 1000 x = 333.\overline\)
- Subtract Equation (1) from Equation (2) to obtain:

999x = 333, which solves to get x = 333/999. Reducing the fraction leads to x = 1/3. Therefore, x = 0.333 = 1/3.

## Related Calculators

To convert a fraction to a decimal, check out the Fraction to Decimal Calculator.

References

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

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