# Calculator for Converting Decimals to Fractions

This tool is designed to help you convert decimal numbers to fractions or mixed numbers. If you're working with repeating decimals, you can enter the number of decimal places that repeat.

**How to Enter Repeating Decimals**

- If you have a repeating decimal like 0.66666... with the digit 6 repeating indefinitely, simply enter 0.6. Since only the trailing decimal place repeats, enter 1 for the number of decimal places to repeat. The answer is 2/3.
- If you have a repeating decimal like 0.363636... with the digits 36 repeating indefinitely, enter 0.36. Since the two trailing decimal places repeat, enter 2 for the number of decimal places to repeat. The answer is 4/11.
- If you have a repeating decimal like 1.8333... with the digit 3 repeating indefinitely, enter 1.83. Since only the trailing decimal place repeats, enter 1 for the number of decimal places to repeat. The answer is 1 5/6.
- If you have a repeating decimal like 0.857142857142857142..., enter 0.857142. Since the trailing six decimal places repeat, enter 6 for the number of decimal places to repeat. The answer is 6/7.

## Converting Negative Decimals to Fractions

Remember, if a = b, it is true that -a = -b.

## Converting Decimals to Fractions

### Example: Converting 2.625 to a Fraction

1. Rewrite the decimal number as a fraction (over 1): \( 2.625 = \dfrac \)

2. Multiply the numerator and denominator by 1000 to eliminate the three 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 125: \( \dfrac{2625 \div 125}{1000 \div 125} = \dfrac \)

4. Simplify the improper fraction if possible.

Remember, the goal is to convert your decimal numbers to fractions or mixed numbers accurately.

Henceforth,

\( 2.625 = 2 \dfrac \) Transformation from Decimal to Fraction- By way of illustration, transpose 0.625 into a fraction.
- Multiply 0.625/1 by 1000/1000 to retrieve 625/1000.
- By reducing, we achieve 5/8.

## Transmute a Repeating Decimal to a Fraction

### Illustration: Transmute the repeating decimal 2.666 into a fraction

1. Establish an equation where x equals the decimal number Equational Statement 1:\( x = 2.\overline \) 2. Ascertain the number of decimal places, y. The recurring decimal group contains 3 digits, thus y = 3. Generate a secondary equation by multiplying both sides of the initial equation by 103 = 1000 Equational Statement 2:

\( 1000 x = 2666.\overline \) 3. Deduct equation (1) from equation (2)

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

4. Determine the value of x

\( x = \dfrac \) 5. Simplify the fraction. Locate the Greatest Common Factor (GCF) of 2664 and 999 and simplify the fraction by dividing both the numerator and denominator by GCF = 333

\( \dfrac{2664 \div 333}{999 \div 333}= \dfrac \) Simplify the improper fraction

Therefore,

\( 2.\overline = 2 \dfrac \) Conversion of Repeating Decimal to Fraction- Consider another example: convert repeating decimal 0.333 into a fraction.
- Establish the first equation with x equating the repeating decimal number: x = 0.333
- There exist 3 recurring decimals. Generate the second equation by multiplying both sides of (1) by 103 = 1000: 1000X = 333.333 (2)
- Subtract equation (1) from (2) to obtain 999x = 333 and solve for x
- x = 333/999
- By simplifying the fraction, we deduce x = 1/3
- Conclusion: x = 0.333 = 1/3

## Associated Calculators

To transform a fraction into a decimal, consult the Fraction to Decimal Calculator.References Wikipedia contributors. "Repeating Decimal," Wikipedia, The Free Encyclopedia. Accessed on July 18, 2016.

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