Decimal to Fraction Calculator

How to Convert a Decimal to a Fraction?

Converting a decimal to a fraction is a simple process, but when dealing with infinite repeating decimals, the steps are slightly more complex. Here are the detailed steps for conversion:

1. Identify the type of decimal

• For terminating decimals (e.g., 0.75), simply express the decimal with a denominator that is a power of 10.
• For repeating decimals (e.g., 0.333...), a specific method must be used (Step 3).

2. Converting a terminating decimal to a fraction

1. Multiply the decimal by an appropriate power of 10 until no decimal places remain.
2. Write the result as a fraction, with the numerator as the multiplied result and the denominator as the corresponding power of 10.
3. Simplify the fraction to its lowest terms.

3. Converting a repeating decimal to a fraction

1. Set a variable: Let \( x \) be the repeating decimal (e.g., \( x = 0.666...\)).
2. Multiply by a power of 10: Multiply \( x \) by the appropriate power of 10 to shift the decimal point (e.g., \( 10x = 6.666...\)).
3. Subtract the original variable: Use \( 10x - x \) to eliminate the repeating part (e.g., \( 10x - x = 6.666... - 0.666... \)).
4. Solve the equation: Solve the resulting equation to obtain the fraction and simplify.

Examples

Example 1: Convert the terminating decimal 0.75 to a fraction.

Example 2: Convert the repeating decimal 0.333... to a fraction.

Example 3: Convert the repeating decimal 0.5833333... to a fraction.