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Convert Decimals to Fractions with Ease

The Decimal to Fraction Calculator is a tool designed to help you convert any terminating decimal number into its equivalent fraction, shown in both improper and mixed number forms. This calculator also provides a step-by-step breakdown of the conversion process.

🔄 How to Use the Calculator

Using this calculator is simple:

1. Enter the Decimal: Type the decimal number you want to convert into the input field. You can use positive or negative decimals (e.g., 3.14, -0.75, 12.0).
2. View Results: The calculator automatically processes your input and displays the results, including the simplified improper fraction, the simplified mixed number, and detailed calculation steps.

The calculator shows the main conversion path and offers a "Further explanation" section for a more detailed textual walkthrough.

🔢 The Conversion Process (for Terminating Decimals)

Here's how a terminating decimal is converted to a fraction:

1. Write as a Fraction: Write the decimal number as a fraction by placing it over a power of 10. The number of zeros in the denominator corresponds to the number of digits after the decimal point.
   Example: 2.475 has 3 decimal places, so it's 2475/1000. 0.5 has 1 decimal place, so it's 5/10.
2. Find the Greatest Common Divisor (GCD): Determine the GCD of the numerator and the denominator of this initial fraction. The GCD is the largest number that divides both without leaving a remainder.
3. Simplify: Divide both the numerator and the denominator by their GCD. This gives you the simplified improper fraction.
   Example: For 2475/1000, GCD is 25. So, (2475 ÷ 25) / (1000 ÷ 25) = 99/40.
4. Convert to Mixed Number (Optional): If the simplified fraction is improper (numerator > denominator), convert it to a mixed number.
   Example: 99/40 becomes 2 19/40 (since 99 ÷ 40 = 2 with a remainder of 19).

💡 Frequently Asked Questions (FAQ)

What is a terminating decimal?

A terminating decimal is a decimal number that has a finite number of digits after the decimal point (e.g., 0.25, 3.14159). This is different from a repeating decimal, which has a pattern of digits that repeats infinitely (e.g., 0.333...).

Why would I convert a decimal to a fraction?

Converting to a fraction is useful for precision, as it avoids rounding. It is also common in fields like cooking (e.g., ½ cup) and construction (e.g., ⅜ inch), where fractional measurements are standard.

Note: This calculator currently handles terminating decimals. Converting repeating decimals (e.g., 0.333...) requires a different method.