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Decimal to Fraction Conversion:
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Decimal to fraction conversion is the process of expressing a decimal number as a simple fraction (a ratio of two integers). This is useful in many mathematical and real-world applications where fractions are preferred over decimal notation.
The calculator uses a continued fraction algorithm to find the best approximation:
Where:
Explanation: The algorithm successively approximates the decimal by testing increasingly precise fractions until the difference is within the specified tolerance.
Details: Fractions are often preferred in engineering, construction, and other fields where exact ratios are more meaningful than decimal approximations. They can also simplify further calculations.
Tips: Enter any decimal value and select the desired precision level. Higher precision will find more accurate fractions but may result in larger numerators and denominators.
Q1: Why doesn't my decimal convert exactly?
A: Many decimals (especially irrational numbers) cannot be expressed exactly as fractions with integer numerators and denominators. The calculator finds the best approximation within the specified tolerance.
Q2: What's the difference between precision levels?
A: Lower precision (e.g., 0.01) will find simpler fractions that are roughly correct. Higher precision (e.g., 0.000001) finds more exact fractions but they may be more complex.
Q3: Can this handle repeating decimals?
A: Yes, the algorithm can find exact fractions for repeating decimals if sufficient precision is selected.
Q4: What's the maximum denominator size?
A: There's no hard limit, but extremely precise conversions may result in very large denominators that are impractical.
Q5: How is this different from rounding?
A: This finds exact fractional representations rather than simply rounding to a certain number of decimal places.