1. What is Decimal to Fraction Conversion?

Decimal to fraction conversion is the process of converting a decimal number to a fraction (a/b) that represents the same value. This can be done either exactly (for terminating decimals) or approximately (for repeating decimals or when simplified fractions are preferred).

2. How Does the Calculator Work?

The calculator uses two different methods:

Exact Conversion: For exact fractions, the calculator uses a continued fraction algorithm to find the precise fractional representation.

Approximate Conversion: For approximate fractions, the calculator matches the decimal to common fractions (like 1/2, 1/3, 1/4 etc.) with the closest value.

3. Importance of Fraction Conversion

Details: Fractions are often more intuitive than decimals in many practical applications like measurements, recipes, and construction. They can also represent exact values that decimals can only approximate (like 1/3).

4. Using the Calculator

Tips: Enter the decimal value you want to convert. Choose between exact fraction (for precise conversion) or approximate fraction (for simplified common fractions). The calculator will display the result in a/b format.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between exact and approximate fractions?
A: Exact fractions represent the precise decimal value, while approximate fractions use common simplified fractions that are close to the decimal value.

Q2: Can all decimals be converted to exact fractions?
A: Terminating decimals can be converted exactly. Repeating decimals can be converted exactly using specific methods. Irrational numbers cannot be converted to exact fractions.

Q3: Why would I use an approximate fraction?
A: Approximate fractions are often easier to work with in practical applications where exact precision isn't required, like measuring ingredients.

Q4: What's the maximum precision supported?
A: The calculator supports up to 6 decimal places for input. For exact fractions, it can handle denominators up to 1,000,000.

Q5: How are mixed numbers handled?
A: For values greater than 1, the calculator will return either an improper fraction or a mixed number depending on which is simpler.