1. What is Decimal to Fraction Conversion?

Decimal to fraction conversion is the process of converting a decimal number to its equivalent fractional representation. This is particularly useful in mathematics, engineering, and various scientific fields where exact fractional values are preferred over decimal approximations.

2. How Does the Calculator Work?

The calculator uses continued fractions to find the best rational approximation:

The algorithm:

• 1. Takes the decimal input
• 2. Finds the nearest integer ratio
• 3. Simplifies the fraction by dividing numerator and denominator by their GCD
• 4. Returns the simplest form of the fraction

3. Importance of Fraction Conversion

Details: Fractions provide exact values while decimals are often approximations. Many mathematical operations and measurements are more precise when expressed as fractions.

4. Using the Calculator

Tips: Enter any positive decimal number. The calculator will return the simplest fractional representation. For repeating decimals, enter as many decimal places as possible for best accuracy.

5. Frequently Asked Questions (FAQ)

Q1: Why convert decimals to fractions?
A: Fractions provide exact representations while decimals are often approximations. Many mathematical operations are more precise with fractions.

Q2: How accurate is the conversion?
A: The calculator provides the most accurate fractional representation within a tolerance of 1.e-6.

Q3: Can it handle repeating decimals?
A: Yes, if you enter enough decimal places, it will find the repeating pattern's fractional equivalent.

Q4: What's the maximum decimal input?
A: There's no strict maximum, but extremely large numbers may result in very large fractions.

Q5: Why does 0.5 return 1/2?
A: The calculator simplifies fractions to their lowest terms, so 0.5 becomes 1/2, not 5/10.