1. What Is Decimal = Numerator / Denominator?

This calculator converts between fractions and decimals using the fundamental mathematical relationship: Decimal = Numerator / Denominator. It helps users easily convert between these two representations of numbers.

2. How Does The Calculator Work?

The calculator uses the basic mathematical formula:

Where:

• Numerator — The top number in a fraction
• Denominator — The bottom number in a fraction
• Decimal — The result of the division

Explanation: The calculator can work in both directions - converting fractions to decimals and decimals to simplified fractions.

3. Importance Of Decimal-Fraction Conversion

Details: Understanding the relationship between fractions and decimals is fundamental in mathematics, engineering, and many practical applications. This conversion is essential for accurate calculations and measurements.

4. Using The Calculator

Tips: Enter any two values to calculate the third. For fraction to decimal conversion, enter numerator and denominator. For decimal to fraction conversion, enter the decimal value and click "Calculate Fraction".

5. Frequently Asked Questions (FAQ)

Q1: What if the denominator is zero?
A: Division by zero is undefined in mathematics. The calculator will display an error message if you attempt to divide by zero.

Q2: How accurate is the fraction conversion?
A: The calculator uses a continued fraction algorithm to find the most accurate fraction representation within a tolerance of 1e-6.

Q3: Can I convert repeating decimals?
A: Yes, the algorithm can handle repeating decimals and will find the appropriate fraction representation.

Q4: What about negative numbers?
A: The calculator handles negative numbers correctly, maintaining the proper sign in both fraction and decimal forms.

Q5: Are there limitations to this conversion?
A: For extremely large or small numbers, there may be precision limitations due to floating point arithmetic constraints.