1. What is Decimal to Fraction Conversion?

Decimal to fraction conversion is the process of expressing a decimal number as a fraction (a ratio of two integers). The simplest form means the numerator and denominator have no common divisors other than 1.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

• \( d \) — Decimal number to convert
• \( a \) — Numerator of the fraction
• \( b \) — Denominator of the fraction
• \( g \) — Greatest common divisor of a and b

Explanation: The calculator first converts the decimal to a fraction, then simplifies it by dividing both numerator and denominator by their greatest common divisor (GCD).

3. Importance of Simplest Form

Details: Fractions in simplest form are easier to understand and work with in mathematical operations. They represent the most reduced form of the ratio between two numbers.

4. Using the Calculator

Tips: Enter any decimal number (positive or negative). The calculator will return either an integer or a fraction in simplest form. For repeating decimals, enter as many decimal places as possible for best accuracy.

5. Frequently Asked Questions (FAQ)

Q1: Can all decimals be converted to exact fractions?
A: Terminating decimals can be converted exactly. Repeating decimals can be converted to exact fractions using special methods. Irrational numbers cannot be converted to exact fractions.

Q2: How does the calculator handle repeating decimals?
A: The calculator uses a continued fraction algorithm that provides the best rational approximation within a certain tolerance.

Q3: What's the maximum decimal precision supported?
A: The calculator handles up to 15-16 significant digits, which is the limit of PHP's floating-point precision.

Q4: How are negative numbers handled?
A: Negative numbers are converted similarly to positive numbers, with the negative sign applied to the numerator.

Q5: What if I enter 0?
A: The calculator will return 0, which is already in its simplest form.