1. What is Fractional Notation?

Fractional notation represents a number as a ratio of two integers (a numerator and denominator). It provides an exact representation of rational numbers, unlike decimal approximations.

2. How Does the Calculator Work?

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

Where:

• \( d \) — Decimal input value
• \( a \) — Integer numerator
• \( b \) — Integer denominator

Algorithm: The calculator uses a continued fraction approach with adjustable precision to find the simplest fraction that matches the decimal within the specified tolerance.

3. Importance of Fractional Notation

Details: Exact fractional notation is crucial in mathematics, engineering, and sciences where decimal approximations can lead to cumulative errors in calculations.

4. Using the Calculator

Tips: Enter the decimal value and select precision level. Higher precision will find more accurate fractions but may result in larger numerators/denominators.

5. Frequently Asked Questions (FAQ)

Q1: Why can't some decimals be converted exactly?
A: Irrational numbers (like π or √2) cannot be expressed as exact fractions - the calculator finds the best approximation within the specified precision.

Q2: What's the difference between low and high precision?
A: Low precision (1/100) finds simpler fractions, while high precision (1/1,000,000) finds more accurate but potentially complex fractions.

Q3: How does this relate to reducing fractions?
A: The calculator automatically provides fractions in their simplest form (lowest terms).

Q4: Can this handle repeating decimals?
A: Yes, the algorithm can find exact fractional representations of repeating decimals like 0.333... = 1/3.

Q5: What's the largest denominator this can handle?
A: The calculator can handle denominators up to 1,000,000, though extremely precise conversions may require manual algebraic methods.