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). This is useful in many mathematical and real-world applications where fractions are preferred over decimals.

2. How Does the Conversion Work?

The conversion uses the following mathematical relationship:

Where:

• \( d \) — Decimal number to convert
• \( a \) — Numerator of the resulting fraction
• \( b \) — Denominator of the resulting fraction

Explanation: The algorithm finds the simplest fraction that accurately represents the decimal value using continued fractions.

3. Common Decimal to Fraction Examples

Common Conversions:

• 0.5 = 1/2
• 0.25 = 1/4
• 0.75 = 3/4
• 0.333... = 1/3
• 0.666... = 2/3
• 0.125 = 1/8
• 0.375 = 3/8

4. Using the Calculator

Tips: Enter any positive decimal value. The calculator will find the simplest fraction representation. 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 algebraic methods. Irrational numbers cannot be exactly represented as fractions.

Q2: How accurate is the conversion?
A: The calculator uses a tolerance of 0.000001 (1e-6) to find the simplest fraction within that accuracy.

Q3: What about negative decimals?
A: The calculator handles positive decimals only. For negative values, convert the absolute value then apply the negative sign to the numerator.

Q4: Why would I need to convert decimals to fractions?
A: Fractions are often preferred in measurements, cooking, construction, and when exact ratios are needed.

Q5: How does the calculator simplify fractions?
A: It uses the continued fractions algorithm to find fractions with the smallest denominators that meet the accuracy requirement.