1. What is the Repeating Decimal to Percent Conversion?

This calculator converts a fraction (a/b) to its equivalent repeating decimal and percentage form. Repeating decimals are numbers that continue infinitely with a repeating pattern, indicated by a bar (vinculum) over the repeating digits.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( d \) — Repeating decimal result
• \( a \) — Numerator of the fraction
• \( b \) — Denominator of the fraction

Explanation: The calculator first divides the numerator by the denominator to get the decimal representation, then multiplies by 100 to convert to percentage.

3. Importance of Repeating Decimal Conversion

Details: Understanding repeating decimals is fundamental in mathematics, especially when working with fractions, ratios, and percentages in real-world applications.

4. Using the Calculator

Tips: Enter the numerator and denominator (must be positive integers, denominator cannot be zero). The calculator will show both the repeating decimal representation and its percentage equivalent.

5. Frequently Asked Questions (FAQ)

Q1: What is bar notation?
A: Bar notation is a way to represent repeating decimals by placing a bar over the digits that repeat infinitely.

Q2: How do you convert 1/3 to percent?
A: 1 ÷ 3 = 0.333... (repeating) × 100 = 33.333...% (repeating).

Q3: What fractions produce repeating decimals?
A: Fractions whose denominators have prime factors other than 2 or 5 produce repeating decimals.

Q4: Can all repeating decimals be converted to fractions?
A: Yes, all repeating decimals are rational numbers and can be expressed as fractions.

Q5: How accurate is this calculator?
A: The calculator shows up to 10 decimal places and identifies repeating patterns for visualization.