1. What is a Repeating Decimal?

A repeating decimal is a decimal number that after some point has a digit or group of digits that repeat infinitely. For example, 1/3 = 0.333... (repeating "3") or 1/7 = 0.142857142857... (repeating "142857").

2. How Does the Calculator Work?

The calculator uses the following mathematical principles:

Where:

• Numerator — The top number in the fraction
• Denominator — The bottom number in the fraction

Explanation: The calculator performs long division to determine the decimal representation and identifies repeating patterns by tracking remainders.

3. Importance of Repeating Decimals

Details: Understanding repeating decimals is fundamental in mathematics, particularly in number theory and when working with rational numbers. They help in precise calculations and conversions between fraction and decimal representations.

4. Using the Calculator

Tips: Enter positive integers for both numerator and denominator. The calculator will show the exact decimal representation with repeating portions in parentheses.

5. Frequently Asked Questions (FAQ)

Q1: What makes a decimal repeat?
A: A fraction in lowest terms has a repeating decimal if and only if its denominator has a prime factor other than 2 or 5.

Q2: How do you find the length of the repeating part?
A: For denominator d, the length of the repetend is the smallest number n such that d divides 10^n - 1.

Q3: Are all fractions repeating decimals?
A: All fractions are either terminating or repeating decimals. Terminating decimals have denominators (in lowest terms) with only 2 and 5 as prime factors.

Q4: What's the difference between repeating and recurring decimals?
A: They mean the same thing - a decimal with an infinitely repeating sequence of digits.

Q5: Can irrational numbers be repeating decimals?
A: No, irrational numbers have decimal expansions that neither terminate nor become periodic.