1. What Are Recurring Decimals?

Recurring decimals are numbers that have digits repeating infinitely after the decimal point. They are also known as repeating decimals. For example, 1/3 = 0.333... where the digit 3 repeats indefinitely.

2. How To Convert Recurring Decimals To Fractions

The conversion process involves algebra to eliminate the repeating part and solve for the fraction.

3. Conversion Formula

Example: Convert 0.4̅5̅ (or 0.(45)) to fraction:

1. Let x = 0.454545...
2. Multiply by 100 (two repeating digits): 100x = 45.454545...
3. Subtract original: 100x - x = 45.454545... - 0.454545...
4. 99x = 45
5. x = 45/99 = 5/11

4. Using The Calculator

Instructions: Enter the recurring decimal in any format:

• 0.333...
• 0.(3)
• 0.3̅ (using combining overline character)

The calculator will display the simplified fraction form.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between terminating and recurring decimals?
A: Terminating decimals have a finite number of digits (e.g., 0.5), while recurring decimals have repeating patterns (e.g., 0.333...).

Q2: Can all recurring decimals be converted to fractions?
A: Yes, all recurring decimals represent exact fractions and can be converted.

Q3: How to handle decimals with non-repeating and repeating parts?
A: The formula accounts for both parts. For example, 0.2333... = 7/30.

Q4: What about decimals with multiple repeating digits?
A: The method works the same way. For 0.142857142857... (1/7), the repeating block is 6 digits.

Q5: How to represent recurring decimals in different formats?
A: Common notations include ellipsis (0.333...), parentheses (0.(3)), or overline (0.3̅).