Converting Recurring Decimals to Fractions
This page provides a comprehensive guide on converting recurring decimals to fractions. The method involves algebraic manipulation to transform repeating decimal numbers into their exact fractional equivalents.
The process begins by assigning a variable (typically x) to represent the recurring decimal. Then, the decimal is multiplied by powers of 10 to shift the decimal point and create equations that can be subtracted to eliminate the repeating part. This algebraic approach allows for solving the resulting equation to find the fractional representation.
Example: Converting 2.742424... to a fraction
- Let x = 2.742424...
- Multiply by 10: 10x = 27.42424...
- Multiply by 100: 100x = 274.2424...
- Multiply by 1000: 1000x = 2742.424...
- Subtract equations to eliminate recurring part
- Solve for x to get the fraction 2468/940
Highlight: The key to converting recurring decimals to fractions is identifying the repeating pattern and using algebraic manipulation to isolate it.
The page also includes additional examples:
- Converting 0.216 to a fraction
- Converting 0.43 to a fraction
- Converting 0.4333... to a fraction
Vocabulary: Recurring decimal - A decimal number in which a digit or group of digits repeats indefinitely after the decimal point.
These examples demonstrate the versatility of this method for different types of recurring decimals, including those with non-recurring parts before the repeating sequence.
Definition: Non-recurring part - The digits that appear before the repeating sequence in a recurring decimal.
By following these steps and practicing with various examples, students can master the skill of converting repeating decimals to fractions without relying on a calculator. This technique is valuable for precise calculations and understanding the relationship between decimal and fractional representations of numbers.
