📚 Topic Summary
Converting repeating decimals to fractions algebraically involves setting the decimal equal to a variable (usually $x$), multiplying both sides by a power of 10 to shift the repeating part to the left of the decimal point, and then subtracting the original equation from the new equation. This eliminates the repeating decimal part, allowing you to solve for $x$ as a fraction in its simplest form. This method provides a precise and reliable way to express repeating decimals as fractions.
🧠 Part A: Vocabulary
Match each term with its definition:
| Term |
Definition |
| 1. Repeating Decimal |
A. A decimal representation of a rational number that eventually terminates or repeats. |
| 2. Fraction |
B. A decimal number that has digits that repeat indefinitely. |
| 3. Algebraic Method |
C. A way to solve a problem by using variables and equations. |
| 4. Terminating Decimal |
D. A number that represents a part of a whole, expressed as a ratio. |
| 5. Variable |
E. A symbol (usually a letter) that represents a value in an equation. |
(Match the correct letter to the number. For example: 1 - B)
✍️ Part B: Fill in the Blanks
To convert a repeating decimal to a fraction, first, let $x$ equal the ________ decimal. Next, multiply both sides of the equation by a power of ______ to shift the repeating part to the left of the decimal. Then, ________ the original equation from the new one. Finally, solve for $x$ to express the decimal as a ________.
🤔 Part C: Critical Thinking
Explain why multiplying by a power of 10 and then subtracting the original equation eliminates the repeating part of the decimal. Give a specific example to illustrate your explanation.