Converting 0.333... to a fraction using algebra: A Grade 8 example

📚 Quick Study Guide

🔢 Repeating Decimals to Fractions: To convert a repeating decimal to a fraction, use algebra to eliminate the repeating part. 💡 Steps:
• ✍️ Let $x$ equal the repeating decimal.
• ➗ Multiply both sides of the equation by a power of 10 so that one repeating block lines up.
• ➖ Subtract the original equation from the new equation to eliminate the repeating part.
• ➗ Solve for $x$.
• ➗ Simplify the resulting fraction if possible.

Practice Quiz

1. What is the first step in converting $0.333...$ to a fraction using algebra?
   1. Let $x = 0.333...$
   2. Multiply $0.333...$ by 100.
   3. Subtract $0.333...$ from 1.
   4. Divide $0.333...$ by 3.
2. If $x = 0.333...$, what is $10x$?
   1. $0.333...$
   2. $3.333...$
   3. $33.333...$
   4. $333.333...$
3. After setting $x = 0.333...$ and finding $10x$, what is the next step to eliminate the repeating decimal?
   1. Add $x$ and $10x$.
   2. Multiply $x$ and $10x$.
   3. Subtract $x$ from $10x$.
   4. Divide $10x$ by $x$.
4. What equation do you get when you subtract $x = 0.333...$ from $10x = 3.333...$?
   1. $9x = 3$
   2. $11x = 3.666...$
   3. $10x = 3$
   4. $9x = 0$
5. If $9x = 3$, what is the value of $x$?
   1. $x = 1$
   2. $x = 27$
   3. $x = \frac{1}{3}$
   4. $x = \frac{1}{9}$
6. In the fraction $\frac{3}{9}$, what is the greatest common factor (GCF) of the numerator and denominator?
   1. 1
   2. 3
   3. 9
   4. 27
7. What is the simplified fraction of $\frac{3}{9}$?
   1. $\frac{1}{9}$
   2. $\frac{1}{3}$
   3. $\frac{2}{3}$
   4. $\frac{3}{3}$