Question

Put the steps in order for changing the repeating decimal, which is rational, to a ratio or fraction. 0.474747.... = what COURSE TOOLS fraction? (5 points) 100x47.474747... Item 5 x=0.47474747... 99x = 47 Subtract x = 0.474747... x=47/99

Answer 1

To convert the repeating decimal \(0.474747...\) into a fraction, you can follow these steps in order:

1. **Let \( x = 0.474747...\)** (This represents the repeating decimal).

2. **Multiply both sides by 100:**
\( 100x = 47.474747...\)
(This shifts the decimal point two places to the right).

3. **Subtract the original equation from this new equation:**
\( 100x - x = 47.474747... - 0.474747...\)
This gives:
\( 99x = 47 \).

4. **Solve for \( x \):**
\( x = \frac{47}{99} \).

Putting it all together, the correct order of the steps is:

1. \( x = 0.474747...\)
2. \( 100x = 47.474747...\)
3. \( 99x = 47 \) (subtracting \( x = 0.474747...\) from both sides).
4. \( x = \frac{47}{99} \).

Thus, \( 0.474747... = \frac{47}{99} \).