Put the steps in order for changing the repeating decimal, which is rational, to a ratio or fraction. 0.474747.... = what fraction?(5 points)

Question

x = 47/99
100x = 47.474747
Subtract x = 0.474747
x = 0.47474747
99x = 47

Answer 1

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

1. Let \(x\) represent the repeating decimal:
   \(x = 0.474747...\)

2. Multiply \(x\) by 100 (to shift the decimal point two places over):
   \(100x = 47.474747...\)

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

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

So, the order of the steps is:

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

Thus, the repeating decimal \(0.474747...\) as a fraction is \(\frac{47}{99}\).