Question

Put the steps in order for changing the repeating decimal, which is rational, to a
ratio or fraction. 0.474747... = what fraction? (5 points)
100x = 47.474747.
= x = 47/99
= 99x = 47
＝ x= 0.47474747...
= Subtract x = 0.474747..

Answer 1

To convert the repeating decimal \(0.474747...\) into a fraction, follow these ordered steps:

1. Let \( x = 0.474747...\).
2. Multiply both sides by 100 (since the decimal repeats every 2 digits):
\( 100x = 47.474747...\).
3. Subtract the original equation from this new equation to eliminate the repeating part:
\( 100x - x = 47.474747... - 0.474747...\).
This simplifies to:
\( 99x = 47\).
4. Solve for \( x \) by dividing both sides by 99:
\( x = \frac{47}{99}\).

Thus, the final answer is:
\( 0.474747... = \frac{47}{99} \).