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)

1. x=47/99
2. 99x=47
3. subtract x = 0.474747...
4. x = 0.47474747...
5. 100x = 47.474747...
put the numbers in order?

Answer 1

1. x = 0.474747...
2. Multiply both sides of the equation by 100 to eliminate the repeating decimal: 100x = 47.474747...
3. Subtract the initial equation from the new equation to eliminate the repeating decimal: 100x - x = 47.474747... - 0.474747...
4. Simplify the equation: 99x = 47
5. Solve for x: x = 47/99