put the steps in order for changing the repeating decimal, which is rational, to a ratio or fraction. 0.474747....= what fraction?
x=47/99
subtract x =0.474747...
100x=47.47474747...
x= 0.47474747...
99x=47
1. Write the repeating decimal as a variable (x) and set it equal to the fraction you want to find.
x = 0.474747...
2. Multiply both sides of the equation by 100 to eliminate the repeating decimal.
100x = 47.474747...
3. Subtract x from 100x to eliminate the repeating decimal on the right side.
100x - x = 47.474747... - 0.474747...
4. Simplify the equation.
99x = 47
5. Solve for x by dividing both sides of the equation by 99.
x = 47/99
Therefore, the fraction equivalent of the repeating decimal 0.474747... is 47/99.