put the steps in order for changing the repeating decimal, which is rational to a ratio or fraction. 0.474747....= what fraction?
=subtract x=0.474747...
=100x=47.474747...
=99x=47
=x=0.47474747...
=x=47/99
1. Set the repeating decimal equal to a variable (e.g., x).
2. Multiply both sides of the equation by 100 to move the decimal point two places to the right (since there are two repeating digits).
3. Subtract the original equation from the equation in step 2 to eliminate the repeating part of the decimal.
4. Simplify the resulting equation to solve for x.
5. Write the value of x as a fraction by putting the numerator as the resulting equation's constant and the denominator as the number of repeating digits (in this case, 99).
Therefore, 0.474747... is equal to the fraction 47/99.