Put the steps in order for changing the repeating decimal, which is rational, to a ratio or fraction. 0.474747.... = what fraction?
To convert the repeating decimal 0.474747... to a fraction, follow these steps in order:
1. Let x be the repeating decimal: x = 0.474747...
2. Multiply x by a power of 10 that eliminates the repeating decimal. Since the repeating part consists of two digits (47), multiply x by 100 to move the decimal point two places to the right: 100x = 47.474747...
3. Subtract the original equation from the one obtained in the previous step to eliminate the repeating part:
100x - x = 47.474747... - 0.474747...
This simplifies to: 99x = 47
4. Divide both sides of the equation by 99 to isolate x:
99x/99 = 47/99
This simplifies to: x = 47/99
Therefore, the fraction equivalent of the repeating decimal 0.474747... is 47/99.