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...
Subtract x = 0.474747...
x = 47/99
99x=47
x = 0.47474747...
1. Set up an equation by multiplying the repeating decimal by a power of 10 that eliminates the repeating part.
2. Let x represent the repeating decimal.
3. Multiply both sides of the equation by 100 to create a whole number to the left of the decimal point.
4. Subtract the original repeating decimal from the equation to eliminate it.
5. Solve the resulting equation for x to find the fraction that represents the repeating decimal.
what order do i put them in though
Apologies for the confusion. Here are the steps in the correct order for changing the repeating decimal to a fraction:
1. Let x represent the repeating decimal.
2. Set up an equation by multiplying the repeating decimal by a power of 10 that eliminates the repeating part. In this case, multiply x by 100 to eliminate the repeating decimals: 100x = 47.474747...
3. Subtract the original repeating decimal from the equation to eliminate it: 100x - x = 47.474747... - 0.474747...
4. Simplify the equation: 99x = 47.000000...
5. Solve the resulting equation for x to find the fraction that represents the repeating decimal: x = 47/99
So, the decimal 0.474747... can be represented as the fraction 47/99.