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... into a fraction, you can follow these steps:
Step 1: Let x be the repeating decimal: x = 0.474747...
Step 2: Multiply both sides of the equation by the power of 10 that eliminates the repeating part. In this case, we can multiply by 100 to get rid of the repeating part:
100x = 47.474747...
Step 3: Subtract the original equation (step 1) from the equation obtained in step 2 to eliminate the repeating part:
100x - x = 47.474747... - 0.474747...
99x = 47
Step 4: Solve for x by dividing both sides of the equation by 99:
x = 47/99
Therefore, the repeating decimal 0.474747... can be represented as the fraction 47/99.