Put the steps in order for changing the repeating decimal, which is rational, to a ratio or fraction. 0.474747.... = what fraction?
what is the correct order?
subract x = 0.474747
100x=47.474747
x=47/99
x=0.47474747...
=99x=47
1. Start with the repeating decimal, 0.474747...
2. Let x be equal to the repeating decimal, so x = 0.474747...
3. Multiply both sides of the equation by 100 to eliminate the repeating decimal: 100x = 47.474747...
4. Subtract the original equation from the new equation to eliminate the repeating decimal: 100x - x = 47.474747 - 0.474747
5. Simplify the equation: 99x = 47
6. Divide both sides of the equation by 99 to solve for x: x = 47/99
7. The repeating decimal 0.474747... is equal to the fraction 47/99.
answer with the answer choices previously shown
Based on the answer choices previously shown, the correct order of steps is:
1. Subtract x = 0.474747...
2. Multiply both sides by 100: 100x = 47.474747...
3. Solve for x: x = 47/99
4. Rewrite x with the repeating decimal: x = 0.474747...
5. Multiply both sides by 99: 99x = 47
is that 100% the correct order?
Apologies for the confusion earlier. No, the order I provided was not 100% correct. Here is the correct order:
1. Start with the repeating decimal, 0.474747...
2. Let x be equal to the repeating decimal: x = 0.474747...
3. Multiply both sides of the equation by 100 to eliminate the repeating decimal: 100x = 47.474747...
4. Subtract the original equation (x = 0.474747...) from the new equation to eliminate the repeating decimal: 100x - x = 47.474747 - 0.474747
5. Simplify the equation: 99x = 47
6. Divide both sides of the equation by 99 to solve for x: x = 47/99
7. The repeating decimal 0.474747... is equal to the fraction 47/99.
The correct order of steps is:
1. Subtract x = 0.474747...
2. Multiply both sides by 100: 100x = 47.474747...
3. Subtract the original equation: 100x - x = 47.474747 - 0.474747
4. Simplify the equation: 99x = 47
5. Divide both sides by 99 to solve for x: x = 47/99
6. The repeating decimal, 0.474747..., is equal to the fraction 47/99.