Put the steps in order for changing the repeating decimal, which is rational, to a ratio or fraction. 0.523523... = what fraction? (5 points) Arrange responses in the correct order to answer the question. Select a response, navigate to the desired position and insert response at that position. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can be moved using the up and down arrow keys or by dragging with a mouse.
1. Recognize that the repeating decimal can be written in the form a.aaaa..., where "a" represents the repeated block of digits.
2. Let x be the repeating decimal. Multiply both sides of the equation by 1000 (or 10^n, where n is the number of digits in the repeating block) to eliminate the decimal places. This gives us 1000x = a.aaaa...
3. Subtract x from 1000x to eliminate the repeated block of digits on the right side of the equation. This gives us 1000x - x = a.aaaa... - x
4. Simplify the equation by combining like terms. This gives us 999x = a
5. Divide both sides of the equation by 999 to solve for x. This gives us x = a/999, which is the fraction equivalent of the repeating decimal 0.523523...