Question

Put the steps in order for changing the repeating decimal, which is rational, to a ratio or fraction.
0.523523... = what fraction?
(5 points)

= Let x = 0.523523...
= 999x = 523


= x= 523/999


= Subtract 1x = 0.523523...
= 1000x = 523.523523.

Answer 1

To convert the repeating decimal \(0.523523...\) into a fraction, the steps should be arranged as follows:

1. **Let \( x = 0.523523...\)**
(Start by letting \(x\) represent the repeating decimal.)

2. **Multiply by 1000 to shift the decimal point:**
\(1000x = 523.523523...\)
(By multiplying by 1000, we align the repeating decimal.)

3. **Subtract the original \(x\) from this equation:**
\(1000x - x = 523.523523... - 0.523523...\)
(This helps to eliminate the repeating part.)

4. **Simplify the equation:**
\(999x = 523\)
(After subtraction, you obtain this equation.)

5. **Solve for \(x\):**
\(x = \frac{523}{999}\)
(Now rearrange to isolate \(x\) and express it as a fraction.)

So, the ordered steps to convert \(0.523523...\) into a fraction are:

1. Let \( x = 0.523523...\)
2. Multiply by 1000: \(1000x = 523.523523...\)
3. Subtract \(x\): \(999x = 523\)
4. Solve for \(x\): \(x = \frac{523}{999}\)