0.18 with just the 8 repeating as a fraction

The decimal \( 0.18\overline{8} \) (with the 8 repeating) can be converted to a fraction as follows:

Let \( x = 0.18\overline{8} \).

### Step 1: Multiply by 10 to move the decimal point one place right.
\[ 10x = 1.8\overline{8} \]

### Step 2: Multiply by 100 to move the decimal point two places right.
\[ 100x = 18.8\overline{8} \]

### Step 3: Subtract the two equations.
Subtract \( 10x = 1.8\overline{8} \) from \( 100x = 18.8\overline{8} \):
\[
100x - 10x = 18.8\overline{8} - 1.8\overline{8}
\]
\[
90x = 17
\]

### Step 4: Solve for \( x \).
\[
x = \frac{17}{90}
\]

So, \( 0.18\overline{8} \) as a fraction is \( \frac{17}{90} \).

Would you like further details on this process or have any questions?

Here are 5 related questions to extend this topic:
1. How do you convert a non-repeating decimal to a fraction?
2. How do you convert other repeating decimals to fractions, like \( 0.2\overline{7} \)?
3. What is the difference between a repeating and terminating decimal?
4. How do you simplify a fraction?
5. How do you convert a fraction back into a decimal?

**Tip:** When converting repeating decimals to fractions, identifying the repeating part of the decimal early helps simplify the process.

Learn how to convert the repeating decimal 0.18 with the 8 repeating to a fraction. This step-by-step guide walks you through using algebraic equations to solve for the fraction form of repeating decimals. Suitable for students in Grades 7-10.

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