https://file.aiquickdraw.com/mathbot/file/1726432416486gq084ndx.jpg

In this image, you are being asked to express 4.135135... as a fraction. The repeating decimal 4.135135... has a repeating block of "135". To convert this repeating decimal into a fraction, let's follow the steps:

### Step 1: Let \( f = 4.135135135... \).

### Step 2: Multiply both sides by 1,000 (since the repeating block has 3 digits):
\[
1000f = 4135.135135135...
\]

### Step 3: Subtract the first equation from the second:
\[
1000f - f = 4135.135135135... - 4.135135135...
\]
\[
999f = 4131
\]

### Step 4: Solve for \( f \):
\[
f = \frac{4131}{999}
\]

So, the fraction representation of 4.135135... is \( \frac{4131}{999} \).

This fraction can be simplified further, but the instructions say not to worry about simplifying. The result as given is \( \frac{4131}{999} \).

Would you like to see how to simplify this fraction or go through any more details? 

Here are five related questions you might explore:
1. How can you simplify \( \frac{4131}{999} \)?
2. How do you convert any repeating decimal to a fraction?
3. What is the significance of repeating blocks in decimals?
4. How do you handle repeating decimals with more complex patterns?
5. What are examples of real-life uses for repeating decimals?

**Tip**: When converting repeating decimals to fractions, the length of the repeating block determines the power of 10 you multiply by (e.g., 3 digits = multiply by 1,000).

Write 4.135 as a fraction. The repeating decimal is 4.135135135...

Learn how to convert the repeating decimal 4.135135... into a fraction using simple algebraic methods. Step-by-step solution showing how to represent repeating decimals as fractions, suitable for Grades 7-9.

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