To convert the decimal 0.41666666666 into a fraction:

1. Recognize the repeating decimal: \( 0.41666666666\ldots \) (where \( 6 \) repeats).
2. Let \( x = 0.41666666666\ldots \).
3. Multiply both sides by 10 to shift the decimal point: 
   \[ 10x = 4.1666666666\ldots \]
4. Subtract \( x \) from \( 10x \):
   \[ 10x - x = 4.1666666666\ldots - 0.4166666666\ldots \]
   \[ 9x = 3.75 \]
5. Solve for \( x \):
   \[ x = \frac{3.75}{9} = \frac{375}{1000} = \frac{5}{12} \]

Thus, \( 0.41666666666\ldots = \frac{5}{12} \).

Would you like a more detailed breakdown or have any questions?

Here are 5 related questions for practice:
1. Convert \( 0.3333\ldots \) into a fraction.
2. Express \( 0.727272\ldots \) as a fraction.
3. How do you convert a terminating decimal into a fraction?
4. What is the fraction representation of \( 0.8333\ldots \)?
5. Simplify \( \frac{24}{72} \).

**Tip:** Repeating decimals can always be written as fractions by using algebraic manipulation!

Learn how to convert the repeating decimal 0.41666666666 into a fraction. This solution demonstrates the use of algebraic manipulation, resulting in the fraction 5/12. Suitable for students in Grades 6-8.

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