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!