To convert the repeating decimal $0.\overline{46}$ to a fraction, we can follow these steps:

Step 1: Set the repeating decimal equal to a variable.

Let $x = 0.\overline{46}$.

This means: $x = 0.46464646\ldots$

Step 2: Eliminate the repeating part by multiplying by an appropriate power of 10.

Since the repeating block "46" has two digits, multiply both sides of the equation by 100: $100x = 46.464646\ldots$

Step 3: Subtract the original equation from the new equation.

Now subtract the first equation $x = 0.464646\ldots$ from $100x = 46.464646\ldots$: $100x - x = 46.464646\ldots - 0.464646\ldots$ $99x = 46$

Step 4: Solve for $x$.

$x = \frac{46}{99}$

Step 5: Simplify the fraction.

The greatest common divisor (GCD) of 46 and 99 is 1, so the fraction is already in its simplest form.

Thus, the fraction representation of $0.\overline{46}$ is: $\boxed{\frac{46}{99}}$

Would you like a further breakdown or additional examples?

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Here are 5 questions to expand on this:

1. How would you convert $0.\overline{123}$ to a fraction?
2. What is the repeating decimal for $\frac{7}{11}$?
3. Can you explain why multiplying by powers of 10 helps remove the repeating part of a decimal?
4. What is the fraction for $0.\overline{7}$?
5. How can you convert a non-repeating decimal like $0.25$ to a fraction?

Tip: Always check if the resulting fraction can be simplified by finding the greatest common divisor (GCD) of the numerator and denominator.