Yes, $0.333\ldots$ (with the 3 repeating) is equal to $\frac{1}{3}$. Here's how you can demonstrate it:

1. Let $x = 0.333\ldots$.
2. Multiply both sides by 10: $10x = 3.333\ldots$.
3. Subtract the original equation from this result: $10x - x = 3.333\ldots - 0.333\ldots$.
4. Simplifying, you get $9x = 3$.
5. Divide both sides by 9: $x = \frac{3}{9} = \frac{1}{3}$.

Thus, $0.333\ldots = \frac{1}{3}$.

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Related Questions:

1. What is the decimal representation of $\frac{2}{3}$?
2. How do you convert repeating decimals to fractions?
3. What is the relationship between repeating decimals and rational numbers?
4. How does rounding affect repeating decimals in practical calculations?
5. Can repeating decimals be accurately represented in all numerical systems?

Tip: When dealing with repeating decimals, remember that they are often exact representations of fractions, which can be helpful in various mathematical contexts.