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The problem asks to demonstrate that \( 0.\overline{3} \times 3 = 1 \) given that \( \frac{1}{3} = 0.\overline{3} \).

### Solution:
1. **Understanding the repeating decimal**:
   \[
   0.\overline{3} \text{ means } 0.33333\ldots
   \]
   This is a repeating decimal that represents \( \frac{1}{3} \).

2. **Multiplying by 3**:
   \[
   0.\overline{3} \times 3 = \left(\frac{1}{3}\right) \times 3
   \]
   Since \( \frac{1}{3} \times 3 = 1 \), we conclude that:
   \[
   0.\overline{3} \times 3 = 1
   \]

Thus, the statement is correct, and \( 0.\overline{3} \times 3 = 1 \) is true.

Would you like further details or have any questions?

Here are some related questions:
1. What is a repeating decimal, and how is it represented?
2. How can you convert repeating decimals to fractions?
3. Why does multiplying \( \frac{1}{3} \) by 3 yield exactly 1?
4. How can you prove that \( 0.\overline{3} \) is equal to \( \frac{1}{3} \) using algebra?
5. What other fractions have repeating decimal representations?

**Tip:** When working with repeating decimals, multiplying or dividing by numbers that relate to the repeating part can often help to simplify the expression or convert it to a fraction.

Sachant que 1/3 = 0.3, démontre que 0.9 = 1.

Understand how to prove that the repeating decimal 0.9 equals 1, starting from the concept that 1/3 equals 0.3 repeating. This problem covers algebraic concepts and repeating decimals, suitable for students in Grades 6-8.

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