QuestionApril 14, 2026

3. How is 0.0overline (25) written as a fraction in simplest form? Enter your answer in the box. square

3. How is 0.0overline (25) written as a fraction in simplest form? Enter your answer in the box. square
3. How is 0.0overline (25) written as a fraction in simplest form?
Enter your answer in the box.
square

Solution
4.3(341 votes)

Answer

\frac{25}{99} Explanation 1. Represent the repeating decimal Let x = 0.0\overline{25}. 2. Shift decimal to align repeats Multiply by 100: 100x = 25.0\overline{25}. 3. Subtract to eliminate repeating part 100x - x = 25.0\overline{25} - 0.0\overline{25} gives 99x = 25. 4. Solve for x x = \frac{25}{99}. 5. Simplify fraction \frac{25}{99} is already in simplest form.

Explanation

1. Represent the repeating decimal<br /> Let $x = 0.0\overline{25}$.<br />2. Shift decimal to align repeats<br /> Multiply by $100$: $100x = 25.0\overline{25}$.<br />3. Subtract to eliminate repeating part<br /> $100x - x = 25.0\overline{25} - 0.0\overline{25}$ gives $99x = 25$.<br />4. Solve for $x$<br /> $x = \frac{25}{99}$.<br />5. Simplify fraction<br /> $\frac{25}{99}$ is already in simplest form.
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