Find nine rational nember between 0 and 0.1.

Explanation

To find nine rational numbers between 0 and 0.1, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Range**: We need to find rational numbers between 0 and 0.1.

2. **Convert 0.1 to a Fraction**:
- We can express 0.1 as a fraction.
- \(0.1 = \frac{1}{10}\).

3. **Find a Common Denominator**:
- To find rational numbers between 0 and 0.1, we can express both 0 and 0.1 with a common denominator.
- Multiply both the numerator and denominator of \(0.1\) by 10 to get:
- \(0.1 = \frac{1 \times 10}{10 \times 10} = \frac{10}{100}\).

4. **List Rational Numbers**:
- Now, we can list the rational numbers between 0 and \(\frac{10}{100}\).
- We can represent 0 as \(\frac{0}{100}\).
- The rational numbers between \(\frac{0}{100}\) and \(\frac{10}{100}\) can be found by taking integers from 1 to 9 as the numerator, keeping the denominator as 100.

5. **Write the Rational Numbers**:
- The rational numbers are:
- \(\frac{1}{100}\)
- \(\frac{2}{100}\)
- \(\frac{3}{100}\)
- \(\frac{4}{100}\)
- \(\frac{5}{100}\)
- \(\frac{6}{100}\)
- \(\frac{7}{100}\)
- \(\frac{8}{100}\)
- \(\frac{9}{100}\)

6. **Final Answer**:
- Therefore, the nine rational numbers between 0 and 0.1 are:
- \(\frac{1}{100}, \frac{2}{100}, \frac{3}{100}, \frac{4}{100}, \frac{5}{100}, \frac{6}{100}, \frac{7}{100}, \frac{8}{100}, \frac{9}{100}\).