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 1: Understand the range
We need to find rational numbers between 0 and 0.1. The number 0.1 can be expressed as a fraction:
\[ 0.1 = \frac{1}{10} \]

### Step 2: Convert the range to a common denominator
To find rational numbers between 0 and \(\frac{1}{10}\), we can express both numbers with a common denominator. We can multiply both the numerator and denominator of \(\frac{1}{10}\) by 10:
\[ 0 = \frac{0}{100} \quad \text{and} \quad 0.1 = \frac{10}{100} \]

### Step 3: Identify rational numbers
Now we need to find rational numbers between \(\frac{0}{100}\) and \(\frac{10}{100}\). We can do this by taking fractions with the denominator of 100. The rational numbers can be:
- \(\frac{1}{100}\)
- \(\frac{2}{100}\)
- \(\frac{3}{100}\)
- \(\frac{4}{100}\)
- \(\frac{5}{100}\)
- \(\frac{6}{100}\)
- \(\frac{7}{100}\)
- \(\frac{8}{100}\)
- \(\frac{9}{100}\)

### Step 4: List the rational numbers
Thus, the nine rational numbers between 0 and 0.1 are:
1. \(\frac{1}{100}\)
2. \(\frac{2}{100}\)
3. \(\frac{3}{100}\)
4. \(\frac{4}{100}\)
5. \(\frac{5}{100}\)
6. \(\frac{6}{100}\)
7. \(\frac{7}{100}\)
8. \(\frac{8}{100}\)
9. \(\frac{9}{100}\)

### Conclusion
These are the nine rational numbers that lie between 0 and 0.1.

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