Write 9 rational numbers between 1 and 2.

Answer

To find 9 rational numbers between 1 and 2, we can follow these steps:

### Step 1: Understand the range
We need to find rational numbers that lie between 1 and 2.

### Step 2: Convert 1 and 2 to have a common denominator
To make it easier to find rational numbers, we can convert 1 and 2 into fractions with a common denominator. We can multiply both 1 and 2 by 10.

- \( 1 = \frac{1 \times 10}{1 \times 10} = \frac{10}{10} \)
- \( 2 = \frac{2 \times 10}{1 \times 10} = \frac{20}{10} \)

Now we have:
- Lower limit: \( \frac{10}{10} \)
- Upper limit: \( \frac{20}{10} \)

### Step 3: Identify rational numbers between the two fractions
Now, we can find rational numbers between \( \frac{10}{10} \) and \( \frac{20}{10} \). We can simply take the numerators from 11 to 19 (since 10 and 20 are not included).

The rational numbers are:
- \( \frac{11}{10} \)
- \( \frac{12}{10} \)
- \( \frac{13}{10} \)
- \( \frac{14}{10} \)
- \( \frac{15}{10} \)
- \( \frac{16}{10} \)
- \( \frac{17}{10} \)
- \( \frac{18}{10} \)
- \( \frac{19}{10} \)

### Step 4: List the rational numbers
So, the 9 rational numbers between 1 and 2 are:
1. \( \frac{11}{10} \)
2. \( \frac{12}{10} \)
3. \( \frac{13}{10} \)
4. \( \frac{14}{10} \)
5. \( \frac{15}{10} \)
6. \( \frac{16}{10} \)
7. \( \frac{17}{10} \)
8. \( \frac{18}{10} \)
9. \( \frac{19}{10} \)