Find two rational numbers between 0.565665666 . . . and 0.585885888 . . . .

Explanation

To find two rational numbers between 0.565665666... and 0.585885888..., we can follow these steps:

### Step 1: Identify the Numbers
We have the two numbers:
- Lower bound: 0.565665666...
- Upper bound: 0.585885888...

### Step 2: Convert to Decimal Form
The numbers can be approximated as:
- 0.565665666... is approximately 0.5667 (considering four decimal places)
- 0.585885888... is approximately 0.5859 (considering four decimal places)

### Step 3: Find a Midpoint
To find two rational numbers, we can first find the midpoint between these two numbers. The midpoint can be calculated as:
\[ \text{Midpoint} = \frac{0.5657 + 0.5859}{2} \]
Calculating this gives:
\[ \text{Midpoint} = \frac{1.1516}{2} = 0.5758 \]

### Step 4: Choose Two Rational Numbers
Now, we can choose two rational numbers around the midpoint:
1. The first rational number can be 0.57.
2. The second rational number can be 0.58.

### Step 5: Verify the Numbers
We need to ensure that both numbers lie between the original bounds:
- 0.57 is greater than 0.565665666... and less than 0.585885888...
- 0.58 is also greater than 0.565665666... and less than 0.585885888...

### Conclusion
The two rational numbers between 0.565665666... and 0.585885888... are:
- 0.57
- 0.58

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