Identifying the Irrational Number Represented by CE on the Given Number Line

Step 1: Understanding Irrational Numbers
- Irrational numbers are real numbers that cannot be written as the ratio of two integers.
- They are non-repeating and non-terminating decimals.

Step 2: Analyzing the Given Number Line
- The number line shows rational and irrational numbers between 0 and 3.
- The irrational numbers are represented by dots, while the rational numbers are represented by tick marks.
- The letter CE lies between two dots on the number line.

Step 3: Finding the Approximate Value of CE
- We can estimate the value of CE by finding the midpoint between the two nearest dots on the number line.
- The nearest dots to CE are located at approximately 2.5 and 2.6.
- Therefore, the approximate value of CE is (2.5 + 2.6)/2 = 2.55.

Step 4: Identifying the Irrational Number Represented by CE
- To identify the irrational number represented by CE, we need to determine which irrational number between 2 and 3 has a decimal expansion that starts with 2.55.
- The only irrational number that satisfies this condition is √6.
- Therefore, CE represents the irrational number √6.

Conclusion
- The irrational number represented by CE on the given number line is √6, which is approximately equal to 2.449.