Which of the following is correct?
3.292929….is

Options

A. an integer
B. a rational number
C. an irrational number
D. not a real number

Answer

To determine the correct classification of the number 3.292929..., we will analyze its properties step by step.

### Step 1: Identify the number
The given number is 3.292929..., which can be expressed as 3.29̅, where the bar indicates that the digits "29" repeat indefinitely.

**Hint:** Look for repeating patterns in the decimal to identify its nature.

### Step 2: Classify the number based on its decimal representation
Since the digits "29" repeat indefinitely, we categorize this number as a non-terminating decimal. However, it is important to note that it is also a repeating decimal.

**Hint:** Remember that repeating decimals can be classified differently from non-repeating decimals.

### Step 3: Determine if the number is rational or irrational
A number is classified as a rational number if it can be expressed as a fraction of two integers (where the denominator is not zero). Since 3.292929... can be expressed as a fraction (for example, by using algebraic methods to convert repeating decimals into fractions), it is a rational number.

**Hint:** Check if the number can be expressed as a fraction to determine if it is rational.

### Step 4: Check if the number is an integer
An integer is a whole number that does not have any fractional or decimal part. Since 3.292929... has a decimal part, it is not an integer.

**Hint:** Remember that integers do not have decimal or fractional components.

### Step 5: Check if the number is irrational or not a real number
An irrational number cannot be expressed as a fraction of two integers. Since we have established that 3.292929... is a rational number, it cannot be classified as irrational. Additionally, all rational numbers are real numbers.

**Hint:** Recall the definitions of rational and irrational numbers to clarify their differences.

### Conclusion
Based on the analysis, the correct classification of the number 3.292929... is that it is a **rational number**.

**Final Answer:** Option B: a rational number.