Express the Decimal 2.31: Different Mathematical Representations

To solve this problem, we'll follow these steps:

• Step 1: Identify the integer and decimal parts of the given number.
• Step 2: Convert the decimal part into a fraction with a denominator of 100.
• Step 3: Form the mixed number by combining the integer part with the fractional part.

Let's execute these steps:
Step 1: The number $2.31$ consists of the integer part $2$ and the decimal $0.31$.
Step 2: The decimal $0.31$ can be expressed as $\frac{31}{100}$ because the decimal places after the decimal point represent hundredths.
Step 3: Combining the integer part $2$ and the fractional part $\frac{31}{100}$, we form the mixed number $2\frac{31}{100}$.

Therefore, the solution to the problem is $2\frac{31}{100}$, which corresponds to choice 3.