Find the Opposite Number: Converting 2.1 to Its Negative Value

To solve the problem, let's follow these steps:

• Step 1: Convert $2.1$ to a fraction.
• Step 2: Find the reciprocal of this fraction.
• Step 3: Simplify the reciprocal.

Now, let's execute each step:

Step 1: Convert $2.1$ to a fraction. Since $2.1$ is a decimal, we express it as a fraction: $2.1 = \frac{21}{10}$.

Step 2: Find the reciprocal. The reciprocal of $\frac{21}{10}$ is $\frac{10}{21}$.

Step 3: Simplify. The fraction $\frac{10}{21}$ is already in its simplest form.

Thus, the reciprocal of $2.1$ is $\frac{10}{21}$, which corresponds to choice 4.

Therefore, the opposite number of $2.1$, interpreted as its reciprocal, is $\frac{10}{21}$.