Problem 88

To identify the rational numbers among the given list, we analyze each number step by step:

1. **For $\frac{7}{8}$:**
- We note that $\frac{7}{8}$ can be expressed as a decimal, $\frac{7}{8} = 0.875$.
- Since $0.875$ is a terminating decimal, it indicates that $\frac{7}{8}$ is a rational number.

2. **For $\sqrt{36}$:**
- Calculating the square root, we find $\sqrt{36} = 6$.
- The number $6$ is an integer, and all integers are rational numbers. Therefore, $\sqrt{36}$ is a rational number.

3. **For $-3\pi$:**
- The number $\pi$ is known to be an irrational number because it is a non-terminating, non-repeating decimal.
- Multiplying an irrational number by $-3$ (or any non-zero real number) keeps it irrational. Thus, $-3\pi$ is an irrational number.

4. **For $\sqrt{7}$:**
- The square root of $7$ cannot be expressed as a fraction of two integers, and its decimal representation is non-terminating and non-repeating.
- This means $\sqrt{7}$ is an irrational number.

5. **For $1.41414141$:**
- The number $1.41414141$ is a finite decimal, which can be expressed as a fraction.
- Finite decimals are always rational numbers, so $1.41414141$ is a rational number.

After analyzing each number, we find that the rational numbers are $\frac{7}{8}$, $\sqrt{36}$, and $1.41414141$. This gives us a total of $3$ rational numbers.

Therefore, the correct answer is $\boxed{C}$.