Answer: $60000$

Explanation:1. Let $M\_A$, $M\_B$, and $M\_C$ be the masses of object A, object B, and object C, respectively.

2. Translate the given percentage statements into equations: - "The mass of object A is $498\%$ of the mass of object B": $M\_A = \dfrac{498}{100} M\_B = 4.98 M\_B$ (Equation 1) - "The mass of object A is $0.830\%$ of the mass of object C": $M\_A = \dfrac{0.830}{100} M\_C = 0.0083 M\_C$ (Equation 2)

3. The question asks: "If the mass of object C is $p\%$ of the mass of object B, what is the value of $p$?" This means we need to find $p$ such that $M\_C = \dfrac{p}{100} M\_B$. Our goal is to find an expression for $M\_C$ in terms of $M\_B$ and then determine $p$.

4. From Equation 1 and Equation 2, we can set the expressions for $M\_A$ equal: $4.98 M\_B = 0.0083 M\_C$

5. Solve for $M\_C$ in terms of $M\_B$: $M\_C = \dfrac{4.98}{0.0083} M\_B$

6. Calculate the fraction $\dfrac{4.98}{0.0083}$: $\dfrac{4.98}{0.0083} = \dfrac{4.980}{0.0083} = \dfrac{49800}{83}$ (multiplying numerator and denominator by $10000$) Perform the division: $49800 \div 83$ $83 \times 6 = 498$. So, $49800 \div 83 = 600$. Therefore, $M\_C = 600 M\_B$.

7. Now compare this with the target form $M\_C = \dfrac{p}{100} M\_B$: We have $600 M\_B = \dfrac{p}{100} M\_B$. Assuming $M\_B \neq 0$, we can divide by $M\_B$: $600 = \dfrac{p}{100}$

8. Solve for $p$: $p = 600 \times 100$ $p = 60000$

9. Conclusion: The value of $p$ is $60000$.