To find the rightmost digit preceding the zeros in $30^{30}$, we focus on $3^{30}$ since $30^{30} = 3^{30} \times 10^{30}$,

Since $10^{30}$ results in a 31-digit number with 30 zeros at the end, the rightmost digit preceding the zeros will be the unit digit of $3^{30}$.

1. Step 1: Last digits of powers of 3 The last digits of powers of 3 repeat in a cycle of 4:

• $3^1 = 3$ (last digit is 3)
• $3^2 = 9$ (last digit is 9)
• $3^3 = 27$ (last digit is 7)
• $3^4 = 81$ (last digit is 1) The last digits of powers of 3 repeat in a cycle: 3, 9, 7, 1. This cycle has a length of 4.

2. Step 2: Find the remainder when 30 is divided by 4 Since $30 \div 4 = 7$ remainder 2 We have, $3^{30} = 3^{4 \cdot 7+2}$ Therefore, the last digit of $3^{30}$ corresponds to the second position in the cycle, which is 9.

3. Conclusion: The rightmost digit preceding the zeros in $30^{30}$ is 9.