Correct Option (D)

To determine the rightmost digit preceding the zeros in $30^{30}$ , the expression can be factorized as follows:

$30^{30} = (3 \times 10)^{30} = 3^{30} \times 10^{30}$

The term $10^{30}$ indicates that the number will terminate with 30 zeros. Consequently, the digit immediately preceding these zeros is the unit digit of $3^{30}$ .

The unit digits of powers of 3 follow a repeating cycle:

Unit digit of $3^{1}$ is 3
Unit digit of $3^{2}$ is 9
Unit digit of $3^{3}$ is 7
Unit digit of $3^{4}$ is 1

This cycle has a length of 4 (3, 9, 7, 1). To ascertain the unit digit of $3^{30}$ , the exponent 30 is divided by the cycle length 4:

$\frac{30}{4} = 7$ with a remainder of 2.

The remainder of 2 signifies that the unit digit will be the second digit in the cycle. Therefore, the unit digit of $3^{30}$ is 9.

Thus, the rightmost digit preceding the zeros in $30^{30}$ is 9.

Incorrect Options:

Options A (1), B (3), and C (7) are incorrect as they do not correspond to the unit digit of $3^{30}$ .

A unit digit of 1 occurs when the exponent, when divided by 4, yields a remainder of 0 (or is a multiple of 4).
A unit digit of 3 occurs when the exponent, when divided by 4, yields a remainder of 1.
A unit digit of 7 occurs when the exponent, when divided by 4, yields a remainder of 3.

Since the exponent 30 leaves a remainder of 2 when divided by 4, the correct unit digit is 9, which is the second element in the cycle of unit digits for powers of 3.