17. What is the rightmost digit preceding the zeros in the value of 30^30 ?

1. A. 1
2. B. 3
3. C. 7
4. D. 9

Answer: D

Explanation

We need to find the rightmost non-zero digit of 30^30. We can write 30^30 as (3 × 10)^30 = 3^30 × 10^30. The term 10^30 indicates that there will be 30 zeros at the end of the number. The digit immediately preceding these zeros will be the unit digit of 3^30. To find the unit digit of 3^30, we observe the cyclicity of the unit digits of powers of 3:
3^1 = 3
3^2 = 9
3^3 = 27 (unit digit 7)
3^4 = 81 (unit digit 1)
3^5 = 243 (unit digit 3)
The cycle of unit digits for powers of 3 is (3, 9, 7, 1), which has a length of 4. To find the unit digit of 3^30, we divide the exponent (30) by the cycle length (4): 30 ÷ 4 = 7 with a remainder of 2. The unit digit will be the same as the 2nd digit in the cycle, which is 9. Therefore, the rightmost digit preceding the zeros in 30^30 is 9. This question tests number properties, specifically the concept of cyclicity of unit digits.