A. 1
B. 3
C. 7
D. 9
Answer: D
To find the rightmost digit preceding the zeros in 3030, we focus on 330 since
3030 = 330 × 1030,
Since 1030 results in a 31-digit number with 30 zeros at the end, the rightmost digit preceding the zeros will be the unit digit of 330.
1. Step 1: Last digits of powers of 3
The last digits of powers of 3 repeat in a cycle of 4:
- 31 = 3 (last digit is 3)
- 32 = 9 (last digit is 9)
- 33 = 27 (last digit is 7)
- 34 = 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 ÷ 4 = 7 remainder 2
We have, 330 = 3(4*7+2)
Therefore, the last digit of 330 corresponds to the second position in the cycle, which is 9.
3. Conclusion:
The rightmost digit preceding the zeros in 3030 is 9.
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