Question

Determine the units digit (ones digit) of the expansion of 2¹23.

A) 1
B) 2
C) 3
D) 4

Answer 1

To determine the units digit (ones digit) of the expansion of 2^123, we need to find the remainder when 123 is divided by 4. The remainder is 3, so the units digit is the third number in the cycle, which is 8.

Step-by-step explanation:

To determine the units digit (ones digit) of the expansion of 2^123, we can use the concept of cyclicity. The units digit of the powers of 2 cycle every 4 digits: 2, 4, 8, 6, 2, 4, 8, 6, ...

Since 123 is not a multiple of 4, we need to find the remainder when 123 is divided by 4.

The remainder is 3.

Therefore, the units digit of the expansion of 2^123 is the third number in the cycle, which is 8. So, the answer is 8 (option D).