Answer:
The number 2^2044 represents 2 raised to the power of 2044. To determine the one digit in this number, we need to find the remainder when dividing 2^2044 by 10.
To solve this, we can look for a pattern in the unit digits of powers of 2. Let's calculate the unit digits for a few powers of 2:
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256
2^9 = 512
2^10 = 1024
From these calculations, we can observe that the units digits repeat in a cycle of 4: 2, 4, 8, 6. This means that every fourth power of 2 will have the same units digit.
Now, let's find the remainder when dividing 2044 by 4: 2044 ÷ 4 = 511 remainder 0. Since the remainder is 0, we know that 2044 is a multiple of 4.
Since 2044 is a multiple of 4, 2^2044 will also have the same units digit as 2^4, which is 6.
Therefore, the one digit in the number 2^2044 is 6.