The last digit of `(1001)^2008 + 1002` is

Options

A. 0
B. 3
C. 4
D. 6

Answer

To find the last digit of the expression \( (1001)^{2008} + 1002 \), we can follow these steps:

### Step 1: Identify the last digit of \( 1001 \)
The last digit of \( 1001 \) is \( 1 \).

**Hint:** When looking for the last digit of a number, focus only on the unit place digit.

### Step 2: Calculate the last digit of \( (1001)^{2008} \)
Since the last digit of \( 1001 \) is \( 1 \), we can simplify our calculation to finding the last digit of \( 1^{2008} \).

Any power of \( 1 \) is \( 1 \):
\[ 1^{2008} = 1 \]

**Hint:** Any number raised to any power that ends in \( 1 \) will always result in \( 1 \).

### Step 3: Add the last digit of \( (1001)^{2008} \) to the last digit of \( 1002 \)
Now, we need to find the last digit of \( 1002 \). The last digit of \( 1002 \) is \( 2 \).

Next, we add the last digits we found:
\[ 1 + 2 = 3 \]

**Hint:** When adding the last digits, ensure you only consider the unit place of the sum.

### Step 4: Determine the last digit of the final result
The last digit of \( (1001)^{2008} + 1002 \) is \( 3 \).

**Final Answer:** The last digit is \( 3 \).