In `13799 xx 96xx 996`, the tenth place digit is?

Options

A. 3
B. 4
C. 5
D. 8

Answer

To find the tenth place digit in the expression \( 13799 \times 96 \times 996 \), we can follow these steps:

### Step 1: Understand the Problem
We need to find the digit in the tenth place of the product \( 13799 \times 96 \times 996 \). The tenth place corresponds to the second digit from the right in a number.

### Step 2: Divide by 100
To focus on the last two digits of the product, we can divide the entire expression by 100. This will help us isolate the last two digits, which include the tenth place digit.

\[ \text{Calculate } (13799 \times 96 \times 996) \mod 100 \]

### Step 3: Calculate Each Factor Modulo 100
We can find the last two digits of each number involved in the multiplication:

- \( 13799 \mod 100 = 99 \)
- \( 96 \mod 100 = 96 \)
- \( 996 \mod 100 = 96 \)

### Step 4: Multiply the Results
Now, we can multiply these results together:

\[ (99 \times 96 \times 96) \mod 100 \]

### Step 5: Calculate \( 99 \times 96 \)
First, calculate \( 99 \times 96 \):

\[ 99 \times 96 = 9504 \]

Now, find \( 9504 \mod 100 \):

\[ 9504 \mod 100 = 04 \]

### Step 6: Multiply by 96 Again
Now, we take the result \( 04 \) and multiply it by \( 96 \):

\[ 04 \times 96 = 384 \]

### Step 7: Find \( 384 \mod 100 \)
Now, find \( 384 \mod 100 \):

\[ 384 \mod 100 = 84 \]

### Step 8: Identify the Tenth Place Digit
The last two digits of the product are \( 84 \). Therefore, the digit in the tenth place is \( 8 \).

### Final Answer
The digit in the tenth place is **8**.

---