The unit digit of expression
`(1 xx 2 xx 3 xx 4 xx 5 xx 6 xx 7 xx 8 xx 9 xx 10)/(100)`.

Options

A. 7
B. 8
C. 9
D. none of these

Answer

To find the unit digit of the expression \((1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9 \times 10) / 100\), we can follow these steps:

### Step 1: Calculate the product of the numbers from 1 to 10
We need to multiply all the integers from 1 to 10 together.

\[ 1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9 \times 10 \]

### Step 2: Break down the multiplication
We can calculate the product step by step:

- \(1 \times 2 = 2\)
- \(2 \times 3 = 6\)
- \(6 \times 4 = 24\)
- \(24 \times 5 = 120\)
- \(120 \times 6 = 720\)
- \(720 \times 7 = 5040\)
- \(5040 \times 8 = 40320\)
- \(40320 \times 9 = 362880\)
- \(362880 \times 10 = 3628800\)

So, the product of numbers from 1 to 10 is \(3628800\).

### Step 3: Divide the product by 100
Now we divide the product by 100:

\[ \frac{3628800}{100} = 36288 \]

### Step 4: Find the unit digit
The unit digit of \(36288\) is \(8\).

### Final Answer
Thus, the unit digit of the expression \((1 \times 2 \times 3 \times 4 \times 5 \times 6 \times 7 \times 8 \times 9 \times 10) / 100\) is **8**.

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