The smallest 4- digit number divisible by 11 is _________

Explanation

To find the smallest 4-digit number that is divisible by 11, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the smallest 4-digit number**:
The smallest 4-digit number is 1000.

2. **Divide 1000 by 11**:
We need to check how many times 11 can fit into 1000.
\[ 1000 \div 11 = 90 \quad \text{(approximately)} \]
To find the exact number of times, we multiply:
\[ 11 \times 90 = 990 \]

3. **Calculate the remainder**:
Now, we subtract 990 from 1000 to find the remainder:
\[ 1000 - 990 = 10 \]
This means that when we divide 1000 by 11, we have a remainder of 10.

4. **Adjust to find the next multiple of 11**:
Since we have a remainder of 10, we need to add the difference to reach the next multiple of 11. The next multiple of 11 can be found by adding:
\[ 11 - 10 = 1 \]
So, we add 1 to 1000:
\[ 1000 + 1 = 1001 \]

5. **Verify if 1001 is divisible by 11**:
Finally, we check if 1001 is divisible by 11:
\[ 1001 \div 11 = 91 \]
Since there is no remainder, 1001 is indeed divisible by 11.

### Final Answer:
The smallest 4-digit number divisible by 11 is **1001**.

---