The number of 4-digit numbers in the Hindu Arabic system is____.

Explanation

To find the number of 4-digit numbers in the Hindu Arabic system, we can follow these steps:

### Step 1: Identify the range of 4-digit numbers
The smallest 4-digit number is 1000, and the largest 4-digit number is 9999.

### Step 2: Set up the sequence of 4-digit numbers
The sequence of 4-digit numbers starts from 1000 and goes up to 9999. This can be represented as:
- First term (A) = 1000
- Last term (L) = 9999

### Step 3: Calculate the total number of terms in the sequence
To find the total number of 4-digit numbers, we can use the formula for the number of terms (n) in an arithmetic progression (AP):
\[ L = A + (n - 1) \times D \]
Where:
- L = Last term (9999)
- A = First term (1000)
- D = Common difference (1)

### Step 4: Rearranging the formula
We can rearrange the formula to solve for n:
\[ 9999 = 1000 + (n - 1) \times 1 \]
This simplifies to:
\[ 9999 - 1000 = n - 1 \]
\[ 8999 = n - 1 \]
\[ n = 8999 + 1 \]
\[ n = 9000 \]

### Conclusion
The total number of 4-digit numbers in the Hindu Arabic system is **9000**.

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