Find the number of Zeros at the end of the expression -
10 + 100 + 1000 + ....... + 100000000

Options

A. 8
B. 28
C. 0
D. 1

Answer

To find the number of zeros at the end of the expression \(10 + 100 + 1000 + \ldots + 100000000\), we can follow these steps:

### Step 1: Identify the series
The given expression is a series of numbers that can be expressed as:
\[ 10 + 100 + 1000 + \ldots + 100000000 \]
This series can be rewritten as:
\[ 10^1 + 10^2 + 10^3 + \ldots + 10^8 \]

### Step 2: Calculate the sum of the series
The sum of a geometric series can be calculated using the formula:
\[ S_n = a \frac{(r^n - 1)}{(r - 1)} \]
where:
- \(a\) is the first term,
- \(r\) is the common ratio,
- \(n\) is the number of terms.

In our case:
- \(a = 10\),
- \(r = 10\),
- \(n = 8\) (since we have terms from \(10^1\) to \(10^8\)).

Now substituting these values into the formula:
\[ S = 10 \frac{(10^8 - 1)}{(10 - 1)} = 10 \frac{(100000000 - 1)}{9} = 10 \frac{99999999}{9} \]

### Step 3: Simplify the sum
Calculating \( \frac{99999999}{9} \):
\[ 99999999 \div 9 = 11111111 \]
Thus, the sum becomes:
\[ S = 10 \times 11111111 = 111111110 \]

### Step 4: Count the number of zeros at the end
Now we need to find the number of zeros at the end of \(111111110\). We can see that there is one zero at the end of this number.

### Conclusion
Therefore, the number of zeros at the end of the expression \(10 + 100 + 1000 + \ldots + 100000000\) is:
\[ \boxed{1} \]