The value of `4 + (44)/(10) + (404)/(100) + (444)/(1000) + (4)/(10000)` is

Options

A. `12.8844`
B. `12.8804`
C. `12.8224`
D. `12.8944`

Answer

To solve the expression \( 4 + \frac{44}{10} + \frac{404}{100} + \frac{444}{1000} + \frac{4}{10000} \), we will break it down step by step.

### Step 1: Convert each term to decimal form
1. The first term is \( 4 \).
2. The second term is \( \frac{44}{10} = 4.4 \).
3. The third term is \( \frac{404}{100} = 4.04 \).
4. The fourth term is \( \frac{444}{1000} = 0.444 \).
5. The fifth term is \( \frac{4}{10000} = 0.0004 \).

### Step 2: Write down the decimal values
Now we have:
- \( 4 = 4.0000 \)
- \( \frac{44}{10} = 4.4 = 4.4000 \)
- \( \frac{404}{100} = 4.04 = 4.0400 \)
- \( \frac{444}{1000} = 0.444 = 0.4440 \)
- \( \frac{4}{10000} = 0.0004 = 0.0004 \)

### Step 3: Align the decimal points for addition
Aligning the numbers for addition:
```
4.0000
+ 4.4000
+ 4.0400
+ 0.4440
+ 0.0004
```

### Step 4: Add the numbers column by column
1. Start from the rightmost column:
- \( 0 + 0 + 0 + 0 + 4 = 4 \)
2. Move to the next column:
- \( 0 + 0 + 4 + 4 + 0 = 8 \)
3. Move to the next column:
- \( 0 + 4 + 0 + 4 + 0 = 8 \)
4. Move to the leftmost column:
- \( 4 + 4 + 4 + 0 + 0 = 12 \)

### Step 5: Combine the results
Putting it all together, we have:
- The whole number part is \( 12 \).
- The decimal part is \( 0.8844 \).

So, the final result is:
\[ 12.8844 \]

### Final Answer
The value of \( 4 + \frac{44}{10} + \frac{404}{100} + \frac{444}{1000} + \frac{4}{10000} \) is \( 12.8844 \).

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