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

Options

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

Answer

To solve the expression \( 4 + \frac{44}{10} + \frac{404}{100} + \frac{444}{1000} + \frac{4}{1000} \), we will follow these steps:

### Step 1: Rewrite the fractions with a common denominator
The common denominator for the fractions is 1000. We will convert each term to have this common denominator.

- The first term \( 4 \) can be written as \( \frac{4000}{1000} \).
- The second term \( \frac{44}{10} \) can be converted to \( \frac{4400}{1000} \) (since \( 44 \times 100 = 4400 \)).
- The third term \( \frac{404}{100} \) can be converted to \( \frac{4040}{1000} \) (since \( 404 \times 10 = 4040 \)).
- The fourth term \( \frac{444}{1000} \) remains as \( \frac{444}{1000} \).
- The fifth term \( \frac{4}{1000} \) remains as \( \frac{4}{1000} \).

### Step 2: Combine all the fractions
Now we can add all the fractions together:

\[ \frac{4000}{1000} + \frac{4400}{1000} + \frac{4040}{1000} + \frac{444}{1000} + \frac{4}{1000} \]

This simplifies to:

\[ \frac{4000 + 4400 + 4040 + 444 + 4}{1000} \]

### Step 3: Calculate the numerator
Now we will calculate the sum of the numerators:

\[ 4000 + 4400 + 4040 + 444 + 4 = 12884 \]

### Step 4: Write the final fraction
Now we can write the final fraction:

\[ \frac{12884}{1000} \]

### Step 5: Convert to decimal
Now we convert this fraction to a decimal:

\[ 12884 \div 1000 = 12.884 \]

### Final Answer
Thus, the value of the expression is \( \boxed{12.884} \).

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