The simplification of
`2.002 + 7.9+{ 2.8-6.3+ ( 3.6-1.5) + 15.6}` gives

Options

A. 2.002
B. 4.2845
C. 40.843
D. 24.102

Answer

To simplify the expression \(2.002 + 7.9 + \{ 2.8 - 6.3 + (3.6 - 1.5) + 15.6 \}\), we will follow these steps:

### Step 1: Convert to Like Decimals
First, we need to convert all the numbers to have the same number of decimal places. The maximum number of decimal places in the given numbers is 3. Therefore, we can rewrite the numbers as follows:
- \(2.002\) remains \(2.002\)
- \(7.9\) becomes \(7.900\)
- \(2.8\) becomes \(2.800\)
- \(6.3\) becomes \(6.300\)
- \(3.6\) becomes \(3.600\)
- \(1.5\) becomes \(1.500\)
- \(15.6\) becomes \(15.600\)

So the expression now looks like:
\[ 2.002 + 7.900 + \{ 2.800 - 6.300 + (3.600 - 1.500) + 15.600 \} \]

### Step 2: Simplify Inside the Braces
Next, we simplify the expression inside the braces:
1. Calculate \(3.600 - 1.500\):
\[ 3.600 - 1.500 = 2.100 \]

2. Now substitute back into the expression:
\[ 2.800 - 6.300 + 2.100 + 15.600 \]

### Step 3: Continue Simplifying Inside the Braces
Now we simplify \(2.800 - 6.300 + 2.100 + 15.600\):
1. Calculate \(2.800 - 6.300\):
\[ 2.800 - 6.300 = -3.500 \]

2. Now substitute back:
\[ -3.500 + 2.100 + 15.600 \]

3. Next, calculate \(-3.500 + 2.100\):
\[ -3.500 + 2.100 = -1.400 \]

4. Finally, add \(-1.400 + 15.600\):
\[ -1.400 + 15.600 = 14.200 \]

### Step 4: Substitute Back to the Original Expression
Now we substitute the result back into the original expression:
\[ 2.002 + 7.900 + 14.200 \]

### Step 5: Final Addition
Now we perform the final addition:
1. First, add \(2.002 + 7.900\):
\[ 2.002 + 7.900 = 9.902 \]

2. Now add \(9.902 + 14.200\):
\[ 9.902 + 14.200 = 24.102 \]

### Final Answer
Thus, the simplification of the expression is:
\[ \boxed{24.102} \]