What is the value of `(0.2)^(2)+(0.02)^(2)+(0.002)^(2)` ?

Options

A. 2.404404
B. 0.040404
C. 0.00404
D. 0.00044

Answer

To solve the expression \( (0.2)^2 + (0.02)^2 + (0.002)^2 \), we can follow these steps:

### Step 1: Calculate each term separately
1. **Calculate \( (0.2)^2 \)**:
\[ (0.2)^2 = 0.2 \times 0.2 = 0.04 \]

2. **Calculate \( (0.02)^2 \)**:
\[ (0.02)^2 = 0.02 \times 0.02 = 0.0004 \]

3. **Calculate \( (0.002)^2 \)**:
\[ (0.002)^2 = 0.002 \times 0.002 = 0.000004 \]

### Step 2: Add the results together
Now, we will add the results from Step 1:
\[ 0.04 + 0.0004 + 0.000004 \]

To add these, we can align them by their decimal points:
\[ \begin{array}{r} 0.040000 \\ + 0.000400 \\ + 0.000004 \\ \hline 0.040404 \\ \end{array} \]

### Final Result
Thus, the value of \( (0.2)^2 + (0.02)^2 + (0.002)^2 \) is:
\[ \boxed{0.040404} \]