The value of `(0.1 xx 0.1 xx 0.1 + 0.2 xx 0.2 xx 0.2 + 0.3 xx 0.3 xx 0.3 - 3 xx 0.1 xx 0.2 xx 0.3)/(0.1 xx 0.1 + 0.2 xx 0.2 + 0.3 xx 0.3 - 0.1 xx 0.2 - 0.2 xx 0.3 - 0.3 xx 0.1)` is

Options

A. 0.006
B. 0.6
C. 0
D. 0.2

Answer

To solve the expression

\[ \frac{(0.1 \times 0.1 \times 0.1 + 0.2 \times 0.2 \times 0.2 + 0.3 \times 0.3 \times 0.3 - 3 \times 0.1 \times 0.2 \times 0.3)}{(0.1 \times 0.1 + 0.2 \times 0.2 + 0.3 \times 0.3 - 0.1 \times 0.2 - 0.2 \times 0.3 - 0.3 \times 0.1)} \]

we will follow these steps:

### Step 1: Calculate the numerator

1. Calculate \(0.1 \times 0.1 \times 0.1\):
\[ 0.1 \times 0.1 \times 0.1 = 0.001 \]

2. Calculate \(0.2 \times 0.2 \times 0.2\):
\[ 0.2 \times 0.2 \times 0.2 = 0.008 \]

3. Calculate \(0.3 \times 0.3 \times 0.3\):
\[ 0.3 \times 0.3 \times 0.3 = 0.027 \]

4. Calculate \(3 \times 0.1 \times 0.2 \times 0.3\):
\[ 3 \times 0.1 \times 0.2 \times 0.3 = 3 \times 0.006 = 0.018 \]

5. Now, substitute these values into the numerator:
\[ 0.001 + 0.008 + 0.027 - 0.018 = 0.018 \]

### Step 2: Calculate the denominator

1. Calculate \(0.1 \times 0.1\):
\[ 0.1 \times 0.1 = 0.01 \]

2. Calculate \(0.2 \times 0.2\):
\[ 0.2 \times 0.2 = 0.04 \]

3. Calculate \(0.3 \times 0.3\):
\[ 0.3 \times 0.3 = 0.09 \]

4. Calculate \(0.1 \times 0.2\):
\[ 0.1 \times 0.2 = 0.02 \]

5. Calculate \(0.2 \times 0.3\):
\[ 0.2 \times 0.3 = 0.06 \]

6. Calculate \(0.3 \times 0.1\):
\[ 0.3 \times 0.1 = 0.03 \]

7. Now, substitute these values into the denominator:
\[ 0.01 + 0.04 + 0.09 - 0.02 - 0.06 - 0.03 = 0.01 + 0.04 + 0.09 - 0.11 = 0.03 \]

### Step 3: Final Calculation

Now, we can substitute the values of the numerator and denominator into the expression:
\[ \frac{0.018}{0.03} = 0.6 \]

Thus, the final value of the expression is

\[ \boxed{0.6} \]