The value of `(0.1 xx 0.1 xx 0.1 + 0.02 xx 0.02 xx 0.02)/(0.2 xx 0.2 xx 0.2 + 0.4 xx 0.04 xx 0.004)` is :

Options

A. A) 0.0125
B. B) 0.125
C. C) 0.25
D. D) 0.5

Answer

To solve the expression \((0.1 \times 0.1 \times 0.1 + 0.02 \times 0.02 \times 0.02)/(0.2 \times 0.2 \times 0.2 + 0.4 \times 0.04 \times 0.004)\), we will break it down step by step.

### Step 1: Calculate the numerator
The numerator consists of two parts:
1. \(0.1 \times 0.1 \times 0.1\)
2. \(0.02 \times 0.02 \times 0.02\)

**Calculating \(0.1 \times 0.1 \times 0.1\):**
\[ 0.1 \times 0.1 = 0.01 \]
\[ 0.01 \times 0.1 = 0.001 \]

**Calculating \(0.02 \times 0.02 \times 0.02\):**
\[ 0.02 \times 0.02 = 0.0004 \]
\[ 0.0004 \times 0.02 = 0.000008 \]

**Adding both results:**
\[ 0.001 + 0.000008 = 0.001008 \]

### Step 2: Calculate the denominator
The denominator also consists of two parts:
1. \(0.2 \times 0.2 \times 0.2\)
2. \(0.4 \times 0.04 \times 0.004\)

**Calculating \(0.2 \times 0.2 \times 0.2\):**
\[ 0.2 \times 0.2 = 0.04 \]
\[ 0.04 \times 0.2 = 0.008 \]

**Calculating \(0.4 \times 0.04 \times 0.004\):**
\[ 0.4 \times 0.04 = 0.016 \]
\[ 0.016 \times 0.004 = 0.000064 \]

**Adding both results:**
\[ 0.008 + 0.000064 = 0.008064 \]

### Step 3: Divide the numerator by the denominator
Now we divide the results from Step 1 and Step 2:
\[ \frac{0.001008}{0.008064} \]

### Step 4: Simplify the division
To simplify this division, we can multiply both the numerator and the denominator by \(1000\) to eliminate the decimals:
\[ \frac{1.008}{8.064} \]

Now, we can simplify:
\[ \frac{1.008 \div 1.008}{8.064 \div 1.008} = \frac{1}{8} \]

### Step 5: Convert the fraction to decimal
The decimal value of \(\frac{1}{8}\) is:
\[ 0.125 \]

### Final Answer
Thus, the value of the expression is:
\[ \boxed{0.125} \]