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 + 0.04 xx 0.04 xx 0.04) ` is :

Options

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

Answer

To solve the expression \( \frac{0.1^3 + 0.02^3}{0.2^3 + 0.04^3} \), we can follow these steps:

### Step 1: Calculate the numerator
The numerator is \( 0.1^3 + 0.02^3 \).

- First, calculate \( 0.1^3 \):
\[ 0.1^3 = 0.1 \times 0.1 \times 0.1 = 0.001 \]

- Next, calculate \( 0.02^3 \):
\[ 0.02^3 = 0.02 \times 0.02 \times 0.02 = 0.000008 \]

- Now, add these two results together:
\[ 0.001 + 0.000008 = 0.001008 \]

### Step 2: Calculate the denominator
The denominator is \( 0.2^3 + 0.04^3 \).

- First, calculate \( 0.2^3 \):
\[ 0.2^3 = 0.2 \times 0.2 \times 0.2 = 0.008 \]

- Next, calculate \( 0.04^3 \):
\[ 0.04^3 = 0.04 \times 0.04 \times 0.04 = 0.000064 \]

- Now, add these two results together:
\[ 0.008 + 0.000064 = 0.008064 \]

### Step 3: Form the fraction
Now we can form the fraction:
\[ \frac{0.001008}{0.008064} \]

### Step 4: Simplify the fraction
To simplify the fraction, we can divide both the numerator and the denominator by \( 0.001008 \):
\[ \frac{0.001008 \div 0.001008}{0.008064 \div 0.001008} = \frac{1}{8} \]

### Step 5: Convert to decimal
Now convert \( \frac{1}{8} \) to decimal:
\[ \frac{1}{8} = 0.125 \]

### Final Answer
Thus, the value of the expression is \( 0.125 \).

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