The value of the following is : `(0.2 xx 0.02 xx 0.002 xx 32)/(0.4 xx 0.04 xx 0.004 xx 16)`

Options

A. 0.2
B. 0.5
C. 0.4
D. 0.25

Answer

To solve the expression \((0.2 \times 0.02 \times 0.002 \times 32)/(0.4 \times 0.04 \times 0.004 \times 16)\), we will simplify it step by step.

### Step 1: Write the expression clearly
We start with the expression:
\[ \frac{0.2 \times 0.02 \times 0.002 \times 32}{0.4 \times 0.04 \times 0.004 \times 16} \]

### Step 2: Simplify the fractions
We can simplify the fractions by breaking down the numbers:
- The numerator: \(0.2 = \frac{2}{10} = \frac{1}{5}\)
- The denominator: \(0.4 = \frac{4}{10} = \frac{2}{5}\)

Thus, we can rewrite the expression as:
\[ \frac{\frac{1}{5} \times 0.02 \times 0.002 \times 32}{\frac{2}{5} \times 0.04 \times 0.004 \times 16} \]

### Step 3: Substitute the decimal values
Next, we convert the decimals in the numerator and denominator:
- \(0.02 = \frac{2}{100} = \frac{1}{50}\)
- \(0.002 = \frac{2}{1000} = \frac{1}{500}\)
- \(0.04 = \frac{4}{100} = \frac{1}{25}\)
- \(0.004 = \frac{4}{1000} = \frac{1}{250}\)

Now substituting these values, we have:
\[ \frac{\frac{1}{5} \times \frac{1}{50} \times \frac{1}{500} \times 32}{\frac{2}{5} \times \frac{1}{25} \times \frac{1}{250} \times 16} \]

### Step 4: Simplify the numerator and denominator
Now we can combine the fractions:
- Numerator:
\[ \frac{32}{5 \times 50 \times 500} = \frac{32}{125000} \]
- Denominator:
\[ \frac{2 \times 16}{5 \times 25 \times 250} = \frac{32}{12500} \]

### Step 5: Form the new fraction
Now we can form the new fraction:
\[ \frac{\frac{32}{125000}}{\frac{32}{12500}} = \frac{32 \times 12500}{32 \times 125000} \]

### Step 6: Cancel out the common terms
The \(32\) cancels out:
\[ \frac{12500}{125000} = \frac{1}{10} \]

### Step 7: Final simplification
Now, we can simplify \(\frac{1}{10}\) to decimal:
\[ \frac{1}{10} = 0.1 \]

### Conclusion
The value of the expression is \(0.1\).