`0.12 xx 12 xx 0.012` = ?

Options

A. 0.01688
B. 0.1728
C. 1.728
D. 0.01728

Answer

To solve the multiplication of the decimals \(0.12 \times 12 \times 0.012\), we can follow these steps:

### Step 1: Convert the decimals to fractions
- \(0.12\) can be expressed as \(\frac{12}{100}\)
- \(0.012\) can be expressed as \(\frac{12}{1000}\)

### Step 2: Rewrite the multiplication
Now we can rewrite the expression using these fractions:
\[ 0.12 \times 12 \times 0.012 = \frac{12}{100} \times 12 \times \frac{12}{1000} \]

### Step 3: Multiply the fractions
Now, we can multiply the fractions together:
\[ \frac{12 \times 12 \times 12}{100 \times 1000} = \frac{12^3}{100 \times 1000} \]

### Step 4: Calculate \(12^3\)
Calculating \(12^3\):
\[ 12^3 = 12 \times 12 \times 12 = 144 \times 12 = 1728 \]

### Step 5: Calculate the denominator
Now calculate the denominator:
\[ 100 \times 1000 = 100000 \]

### Step 6: Combine the results
Now we can combine the results:
\[ \frac{1728}{100000} \]

### Step 7: Convert back to decimal
To convert \(\frac{1728}{100000}\) back to decimal, we can move the decimal point 5 places to the left:
\[ 1728 \div 100000 = 0.01728 \]

### Final Answer
Thus, the final result of \(0.12 \times 12 \times 0.012\) is:
\[ \boxed{0.01728} \]