`72.432 xx 461.2 xx 0.0034 `is same as _____

Options

A. `7.2432 xx 4.612 xx 3.4 `
B. `7.2432 xx 4.612 xx 0.34 `
C. `7.2432 xx 4612 xx0.0000034 `
D. `7243.2 xx 4.612 xx 0.000034 `

Answer

To solve the problem \(72.432 \times 461.2 \times 0.0034\) and find an equivalent expression, we can manipulate the numbers by shifting the decimal points. Here’s the step-by-step solution:

### Step 1: Rewrite the numbers by shifting the decimal points
- **Original numbers**:
- \(72.432\)
- \(461.2\)
- \(0.0034\)

- **Shifting the decimal points**:
- For \(72.432\), we can shift the decimal point 1 place to the left:
\[ 72.432 = \frac{72.432}{10} = 7.2432 \]
- For \(461.2\), we can shift the decimal point 2 places to the left:
\[ 461.2 = \frac{461.2}{100} = 4.612 \]
- For \(0.0034\), we can shift the decimal point 3 places to the right:
\[ 0.0034 = 3.4 \times 10^{-3} = 3.4 \]

### Step 2: Combine the modified numbers
Now we can rewrite the original expression using the modified numbers:
\[ 72.432 \times 461.2 \times 0.0034 = \left( \frac{72.432}{10} \right) \times \left( \frac{461.2}{100} \right) \times (3.4 \times 10^{-3}) \]

### Step 3: Simplify the expression
Now we can combine the factors:
\[ = 7.2432 \times 4.612 \times 3.4 \times \frac{1}{10} \times \frac{1}{100} \times 10^{-3} \]
\[ = 7.2432 \times 4.612 \times 3.4 \times 10^{-5} \]

### Step 4: Final expression
Thus, the equivalent expression for \(72.432 \times 461.2 \times 0.0034\) is:
\[ 7.2432 \times 4.612 \times 3.4 \times 10^{-5} \]

### Conclusion
The final answer is:
\[ \text{The expression } 72.432 \times 461.2 \times 0.0034 \text{ is the same as } 7.2432 \times 4.612 \times 3.4 \times 10^{-5}. \]