Solve with due regard to significant figures:
`( 5.42 xx 0.6753)/( 0.085)`

Options

A. `43.06030`
B. `43.1`
C. `43`
D. `43.0`

Explanation

To solve the expression \(( 5.42 \times 0.6753) / (0.085)\) with due regard to significant figures, we will follow these steps:

### Step 1: Multiply the numbers in the numerator
First, we multiply \(5.42\) and \(0.6753\).

\[ 5.42 \times 0.6753 = 3.66016 \]

### Step 2: Determine the significant figures in the multiplication
Now, we need to consider the significant figures of the numbers we multiplied:
- \(5.42\) has **3 significant figures**.
- \(0.6753\) has **4 significant figures**.

The result of a multiplication should be reported with the same number of significant figures as the factor with the least significant figures. Therefore, we round \(3.66016\) to **3 significant figures**:

\[ 3.66016 \approx 3.66 \]

### Step 3: Divide by the denominator
Next, we divide the result by \(0.085\):

\[ \frac{3.66}{0.085} = 43.1764705882353 \]

### Step 4: Determine the significant figures in the division
Now, we consider the significant figures in the division:
- \(3.66\) has **3 significant figures**.
- \(0.085\) has **2 significant figures**.

Since \(0.085\) has the least number of significant figures (2), we round \(43.1764705882353\) to **2 significant figures**:

\[ 43.1764705882353 \approx 43 \]

### Final Answer
Thus, the final answer, taking into account significant figures, is:

\[ \boxed{43} \]

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