The value of `42 xx 0.041` with due regard to significant figures is

Options

A. `1.722`
B. `1.72`
C. `1.7`
D. `1.8`

Answer

To solve the problem of finding the value of \(42 \times 0.041\) with due regard to significant figures, we can follow these steps:

### Step 1: Perform the multiplication
First, we multiply the two numbers:
\[ 42 \times 0.041 \]

Calculating this gives:
\[ 42 \times 0.041 = 1.722 \]

### Step 2: Determine the number of significant figures
Next, we need to determine the number of significant figures in each of the numbers we multiplied:
- The number **42** has **2 significant figures** (both digits are non-zero).
- The number **0.041** has **2 significant figures** (the leading zeros are not counted).

### Step 3: Apply the rule for significant figures in multiplication
When multiplying numbers, the result should have the same number of significant figures as the factor with the least significant figures. In this case, both numbers have **2 significant figures**.

### Step 4: Round the result to the appropriate number of significant figures
The result from our multiplication is **1.722**. Now we need to round this to **2 significant figures**:
- The first two significant figures in **1.722** are **1** and **7**.
- The next digit (which is used for rounding) is **2** (less than 5), so we do not round up.

Thus, rounding **1.722** to **2 significant figures** gives us:
\[ 1.7 \]

### Final Answer
Therefore, the value of \(42 \times 0.041\) with due regard to significant figures is:
\[ \boxed{1.7} \]

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