The value of `117.3 xx 0.0024` with due regard to significant figures is

Options

A. `0.2808`
B. `0.281`
C. `0.28`
D. `0.29`

Answer

To solve the problem of finding the value of \(117.3 \times 0.0024\) with due regard to significant figures, we can follow these steps:

### Step 1: Identify the significant figures in each number.
- The number \(117.3\) has **four significant figures** (1, 1, 7, and 3).
- The number \(0.0024\) has **two significant figures** (2 and 4). The leading zeros do not count as significant figures.

### Step 2: Determine the limiting factor for significant figures.
In multiplication, the result should be reported with the same number of significant figures as the factor with the least number of significant figures. Here, \(0.0024\) has the least significant figures (2 significant figures).

### Step 3: Perform the multiplication.
Now, we calculate the product:
\[ 117.3 \times 0.0024 = 0.2808 \]

### Step 4: Round the result to the appropriate number of significant figures.
Since we need to round \(0.2808\) to **two significant figures**, we look at the first two significant digits, which are \(2\) and \(8\). The next digit is \(0\), which is less than \(5\), so we do not round up.

Thus, rounding \(0.2808\) to two significant figures gives:
\[ 0.28 \]

### Final Answer:
The value of \(117.3 \times 0.0024\) with due regard to significant figures is **0.28**.

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