A rectangular wooden block has length 1.4 m and width 84 cm. What is the area of wooden block in appropriate significant figure?

Options

A. 2.75 cm
B. 3.75 cm
C. `1.2m^(2)`
D. `1.12m^(2)`

Explanation

To find the area of the rectangular wooden block, we will follow these steps:

### Step 1: Convert all measurements to the same unit
The length is given as 1.4 m and the width is given as 84 cm. We need to convert the width from centimeters to meters for consistency in SI units.

\[ \text{Width in meters} = 84 \text{ cm} \times \frac{1 \text{ m}}{100 \text{ cm}} = 0.84 \text{ m} \]

### Step 2: Calculate the area
Now that both measurements are in meters, we can calculate the area of the rectangle using the formula:

\[ \text{Area} = \text{Length} \times \text{Width} \]

Substituting the values we have:

\[ \text{Area} = 1.4 \text{ m} \times 0.84 \text{ m} = 1.176 \text{ m}^2 \]

### Step 3: Determine the appropriate significant figures
Next, we need to express the area in the correct number of significant figures. The length (1.4 m) has 2 significant figures, and the width (0.84 m) has 2 significant figures as well. Therefore, our final answer should also be expressed with 2 significant figures.

### Step 4: Round the area to the correct significant figures
The calculated area is 1.176 m². To round this to 2 significant figures, we look at the third digit after the decimal point:

- The first two significant figures are "1" and "1".
- The third digit is "7", which is greater than 5.

Thus, we round the second significant figure up:

\[ 1.176 \text{ m}^2 \approx 1.2 \text{ m}^2 \]

### Final Answer
The area of the wooden block, expressed in appropriate significant figures, is:

\[ \text{Area} = 1.2 \text{ m}^2 \]

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