A rectangle has length of `2.21 xx10^(-1)` m and width equal to `2.2 xx 10^(-1)` m . Its area is

Options

A. `4.862 xx10^(-2) m^2`
B. `4.86 xx 10^(-2)m^2`
C. `4.8 xx 10^(-2) m^2`
D. `4.9 xx 10^(-2)m^2`

Answer

To find the area of the rectangle with the given dimensions, we can follow these steps:

### Step 1: Identify the dimensions
The length \( L \) of the rectangle is given as:
\[ L = 2.21 \times 10^{-1} \, \text{m} \]
The width \( W \) of the rectangle is given as:
\[ W = 2.2 \times 10^{-1} \, \text{m} \]

### Step 2: Use the formula for the area of a rectangle
The area \( A \) of a rectangle is calculated using the formula:
\[ A = L \times W \]

### Step 3: Substitute the values into the formula
Now, substituting the values of length and width into the area formula:
\[ A = (2.21 \times 10^{-1}) \times (2.2 \times 10^{-1}) \]

### Step 4: Multiply the coefficients and the powers of ten
First, multiply the coefficients:
\[ 2.21 \times 2.2 = 4.862 \]
Next, multiply the powers of ten:
\[ 10^{-1} \times 10^{-1} = 10^{-2} \]
Thus, we have:
\[ A = 4.862 \times 10^{-2} \, \text{m}^2 \]

### Step 5: Consider significant figures
Now, we need to consider the significant figures. The length has 3 significant figures (2.21) and the width has 2 significant figures (2.2). The result should be reported with the least number of significant figures, which is 2.

### Step 6: Round the result
Rounding \( 4.862 \) to 2 significant figures gives us:
\[ 4.9 \times 10^{-2} \, \text{m}^2 \]

### Final Answer
Thus, the area of the rectangle is:
\[ \boxed{4.9 \times 10^{-2} \, \text{m}^2} \]