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 a rectangle given its length and width, we can follow these steps:

### Step 1: Identify the given dimensions
The length of the rectangle is given as:
\[ L = 2.21 \times 10^{-1} \, \text{m} \]
The width 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
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: Perform the multiplication
To multiply the numbers, we can first multiply the coefficients and then the powers of ten:
1. Multiply the coefficients:
\[ 2.21 \times 2.2 = 4.862 \]
2. Multiply the powers of ten:
\[ 10^{-1} \times 10^{-1} = 10^{-2} \]

Combining these results gives:
\[ A = 4.862 \times 10^{-2} \, \text{m}^2 \]

### Step 5: Determine the significant figures
Next, we need to consider the significant figures. The number of significant figures in the measurements is important:
- \( 2.21 \) has 3 significant figures.
- \( 2.2 \) has 2 significant figures.

The result must be reported with the least number of significant figures, which is 2. Therefore, we round \( 4.862 \) to 2 significant figures:
\[ A \approx 4.9 \times 10^{-2} \, \text{m}^2 \]

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

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