The accuracy of measurement also lies in the way the results is expressed. The number of digits to which a value is to be expressed is one digit more than number of digits after after an operation is carried out on the given values. The error can be minimised by many trials and using the correct methods are instruments.
If the length and breadth are measured as `4.234 and 1.05 m`, the area of the rectangle is

Options

A. `4.4457 m^(2)`
B. `4.45 m^(2)`
C. `4.446 m^(2)`
D. `0.4446 m^(2)`

Explanation

To solve the problem of finding the area of a rectangle given its length and breadth, we will follow these steps:

### Step 1: Identify the given measurements
The length and breadth of the rectangle are given as:
- Length (L) = 4.234 m
- Breadth (B) = 1.05 m

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

Substituting the values:
\[ A = 4.234 \, \text{m} \times 1.05 \, \text{m} \]

### Step 3: Perform the multiplication
Now, we will calculate the product:
\[ A = 4.234 \times 1.05 = 4.4457 \, \text{m}^2 \]

### Step 4: Determine the significant figures
Next, we need to express the area with the correct number of significant figures.
- The length (4.234 m) has **4 significant figures**.
- The breadth (1.05 m) has **3 significant figures**.

The result should be expressed with the least number of significant figures, which is **3 significant figures** (from the breadth).

### Step 5: Round the result to 3 significant figures
The calculated area is 4.4457 m². To round this to 3 significant figures:
- The first three significant figures are 4.44.
- The next digit is 5 (from 4.4457), which means we round up.

Thus, rounding 4.4457 to 3 significant figures gives us:
\[ A \approx 4.45 \, \text{m}^2 \]

### Final Answer
The area of the rectangle is:
\[ \text{Area} = 4.45 \, \text{m}^2 \]

### Conclusion
The correct option is **B: 4.45 m²**.

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