The length and breadth of a metal sheet are 3.124m and 3.002m respectively. The area of this sheet upto correct significant figure is

Options

A. a) `9.378 m^2`
B. b) `9.37 m^2`
C. c) `9.4 m^2`
D. d) None of these

Explanation

To find the area of the metal sheet given its length and breadth, we will follow these steps:

### Step 1: Identify the given values
- Length (L) = 3.124 m
- Breadth (B) = 3.002 m

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

### Step 3: Substitute the values into the formula
Substituting the values of length and breadth:
\[ A = 3.124 \, \text{m} \times 3.002 \, \text{m} \]

### Step 4: Perform the multiplication
Calculating the area:
\[ A = 3.124 \times 3.002 = 9.378248 \, \text{m}^2 \]

### Step 5: Determine the significant figures
- The length (3.124 m) has 4 significant figures.
- The breadth (3.002 m) also has 4 significant figures.
- When multiplying, the result should be reported with the same number of significant figures as the measurement with the least number of significant figures. In this case, both measurements have 4 significant figures.

### Step 6: Round the result to the correct significant figures
The calculated area is 9.378248 m². Rounding this to 4 significant figures gives:
- The first four digits are 9.378.
- The next digit (2) does not round up the last digit (8).

Thus, the area of the metal sheet, rounded to the correct significant figures, is:
\[ A = 9.378 \, \text{m}^2 \]

### Final Answer
The area of the metal sheet up to correct significant figures is **9.378 m²**.

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