The area of a sheet of length 10.2 cm and width 68 cm addressed upto proper number of significant figures is

Options

A. `69.26 cm^2`
B. `69.4 cm^2`
C. `69 cm^2`
D. `70 cm^2`

Answer

To solve the problem of finding the area of a sheet with a length of 10.2 cm and a width of 68 cm, we will follow these steps:

### Step 1: Identify the formula for the area of a rectangle.
The area \( A \) of a rectangle is calculated using the formula:
\[ A = \text{length} \times \text{width} \]

### Step 2: Substitute the given values into the formula.
Here, the length \( L = 10.2 \, \text{cm} \) and the width \( W = 68 \, \text{cm} \). Therefore, we substitute these values into the formula:
\[ A = 10.2 \, \text{cm} \times 68 \, \text{cm} \]

### Step 3: Perform the multiplication.
Now, we calculate the area:
\[ A = 10.2 \times 68 = 693.6 \, \text{cm}^2 \]

### Step 4: Determine the number of significant figures.
Next, we need to consider the significant figures in our measurements:
- The length \( 10.2 \, \text{cm} \) has **3 significant figures**.
- The width \( 68 \, \text{cm} \) has **2 significant figures**.

The result should be reported with the least number of significant figures from the measurements used in the calculation, which is **2 significant figures**.

### Step 5: Round the result to the correct number of significant figures.
The calculated area is \( 693.6 \, \text{cm}^2 \). To round this to 2 significant figures:
- The first two digits are **69**.
- The next digit (3) is less than 5, so we do not round up.

Thus, the area rounded to 2 significant figures is:
\[ A \approx 69 \, \text{cm}^2 \]

### Final Answer:
The area of the sheet, addressed to the proper number of significant figures, is \( 69 \, \text{cm}^2 \).

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