Three measurements 7.13, 7.2) and 6.7J are made as experiment the result with correct number of significant figures is

Options

A. 7.1 J
B. 7.06 J
C. 7.0 J
D. 7J

Answer

To solve the problem of determining the result of the measurements 7.13 J, 7.2 J, and 6.7 J with the correct number of significant figures, we will follow these steps:

### Step 1: Add the Measurements
First, we need to add the three measurements together:
- 7.13 J
- 7.2 J
- 6.7 J

Calculating the sum:
\[ 7.13 + 7.2 + 6.7 = 21.03 \text{ J} \]

### Step 2: Calculate the Average
Next, we divide the total by the number of measurements (which is 3) to find the average:
\[ \text{Average} = \frac{21.03 \text{ J}}{3} = 7.01 \text{ J} \]

### Step 3: Determine the Significant Figures
Now, we need to consider the significant figures of the original measurements:
- 7.13 J has **3 significant figures**.
- 7.2 J has **2 significant figures**.
- 6.7 J has **2 significant figures**.

The minimum number of significant figures among these measurements is **2**.

### Step 4: Round the Average to the Correct Significant Figures
Since our average (7.01 J) has **3 significant figures**, we need to round it to **2 significant figures**.

Looking at the digits:
- The first two significant figures are **7** and **0**.
- The next digit is **1**, which is less than 5, so we do not round up.

Thus, rounding 7.01 J to 2 significant figures gives us:
\[ 7.0 \text{ J} \]

### Final Answer
The result with the correct number of significant figures is:
\[ \boxed{7.0 \text{ J}} \]

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