While measuring length of small iron rod, following five reading wee obtained.
`12.66 mm, 12.58 mm, 12.62 mm, 12.80 mm and 12.72mm`
The experimenter reported the result of the experiment based on the obove readings.

Options

A. Number of significant figures in the length reported will be `3`.
B. Number of significant figures in the lenth reported will be `4`.
C. Number of significant figure in the error reported will be `1`.
D. Number of significant figures in the error reported will be `2`.

Answer

To solve the problem of determining the reported result of the length of the small iron rod based on the given readings, we will follow these steps:

### Step 1: List the Readings
The readings obtained while measuring the length of the iron rod are:
- 12.66 mm
- 12.58 mm
- 12.62 mm
- 12.80 mm
- 12.72 mm

### Step 2: Calculate the Sum of the Readings
We need to sum all the readings:
\[ \text{Sum} = 12.66 + 12.58 + 12.62 + 12.80 + 12.72 \]
Calculating this gives:
\[ \text{Sum} = 12.66 + 12.58 + 12.62 + 12.80 + 12.72 = 63.38 \text{ mm} \]

### Step 3: Calculate the Mean Value
To find the mean value, we divide the sum by the number of readings (which is 5):
\[ \text{Mean} = \frac{\text{Sum}}{\text{Number of Readings}} = \frac{63.38}{5} \]
Calculating this gives:
\[ \text{Mean} = 12.676 \text{ mm} \]

### Step 4: Rounding to Significant Figures
The readings have 4 significant figures (as seen from the least precise reading, which is 12.58 mm). Therefore, we need to round the mean value to 4 significant figures:
\[ \text{Rounded Mean} = 12.68 \text{ mm} \]

### Step 5: Report the Result
The experimenter reports the result of the experiment as:
\[ \text{Reported Length} = 12.68 \text{ mm} \]

### Final Answer
The reported result of the length of the small iron rod is **12.68 mm**.

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