The accuracy in the measurement of speed of light is `3.00xx10^(8)m//s` is

Options

A. `(1)/(300)%`
B. `(1)/(3)%`
C. `3%`
D. `(1)/(30)%`

Answer

To find the accuracy in the measurement of the speed of light given as \(3.00 \times 10^8 \, \text{m/s}\), we will calculate the maximum possible percentage error.

### Step-by-Step Solution:

1. **Identify the Measurement**:
The speed of light is given as \(c = 3.00 \times 10^8 \, \text{m/s}\).

2. **Determine the Least Count**:
The least count refers to the smallest increment that can be measured accurately. For the measurement \(3.00\), the least count can be considered as \(0.01\) when expressed in scientific notation. Therefore, we have:
\[ \Delta c = 0.01 \times 10^8 \, \text{m/s} \]

3. **Calculate the Percentage Error**:
The formula for percentage error is given by:
\[ \text{Percentage Error} = \left(\frac{\Delta c}{c}\right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Error} = \left(\frac{0.01 \times 10^8}{3.00 \times 10^8}\right) \times 100 \]

4. **Simplify the Expression**:
Simplifying the fraction:
\[ \text{Percentage Error} = \left(\frac{0.01}{3.00}\right) \times 100 \]
\[ = \frac{1}{3} \times 100 \]
\[ = \frac{100}{3} \approx 33.33\% \]

5. **Final Result**:
Thus, the maximum possible percentage error in the measurement of the speed of light is:
\[ \text{Accuracy} \approx 0.33 \, \text{or} \, \frac{1}{3} \% \]

### Conclusion:
The accuracy in the measurement of the speed of light is approximately \( \frac{1}{3} \% \).

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