Which of the following is the most precise measurement?

Options

A. `3xx10^(-3)m`
B. 0.0030 m
C. `30xx10^(-4)m`
D. `300xx10^(-5)m`

Answer

To determine which of the given measurements is the most precise, we need to analyze each option based on the number of digits after the decimal point, as this indicates the precision of the measurement.

### Step-by-Step Solution:

1. **Understand Precision**: Precision in measurements is determined by the least count of the measuring instrument, which is reflected in the number of digits after the decimal point. The more digits there are after the decimal, the more precise the measurement.

2. **Convert Each Option to Decimal Form**:
- **Option 1**: \(3 \times 10^{-3} \, \text{m} = 0.003 \, \text{m}\) (3 digits after the decimal)
- **Option 2**: \(30 \, \text{m} = 30.000 \, \text{m}\) (0 digits after the decimal)
- **Option 3**: \(30 \times 10^{4} \, \text{m} = 300000 \, \text{m} = 300000.000 \, \text{m}\) (0 digits after the decimal)
- **Option 4**: \(300 \times 10^{-5} \, \text{m} = 0.00300 \, \text{m}\) (5 digits after the decimal)

3. **Count the Digits After the Decimal**:
- **Option 1**: 3 digits (0.003)
- **Option 2**: 0 digits (30.000)
- **Option 3**: 0 digits (300000.000)
- **Option 4**: 5 digits (0.00300)

4. **Determine the Most Precise Measurement**:
- From the analysis, Option 4 has the highest number of digits after the decimal point (5 digits), indicating that it is the most precise measurement.

5. **Conclusion**: Therefore, the most precise measurement among the options is **Option 4**: \(300 \times 10^{-5} \, \text{m}\).