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 significant figures they represent. Precision in measurements is often indicated by the number of digits after the decimal point.

### Step-by-Step Solution:

1. **Convert Each Option to Decimal Form:**
- **Option 1:** \(3 \times 10^{-3} = 0.003\)
- **Option 2:** \(0.0030\)
- **Option 3:** \(30 \times 10^{-4} = 0.0030\)
- **Option 4:** \(300 \times 10^{-5} = 0.00300\)

2. **Count the Number of Digits After the Decimal Point:**
- **Option 1:** \(0.003\) has **3 digits** after the decimal point.
- **Option 2:** \(0.0030\) has **4 digits** after the decimal point.
- **Option 3:** \(0.0030\) has **4 digits** after the decimal point.
- **Option 4:** \(0.00300\) has **5 digits** after the decimal point.

3. **Determine the Most Precise Measurement:**
- The precision of a measurement is indicated by the number of significant figures. The more digits after the decimal point, the more precise the measurement.
- Comparing the options:
- Option 1: 3 digits
- Option 2: 4 digits
- Option 3: 4 digits
- Option 4: 5 digits
- Therefore, **Option 4 (300 × 10^(-5) or 0.00300)** is the most precise measurement as it has the highest number of digits after the decimal point.

### Conclusion:
The most precise measurement is **Option D: 300 × 10^(-5)**.

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