Of the following which is the most precisely reported value of a speed measurement?
125.00 km/s
Understanding Measurement Precision
When reporting a measurement in science, the way the value is written tells us about its precision. Precision refers to the level of detail or the fineness of the measurement. A more precise measurement has more significant figures or is reported to a smaller fractional part.
Significant Figures and Precision
Significant figures are the digits in a number that carry meaningful contributions to its measurement resolution. They include all non-zero digits, zeros between non-zero digits, and trailing zeros in a number containing a decimal point.
Generally, a value reported with more significant figures is considered more precise, assuming the measurement was performed with a suitable instrument.
Analyzing the Speed Measurements
Let's look at each given speed measurement option and determine the number of significant figures it contains:
- Option 1: 125 km/s
- The non-zero digits (1, 2, 5) are significant.
- Number of significant figures = 3.
- Option 2: 12.5 × 10 km/s
- This value is equal to 125 km/s.
- Similar to option 1, the non-zero digits (1, 2, 5) are significant.
- Number of significant figures = 3.
- Option 3: 125.00 km/s
- The non-zero digits (1, 2, 5) are significant.
- The zeros after the decimal point and after a non-zero digit are significant. The two zeros (0, 0) are significant.
- Number of significant figures = 5.
- Option 4: 1.250 × 102 km/s
- This value is in scientific notation. The significant figures are determined from the mantissa (the part before the × 10power).
- The mantissa is 1.250. The non-zero digits (1, 2, 5) are significant. The trailing zero after the decimal point (0) is also significant.
- Number of significant figures = 4.
Comparing Precision
We can compare the precision of the measurements by looking at the number of significant figures:
| Speed Measurement | Value | Significant Figures |
|---|---|---|
| Option 1 | 125 km/s | 3 |
| Option 2 | 12.5 × 10 km/s | 3 |
| Option 3 | 125.00 km/s | 5 |
| Option 4 | 1.250 × 102 km/s | 4 |
The value with the highest number of significant figures represents the most precise measurement among the given options. Option 3, 125.00 km/s, has 5 significant figures, which is more than the other options.
Therefore, 125.00 km/s is the most precisely reported value.
Important Questions from Data Interpretation
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