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 × 10^power).
• 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:

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.