Problem 9 - Applied Physics

Question

Determine the precision of each measurement. \(187.40 \mathrm{~m}\)

Step-by-Step Solution

Answer

The precision is indicated by 5 significant figures.

Step 1: Understanding Precision

Precision of a measurement refers to the number of significant figures used in representing it. It indicates the exactness of a measurement.

Step 2: Counting Significant Figures

To determine the precision, count the number of significant figures in the measurement. For the number 187.40 m, the significant figures are: '1', '8', '7', '4', and '0' which are all significant.

Step 3: Verifying Significant Figures

Ensure that all figures are accounted for, including zeros that are accounted for due to their position after a decimal point, as they contribute to the precision of the measurement.

Key Concepts

Significant Figures

Significant figures are the digits in a number that carry meaningful information contributing to its measurement precision. They help tell us how exact a measurement is. When we measure something like a distance or a weight, the number of significant figures indicates the reliability of the measurement. In the given example, 187.40 meters has five significant figures. Each digit, including the final zero, plays a crucial role. The zero here is not just a placeholder but a part of the precision, showing the measurement is exact up to one-hundredths of a meter.

• Each nonzero number is always significant.
• Zeros between nonzero digits are significant.
• Leading zeros are not significant.
• Trailing zeros after a decimal are significant.

Understanding these rules helps when properly recording or working with measurements.

Exactness of Measurement

Exactness of measurement refers to how close a recorded measurement is to the true value. It is often revealed through the number of significant figures. More significant figures imply more exactness. In practice, this means the measurement is closer to what would be considered the true value.
It is important to consider both the instrument used and how the measurement is recorded. For example, using a digital caliper would likely provide more exact readings than a simple ruler.
Through proper calculation and recording, measurements align closer to their true values, reducing potential errors.

Precision in Measurements

Precision in measurements refers to the consistency of several measurements or the fineness of a single measurement's scale. Precision is critical in providing reliable data as it ensures that repeated readings are very close to each other. If you measure something several times and get nearly the same result, your measurements are precise. Precision is distinct from accuracy, although they are related concepts.
Instruments that provide readings with more decimal places, like our example of 187.40 meters, offer greater precision. Precision doesn't necessarily indicate that the measurement is correct, just that it is consistent.
Using precise instruments and maintaining consistent measurement processes improves overall precision, leading to better and more reliable data collection.