Exercise 1: Accuracy, Precision, and Significant Figures in Surveying | Summaries Engineering

TECHNICAL MEMORANDUM

SUBJECT: Exercise 1 Accuracy, Precision, and Significant Figures

FROM: Group 1

Name Field Survey Tech Memo

Celu Jay Cornita Surveyor/Recorder introduction

Eugene Andrei Canasa Surveyor/Recorder results and

discussion

Jeremiah Pelegrina Surveyor/Recorder methodology

Steven John Matala Surveyor/Recorder data

computation / conclusion and

recommendations

SUMMARY

In surveying, accuracy signifies closeness to the true value, while precision

reflects consistency in repeated measurements, often impacted by significant

figures and inherent errors. The exercise aims to teach the group to differentiate

accuracy and precision, determine the right significant figures for measurements,

identify them in recorded data, and make decisions about significant figures in

mathematical operations with multiple measurements.

The group initially characterized the precision of measuring instruments by

considering the minor divisions and significant figures in decimal form. They then

measured sides AB and BC of a table using three different instruments and recorded

significant figures to indicate precision. The group calculated and compared

average lengths, assessed device accuracy, computed the table's perimeter

following significant figure rules, and determined its surface area with consistent

significant figures throughout.

In this experiment, measurements of a table's dimensions were taken using

three different tools: measuring tape, meter stick, and steel ruler. Each tool had a

distinct smallest division, and measurements were recorded with a specific number

of significant figures. The most probable values MPVs for the table's length AB and

width BC were calculated based on the averages of measurements from each tool.

Additionally, the perimeter and area of the table were computed, and the percent

error was assessed by comparing the results from the different tools to those

obtained from the measuring tape, which was assumed to provide the most

accurate values. The steel ruler showed the smallest division, and its percent error

was lower than that of the meter stick.

The group's analysis suggests that the measuring tape provides the least

precision due to its larger smallest division, while the steel ruler appears to be the

most precise, reflected in their respective numbers of significant figures. Comparing

the most probable values MPVs of the steel ruler and meter stick to the measuring

tape, the steel ruler seems more accurate with lower error. However, the group

notes that for measuring larger objects like a table, the measuring tape is preferred

despite potentially lower precision because small errors can have a significant

impact on highly precise tools like the steel ruler. Therefore, precision, accuracy,

and the use of significant figures are crucial considerations in measurements and

scientific work.

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TECHNICAL MEMORANDUM

SUBJECT: Exercise 1 Accuracy, Precision, and Significant Figures FROM: Group 1 Name Field Survey Tech Memo Celu Jay Cornita Surveyor/Recorder introduction Eugene Andrei Canasa Surveyor/Recorder results and discussion Jeremiah Pelegrina Surveyor/Recorder methodology Steven John Matala Surveyor/Recorder data computation / conclusion and recommendations SUMMARY In surveying, accuracy signifies closeness to the true value, while precision reflects consistency in repeated measurements, often impacted by significant figures and inherent errors. The exercise aims to teach the group to differentiate accuracy and precision, determine the right significant figures for measurements, identify them in recorded data, and make decisions about significant figures in mathematical operations with multiple measurements. The group initially characterized the precision of measuring instruments by considering the minor divisions and significant figures in decimal form. They then measured sides AB and BC of a table using three different instruments and recorded significant figures to indicate precision. The group calculated and compared average lengths, assessed device accuracy, computed the table's perimeter following significant figure rules, and determined its surface area with consistent significant figures throughout. In this experiment, measurements of a table's dimensions were taken using three different tools: measuring tape, meter stick, and steel ruler. Each tool had a distinct smallest division, and measurements were recorded with a specific number of significant figures. The most probable values MPVs for the table's length AB and width BC were calculated based on the averages of measurements from each tool. Additionally, the perimeter and area of the table were computed, and the percent error was assessed by comparing the results from the different tools to those obtained from the measuring tape, which was assumed to provide the most accurate values. The steel ruler showed the smallest division, and its percent error was lower than that of the meter stick. The group's analysis suggests that the measuring tape provides the least precision due to its larger smallest division, while the steel ruler appears to be the most precise, reflected in their respective numbers of significant figures. Comparing the most probable values MPVs of the steel ruler and meter stick to the measuring tape, the steel ruler seems more accurate with lower error. However, the group notes that for measuring larger objects like a table, the measuring tape is preferred despite potentially lower precision because small errors can have a significant impact on highly precise tools like the steel ruler. Therefore, precision, accuracy, and the use of significant figures are crucial considerations in measurements and scientific work.

INTRODUCTION

In surveying, accuracy, and precision are fundamental concepts in measurement, where accuracy signifies the proximity to the actual value and precision denotes the consistency among repeated measures, frequently influenced by the number of significant figures and inherent process-related errors. Upon completing the exercise, the group must acquire the ability to distinguish between accuracy and precision, establish the appropriate number of significant figures for recording measurements, identify the number of significant figures in recorded measurements, and form decisions regarding the correct number of significant figures for mathematical operations involving multiple measured values. METHODOLOGY 1 measuring tape 1 table (assumed to be a perfect rectangle) 1 steel ruler 1 meter stick In this exercise, the group commenced by characterizing the precision of measuring instruments by determining the most minor divisions in decimal form (unit length of m) of each measuring instrument and considering the number of significant figures. Subsequently, each member took multiple measurements of the sides of the table, namely sides AB (length) and BC (width) using three different instruments (measuring tape, steel ruler, and meter stick), with the number of significant figures recorded for each measurement as an indicator of precision. The group then tabulated, computed, and compared the average lengths of sides AB and BC, and assessed the accuracy of alternative measuring devices assuming that the most probable values taken from the measuring tape are the closest to the true values of the table’s dimension. Moreover, the group also calculated the table’s perimeter while adhering to significant figure rules for precision in arithmetic operations, and determined the table’s surface area, maintaining the appropriate number of significant figures throughout the calculations. RESULTS AND DISCUSSION Table 1. Measuring Tape Member Tool Length (m) Significant Figures Width (m) Significant Figures Celu Measuring Tape

Eugene Measuring Tape

Jerem Measuring Tape

Luke Measuring Tape

Smallest Division: 0.002 m Most Probable Value: AB = 2.454 m BC =1.235 m Perimeter: 7.377 m

Eugene Steel Ruler

Jerem Steel Ruler

Luke Steel Ruler

Smallest Division: 0.0005 m Most Probable Value: AB = 2.4475 m BC =1.2345 m Perimeter: 7.3640 m Area: 3.0214 m 2 %error: AB = 0.3% BC = 0.02% ≈ 0.0% Table 3 shows the measured values of the table using the steel ruler. The smallest division distinguishable from the steel ruler is 0.0005 m. The values were expressed up to 5 significant figures. The group computed the most probable value of lengths AB and BC by getting the average of the measured values, namely; 2.4475 m for side AB and 1.2345 m for side BC. The group also solved for the perimeter and area of the table assuming that it is a perfect rectangle. Using the values obtained from measuring the table with a steel ruler. The perimeter computed is 7.3640 m, while the area is 3.0214 m 2

. To assess the accuracy of the values, the %error formula of the values gathered from the steel ruler compared to the measuring tape is used. The %error of the MPVs of AB and BC are 0.3% and 0.0%, respectively. Table 4. Summary of Results Tool Smallest Division, m MPVAB, m MPVBC, m Significant Figures Perimeter, m Area, m^2 %errorAB %errorBC Measuring Tape 0.002 2.454 1.235 4 7.377 3.030 - - Meter Stick 0.001 2.4461 1..2274 5 7.3470 3.0023 0.3% 0.6% Steel Ruler 0.0005 2.4475 1.2345 5 7.3640 3.0214 0.3% 0.02% ≈ 0% The table above presents the summary of the measured and computed values using measuring tape, meter stick and steel ruler. It can be observed that the measured values from the measuring tape are expressed in the least number of significant figures. Also, it has the highest value of the smallest division. Additionally, the steel ruler has the smallest value of division that can be distinguished. Furthermore, when it comes to the accuracy, assuming that the measuring tape provides the most accurate value, the steel ruler has a lower percent error compared to the meter stick. CONCLUSION AND RECOMMENDATION Based on the obtained values, the group concludes that the measuring tape provides the least precise as it has the highest value among the smallest divisions followed by the meter stick, whereas the steel ruler appears to be the most precise of the three. This is the reason why the measured values from the measuring tape are expressed in 4 significant figures while the other two are expressed in 5 significant figures. Upon comparing the MPV of the steel ruler and meter stick to the

MPV of the measuring tape, it appears that the steel ruler is more accurate as it has the least value of error compared to the meter stick. This provides the beautiful result that the steel ruler is more accurate and more precise. However, why do we still use measuring tape instead of steel rulers to measure huge objects like the table? It may appear that the ruler is more precise than the measuring tape, but we still use the measuring tape for measuring huge objects like the table as it provides more accurate results. One of the possible reasons for this is because the ruler is so small compared to the object being measured, it can be subjected to different errors. Since the ruler is more precise and detailed, any small error can induce a huge effect on its results. Precision in measurements refers to the ability to consistently obtain similar values when a measurement is repeated, but it does not guarantee accuracy. Systematic errors, calibration issues, measurement bias, sampling errors, measurement limitations, environmental factors, and human error can all lead to inaccuracies, even if precision is high. Accuracy, which relates to how closely measurements align with the true value, depends on addressing these sources of inaccuracy. In summary, precision and accuracy are related but distinct concepts. While precision reflects the repeatability and consistency of measurements, accuracy refers to how closely those measurements align with the true or accepted value. Achieving both precision and accuracy is essential in scientific and engineering work, as high precision alone does not ensure the correctness of results. Researchers and engineers must address systematic errors, calibration, sampling, and other sources of inaccuracy to obtain reliable and meaningful data. Moreover, aside from accuracy and precision. We must also take into consideration the importance of significant figures in expressing and computing values. Using the correct number of significant figures in presenting measurements or results of engineering and scientific calculations is crucial because it accurately conveys the precision and reliability of the data, preventing potential misinterpretation or misleading information. It ensures consistency in reporting, facilitates error analysis, aids in experimental design and instrument selection, and demonstrates professionalism within the scientific and engineering communities. Furthermore, adherence to significant figure conventions is often necessary for legal compliance and quality control, ultimately upholding the integrity and trustworthiness of research, engineering, and industrial processes. APPENDICES Table 3. Steel Ruler Member Tool Length (m) Significant Figures Width (m) Significant Figures Celu Steel Ruler 2.4445 5 1.2365 5 Eugene Steel Ruler 2.4525 5 1.2325 5 Jerem Steel Ruler 2.4435 5 1.2345 5 Luke Steel Ruler 2.4495 5 1.2345 5 Sample Solution Most Probable Value:

Exercise 1: Accuracy, Precision, and Significant Figures in Surveying, Summaries of Engineering

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TECHNICAL MEMORANDUM

INTRODUCTION