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

Download Exercise 1: Accuracy, Precision, and Significant Figures in Surveying and more Summaries Engineering in PDF only on Docsity! 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 2.445 4 1.235 4 Eugene Measuring Tape 2.463 4 1.234 4 Jerem Measuring Tape 2.454 4 1.235 4 Luke Measuring Tape 2.453 4 1.235 4 Smallest Division: 0.002 m Most Probable Value: AB = 2.454 m BC =1.235 m Perimeter: 7.377 m 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: Length Width MPV AB= ∑ AB 4 MPV AB= 2.4445m+2.4525m+2.4435m+2.4495m 4 MPV AB= 9.7900 4 m MPV AB=2.4475m MPV BC= ∑ BC 4 MPV BC= 1.2365m+1.2325m+1.2345m+1.2345m 4 MPV BC= 4.938 4 m MPV BC=1.2345m MPV BC=1.2345m Perimeter Area P=2 AB+2BC P=2 (2.4475m )+2 (1.2345m ) P=4.8950m+2.4690m P=7.3640m A=AB x BC A=(2.4475m) (1.2345m ) A=3.02143875 A=3.0214m2 %errorAB= true value−experimental value true value x 100% %errorAB= 2.45375m−2.4475m 2.45375m x100% %error AB= 0.00625m 2.45375m x100% %errorAB=0.0025471218 x 100% %errorAB=0.25471218% %errorAB=0.3% errorBC= true value−experimentalvalue true value x100% %error BC= 1.23475m−1.2345m 1.23475m x100% %errorBC= 0.00025m 1.23475m x 100% %errorBC=0.0002024701 x 100% %errorBC=0.02024701% %errorBC=0.02%≈0%