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Exercise 4: Perform the following operations and express your answers with the correct number of significant figures: 1) 2 (270 kg)(16.4 m/s)? = 2) (213 m)(65.3 m) - (175 m)(44.5 m)= 3) A rectangle is measured to have a length of 54.7 m and a width of 20 m. What is its area?

Exercise 4: Perform the following operations and express your answers with the correct number of significant figures: 1) 2 (270 kg)(16.4 m/s)? = 2) (213 m)(65.3 m) - (175 m)(44.5 m)= 3) A rectangle is measured to have a length of 54.7 m and a width of 20 m. What is its area?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Exercise 4:
1) 4200km - 975km = 3225km - 3200 km (the 4200 km determines the precision to be in the 100's place) 2) 185km/4.5h = 41 km/h (the 4.5 h has 2 significant figures, so your answer can have only 2 significant figures) The units will be mixed; you cannot simplify km and h since they measure two different fundamental quantities. 3) (4.00 m)(12.65 m) + (24.6 m)² = 656 m? (3 significant figures in the multiplication step gives 50.6 m2; the (24.6 m)? with 3 significant figures gives 605 m²; the result of adding must be rounded to the unit's (one's) place because of the 605 m² term)' Exercise 4: Perform the following operations and express your answers with the correct number of significant figures: 1) 2 (270 kg)(16.4 m/s)? = 2) (213 m)(65.3 m) - (175 m)(44.5 m)= 3) A rectangle is measured to have a length of 54.7 m and a width of 20 m. What is its area? nthe 1'With calculators, this rule has been relaxed to a certain degree. Most instructors will allow all the calculations done in the calculator and then the final result expressed with the appropriate number of significant figures. Check with your instructor.
Transcribed Image Text:1) 4200km - 975km = 3225km - 3200 km (the 4200 km determines the precision to be in the 100's place) 2) 185km/4.5h = 41 km/h (the 4.5 h has 2 significant figures, so your answer can have only 2 significant figures) The units will be mixed; you cannot simplify km and h since they measure two different fundamental quantities. 3) (4.00 m)(12.65 m) + (24.6 m)² = 656 m? (3 significant figures in the multiplication step gives 50.6 m2; the (24.6 m)? with 3 significant figures gives 605 m²; the result of adding must be rounded to the unit's (one's) place because of the 605 m² term)' Exercise 4: Perform the following operations and express your answers with the correct number of significant figures: 1) 2 (270 kg)(16.4 m/s)? = 2) (213 m)(65.3 m) - (175 m)(44.5 m)= 3) A rectangle is measured to have a length of 54.7 m and a width of 20 m. What is its area? nthe 1'With calculators, this rule has been relaxed to a certain degree. Most instructors will allow all the calculations done in the calculator and then the final result expressed with the appropriate number of significant figures. Check with your instructor.
The number of significant figures in a measurement is also sometimes called the accuracy of the measurement (but it has nothing to do with how well you performed in making the measurement!). When using the rules of significant figures in calculations, it will depend on the calculation: When multiplying or dividing two or more quantities, the number of significant figures in the final result is the same as the number of significant figures in the least accurate of the factors being combined. This will be the rule you will need to follow most often in lab. However, you may also have to add or subtract measurements. Another rule then applies, one that looks at the precision of the measurement. The precision is the smallest unit in which the measurement was made, the decimal position of the last significant figure. The rule is: When adding or subtracting measurements, be sure all the units are the same. Then perform the operation and round the result to the same precision as the least precise measurement. If you have a combination of operations, use same order of operations with the significant figures as you do when performing the operation itself. Remember, using these rules will approximate the uncertainty by giving a reasonable number of significant figures to use in the answer. To find the true uncertainty, you would need to go through a series of calculations. Еxamples:
Transcribed Image Text:The number of significant figures in a measurement is also sometimes called the accuracy of the measurement (but it has nothing to do with how well you performed in making the measurement!). When using the rules of significant figures in calculations, it will depend on the calculation: When multiplying or dividing two or more quantities, the number of significant figures in the final result is the same as the number of significant figures in the least accurate of the factors being combined. This will be the rule you will need to follow most often in lab. However, you may also have to add or subtract measurements. Another rule then applies, one that looks at the precision of the measurement. The precision is the smallest unit in which the measurement was made, the decimal position of the last significant figure. The rule is: When adding or subtracting measurements, be sure all the units are the same. Then perform the operation and round the result to the same precision as the least precise measurement. If you have a combination of operations, use same order of operations with the significant figures as you do when performing the operation itself. Remember, using these rules will approximate the uncertainty by giving a reasonable number of significant figures to use in the answer. To find the true uncertainty, you would need to go through a series of calculations. Еxamples:
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