Measurements
Making Measurements Parallax – apparent shift in position because the object is viewed at different angles. Read instruments looking at eye level, directly at the instrument – not at an angle. When working in a lab group, readings of the same type should be made by the same person.
Accuracy How close a measurement is to the standard. Depends on the equipment and how well you use it. Standards are published in literature (books). Percent Error is a calculation to determine how accurate you are.
Precision How repeatable your measurement is. How well you repeat the measurement and get the same answer. Percent Difference is a calculation to determine how precise your measurements are.
Each of 4 physics students measured the mass of a physics textbook Each of 4 physics students measured the mass of a physics textbook. They each weighed the book 4 times. Knowing that the true mass is 2.31 kg, which student(s) weighed the book: Accurately and precisely Inaccurately but precisely Inaccurately and imprecisely Student 1 Student 2 Student 3 Student 4 2.38 kg 2.06 kg 2.32 kg 2.71 kg 2.23 kg 1.94 kg 2.30 kg 2.63 kg 2.07 kg 2.09 kg 2.31 kg 2.66 kg 2.55 kg 2.40 kg 2.68 kg
Accurate? Precise?
Measurements in Lab When making measurements in lab: and you are asked to compare your results to the standard, calculate the percent error. “compare your measured acceleration due to gravity (g) to the accepted value of 9.81 m/s2” – calculate percent error.
And you are asked to compare your results between measurements, calculate the percent difference. “compare the constant force from your data table with the constant force from your graph” calculate the percent difference. DO NOT WRITE – we were a little off or off by 1.5 kg. How well your experiment is conducted is determined by percent error or percent difference!
Significant Figures
Last digit you read is an estimate, and it is counted as significant!
Measure using the correct number of significant digits! 2.15 cm 3.10 cm 4.00 cm
Digits other than zero are always significant. 123 m (3) 344 m (3) 56,789 m (5)
Zeros between two other significant digits are always significant 102 m (3) 100.1 m (4) 100.09 m (5)
One or more final zeros used after the decimal point are always significant. 12.0 m (3) 12.30 m (4) 12.301000 m (8)
Zeros used solely for spacing the decimal point are not significant. 0.01 m (1) 100 m (1) 0.0033 m (2) 0.0303 m (3)
Counting numbers (conversion factors) have infinite number of significant digits. 5 days 1000 g = 1 kg 2 students
How many sig figs? 0.0013 g 70.020 g 100,000 mg 200,000.0 mm 1.000300 g 1,000,300 mg 937 kg 0.223 g 0.002300 g
Rounding to the correct number of sig figs Round 12.783456 cm to : 2 sig figs : 5 sig figs : 6 sig figs : 7 sig figs : 3.2 3.1 13 cm 12.783 cm 12.7835 cm 12.78346 cm
Round each to 4 sig figs 84,791 kg → 38.5432 g → 256.75 cm → 0.00054818 g → 2.0145 mL → 89,218 g → 199,870 mm → 126,778.43 L → 84,790 kg 38.54 g 256.8 cm 0.0005482 g 2.015 mL 89,220 g 199,900 mm 126,800 L
Calculations using Significant Figures
Addition and Subtraction – in addition and subtraction, the answer may contain only as many decimal places as the measurement having the least number of decimal places – least position. 966.5 kg + 25.26 kg = 991.76 kg Least position at tenth = 991.8 kg 745.88 kg - 101 kg = 644.88 kg Least position at ones = 645 kg
1.37 g + 1.251 g = 2.6210 g Least position at hundredths = 2.62 g 1287 m – 200 m = 1087 m Least position at hundreds = 1100 m
Multiplication and Division – In multiplication and division, the answer may contain only as many significant digits as the measurement with the least number of significant digits. 25.301 m x 2.01 m = 50.855 m2 (5) (3) → (3) = 50.9 m2 125.2 kg 101.456 m3 = 1.2340 kg/m3 (4) (6) → (4) = 1.234 kg/m3
Using Scientific Notation and Significant Digits! (6.96 x 102 kg) x (1.2 x 10-1 m/s) = ? 8.4 x 101 kg m/s 5.5 x 10-1 mm + 2.1 x 10-3 cm = ? 5.7 x 10-1 mm or 5.7 x 10-2 cm 0.1387 kg/[(0.121 m)(0.021 m)(2.00 m)] = ? 2.7 x 101 kg/m3 1.5 km – 355 m = ? 1.1 x 103 m or 1.1 x 100 km
Homework Measurements