QUESTION: The volume of a sphere of radius r is given by the formula: V = (4/3) ()(r3) The radius of a sphere is measured to be 5.00 cm. What is the proper way to report the volume? Note:  = 3.141592653589793238462643383279... A. 520 cm3, B. 523 cm3, C. 524 cm3 V = (4/3) (3.1) (5.00 cm)3 = 516.66.. cm3  520 cm3 V = (4/3) (3.14) (5.00 cm)3 = 523.3 cm3  523 cm3 V = (4/3) (3.142) (5.00 cm)3 = 523.66.. cm3  524 cm3 V = (4/3) (3.1416) (5.00 cm)3 = 523.6 cm3  524 cm3 V = (4/3) () (5.00 cm)3 = 523.59877559829887307710723054... 524 cm3 The volume of a sphere of radius r is given by the formula: volume equals four-thirds of pi times r cubed The radius of a sphere is measured to be 5.00 cm. What is the proper way to report the volume? A. 520 cm3, B. 523 cm3, C. 524 cm3 PAUSE 2 seconds CLICK Although pi is, strictly speaking, an exact number, it is also an irrational number and we can’t write it exactly. The question is, how should we round it off for this calculation? CLICK If we plug in 3.1 for pi, it would be less precise than 5.00 cm. So we would need to round off our answer to two significant digits. and the answer would be 520 cubic centimeters. HIGHLIGHT 520 If we use 3.14, CLICK we should have three significant digits in the answer, and the answer would be 523 cubic centimeters. HIGHLIGHT 523 If we use more significant digits for pi, we should still have only 3 significant digits in the final answer because 5.00 would be the precise term and it only has 3 significant digits. Here’s what we get if we use four significant digits for pi. HIGHLIGHT 524 Our answer in this case turns out to be 524 cubic centimeters. What we find in this case is that using more than four significant digits does not change our final answer. CLICK Here’s what we get if we round off pi to 5 significant digits... CLICK And here’s what we get if we use as many significant digits for pi as a typical calculator would give us. The point of this question is that whenever you are multiplying or dividing, quantities that have much more significant digits than the less precise term can be rounded off to fewer significant digits even before you do the calculation. But do so in a manner that still makes it more precise than the least precise term. Here, the least precise term is 5.00 cubic centimeters. It has 3 significant figures. So, if you have any other quantity, that has more significant digits, you can round off that quantity to 4 significant figures before you do the calculation. The correct answer is C. PAUSE END RECORDING

Video ID: 1A-4-7 © 2008, Project VALUE (Video Assessment Library for Undergraduate Education), Department of Physical Sciences Nicholls State University Author: Glenn V. Lo Funded by Louisiana Board of Regents Contract No. LA-DL-SELECT-13-07/08