- #1
shuxue
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The authors of a physics textbook want to determine the number of grains, N in a beach of 500 m long, 100 m wide, and 3 m deep. They assumed that each grain is 1-mm-diameter sphere. They also assumed that the grains are so tightly packed that the volume of the space between the grains is negligible compared to the volume of the sand itself. The authors found the answer as follows:
Volume of the beach = N X Volume of each grain
N = (Volume of the beach) / (Volume of each grain)
[tex]N=\frac{(500)(100)(3)}{(\frac{4}{3}\pi)(0.5\times10^{-3})^3}=2.9\times10^{14}\approx3\times10^{14}[/tex]
Why equal sign is used between [tex]\frac{(500)(100)(3)}{(\frac{4}{3}\pi)(0.5\times10^{-3})^3}[/tex] and [tex]2.9\times10^{14}[/tex] instead of approximation sign? Why approximation sign is used between [tex]2.9\times10^{14}[/tex] and [tex]3\times10^{14}[/tex] instead of equal sign?
Volume of the beach = N X Volume of each grain
N = (Volume of the beach) / (Volume of each grain)
[tex]N=\frac{(500)(100)(3)}{(\frac{4}{3}\pi)(0.5\times10^{-3})^3}=2.9\times10^{14}\approx3\times10^{14}[/tex]
Why equal sign is used between [tex]\frac{(500)(100)(3)}{(\frac{4}{3}\pi)(0.5\times10^{-3})^3}[/tex] and [tex]2.9\times10^{14}[/tex] instead of approximation sign? Why approximation sign is used between [tex]2.9\times10^{14}[/tex] and [tex]3\times10^{14}[/tex] instead of equal sign?