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Chapter 1: Problem 20
A year is very nearly \(\pi \times 10^{7}\) s. By what percentage is this figure in error?
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Find the cube root of \(6.4 \times 10^{19}\) without a calculator.
Emissions of carbon dioxide from fossil-fuel combustion are often expressed in gigatonnes per year, where 1 tonne \(=1000 \mathrm{kg}\) But sometimes \(\mathrm{CO}_{2}\) emissions are given in petagrams per year. How are the two units related?
To see why it's important to carry more digits in intermediate calculations, determine \((\sqrt{3})^{3}\) to three significant figures in two ways: (a) Find \(\sqrt{3}\) and round to three significant figures, then cube and again round; and (b) find \(\sqrt{3}\) to four significant figures, then cube and round to three significant figures.
To raise a power of 10 to another power, you multiply the exponent by the power. Explain why this works.
The human body contains about \(10^{14}\) cells, and the diameter of a typical cell is about \(10 \mu \mathrm{m}\). Like all ordinary matter, cells are made of atoms; a typical atomic diameter is \(0.1 \mathrm{nm}\). The volume of a cell is about \(\begin{array}{ccc}\text { a. } 10^{-10} \mathrm{m}^{3} . & \text { b. } 10^{-15} \mathrm{m}^{3} . & \text { c. } 10^{-20} \mathrm{m}^{3} . \quad \text { d. } 10^{-30} \mathrm{m}^{3}\end{array}\)
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