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Chapter 1: Problem 29
A radian is how many degrees?
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Add \(1.46 \mathrm{m}\) and \(2.3 \mathrm{cm} .\)
When we write the number 3.6 as typical of a number with two significant figures, we're saying that the actual value is closer to 3.6 than to 3.5 or \(3.7 ;\) that is, the actual value lies between 3.55 and \(3.65 .\) Show that the percent uncertainty implied by such two-significant-figure precision varies with the value of the number, being the lowest for numbers beginning with 9 and the highest for numbers beginning with \(1 .\) In particular, what is the percent uncertainty implied by the numbers (a) \(1.1,\) (b) \(5.0,\) and (c) \(9.9 ?\)
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.
A hydrogen atom is about \(0.1 \mathrm{nm}\) in diameter. How many hydrogen atoms lined up side by side would make a line \(1 \mathrm{cm}\) long?
Bubble gum's density is about \(1 \mathrm{g} / \mathrm{cm}^{3} .\) You blow an \(8-\mathrm{g}\) wad of gum into a bubble \(10 \mathrm{cm}\) in diameter. What's the bubble's thickness? (Hint: Think about spreading the bubble into a flat sheet. The surface area of a sphere is \(4 \pi r^{2} .\) )
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