ABSTRACT
Good old elementary fractions sit at the core of our discussion in this chapter. Just as they did in school, fractions can seem innocuous at first, only to cause you unbelievable confusion as soon as you take your eyes off them for a second. A classic puzzle, resurrected in one of National Public Radio’s Car Talk books (Magliozzi et al., 1999), asks the following teaser: you have a 100-lb bag of potatoes in your car and your prize vegetables comprise 99% water and 1% solid potato, where solid material and water content are assumed to weigh the same. You are worried that your buyers will find the potatoes too mushy and so you set out to extract some of the water. But it is difficult and, after much huffing and puffing, you can only reduce the water content to 98%. After you throw away the extracted water, how much does your bag of potatoes weigh? The answer is not 99 lb, not 98 lb, but just 50 lb! The moral of the story is that doubling a small proportion can have a much bigger impact even when portrayed as reducing a fraction from 99 to 98%.
