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Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin

Lawrence Weinstein
John A. Adam
Copyright Date: 2008
Pages: 320
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  • Book Info
    Book Description:

    Guesstimationis a book that unlocks the power of approximation--it's popular mathematics rounded to the nearest power of ten! The ability to estimate is an important skill in daily life. More and more leading businesses today use estimation questions in interviews to test applicants' abilities to think on their feet.Guesstimationenables anyone with basic math and science skills to estimate virtually anything--quickly--using plausible assumptions and elementary arithmetic.

    Lawrence Weinstein and John Adam present an eclectic array of estimation problems that range from devilishly simple to quite sophisticated and from serious real-world concerns to downright silly ones. How long would it take a running faucet to fill the inverted dome of the Capitol? What is the total length of all the pickles consumed in the US in one year? What are the relative merits of internal-combustion and electric cars, of coal and nuclear energy? The problems are marvelously diverse, yet the skills to solve them are the same. The authors show how easy it is to derive useful ballpark estimates by breaking complex problems into simpler, more manageable ones--and how there can be many paths to the right answer. The book is written in a question-and-answer format with lots of hints along the way. It includes a handy appendix summarizing the few formulas and basic science concepts needed, and its small size and French-fold design make it conveniently portable. Illustrated with humorous pen-and-ink sketches,Guesstimationwill delight popular-math enthusiasts and is ideal for the classroom.

    eISBN: 978-1-4008-2444-1
    Subjects: Mathematics, Business, Education

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. Table of Contents
    (pp. vii-x)
  3. Acknowledgments
    (pp. xi-xii)
  4. Preface
    (pp. xiii-xviii)
  5. Chapter 1 How to Solve Problems
    (pp. 1-10)

    STEP 1: Write down the answer [4]. In other words, come up with a reasonably close solution. This is frequently all the information you need.

    For example, if it is 250 miles from New York to Boston, how long will it take to drive? You would immediately estimate that it should take about four or five hours, based on an average speed of 50–60 mph. This is enough information to decide whether or not you will drive to Boston for the weekend. If you do decide to drive, you will look at maps or the Internet and figure out...

  6. Chapter 2 Dealing with Large Numbers
    (pp. 11-18)

    As you may have noticed, we used 10⁸ instead of 100,000,000 to represent 100 million. We do this for two reasons. The first is that, if we multiply 3 trillion times 20 quadrillion like this:\[\begin{array}{r} 3000000000000 \times 20000000000000000 \\ = 6000000 \ldots\ldots \\ \end{array}\]we will almost certainly miscount all those pesky zeros. If we use a calculator, we will first miscount the pesky zeros and then we will enter the incorrect number of zeros in the calculator so the number will be even more wrong. We’ll get an answer with the correct first digit (6) but the incorrect size. That’s like getting $60 when you should have...

  7. Chapter 3 General Questions
    (pp. 19-54)

    If all the humans in the world were crammed together, how much area would we require? Compare this to the area of a large city, a state or small country, the US, Asia.

    How much area would we need if we gave every family a house and a yard (i.e., a small plot of land)?

    ANSWER: Okay, 6 billion people is 6 × 10⁹ of us. How many can we cram into a square meter (i.e., 3 ft by 3 ft)? We’re not sure, but it is certainly between 3 and 10. We’ll choose 6. (That ignores the space needed...

  8. Chapter 4 Animals and People
    (pp. 55-86)

    How many cells are there in the human body?

    ANSWER: Sorry to ask such a personal question, since we hardly know one another, but what’s your volume? It’s on your driver’s licence, along with your surface area . . . oops, we were being futuristic. Since you didn’t answer the question, let’s figure it out. Let’s estimate your mass, Mr. Jones, at a nice even 100 kg (or approximately 200 lb; ladies, you can modify this to suit your own figures). Since we can safely assume that you float,*your average density is rather close to that of water or...

  9. Chapter 5 Transportation
    (pp. 87-112)

    How many total miles (or kilometers) do all Americans drive in one year? How does this compare to the circumference of the Earth (2.5 × 10⁴ mi), the distance to the Moon (2.4 × 10⁵ mi), the distance to the Sun (9 × 10⁷ mi), or the distance to Saturn (10⁹ mi)?

    ANSWER: To answer this question we need (1) how many miles each American drives and (2) the total number of Americans who drive. There are many ways to estimate our average mileage. You could look it up, but that would violate the spirit of this book, and besides,...

  10. Chapter 6 Energy and Work
    (pp. 113-144)

    Gravity sucks! If you drop something, it will fall. The gravitational acceleration at the surface of the Earth isg= 10m/s².*This means that a falling object will increase its speed by 10 ms (about 20 mph or 36 kph) every second. If you fell for 5 s, you would hit the ground at 50 ms or 110 mph or 180 kph. Ouch!

    gis also the gravitational force (measured in newtons (N)) exerted on an object of mass 1 kg (1 kg is about the mass of 2 lb) at the surface of the Earth. Thus, a 1-kg...

  11. Chapter 7 Hydrocarbons and Carbohydrates
    (pp. 145-178)

    Unless we are capable of photosynthesis, we get most of our energy from chemical reactions: from eating food and from burning hydrocarbon fuels. In a typical chemical reaction, one electron is exchanged between two atoms. The energy of this exchange is about 1.5 electron volts or 1.5 eV.*If you want more precision than that, ask a chemist or look it up. To convert this to a useful number, we need to know two things:

    The conversion from electron volts to joules: 1 eV ≈ 2 × 10–19J

    The number of molecules involved in the reaction

    To determine the...

  12. Chapter 8 The Earth, the Moon, and Lots of Gerbils
    (pp. 179-212)

    What is the orbital speed of the Earth around the Sun? What is its kinetic energy?

    ANSWER: To estimate the speed, we need the distance traveled and the time elapsed. The Earth takes one year to travel entirely around the Sun. The distance traveled is the circumference of the circle. The radius of that circle is the distance from the Earth to the Sun, orR= 1.5 × 1011m. If you usedR= 93 million miles, that’s fine too (93 million miles = 150 million kilometers = 1.5 × 1011m). Thus, the Earth’s speed is\[\begin{array}{l} \upsilon = \frac{\text{distance traveled}}{\text{time}}\\ \quad =\frac{2 \pi \times 1.5 \times 10^{11}\ \text{m}}{1\ \text{year}} = \frac{2 \pi \times 1.5 \times 10^{11} \ \text{m}}{\pi \times 10^{7}\ \text{s}}\\ \quad = 3 \times 10^{4}\ \text{m}/\text{s}\\ \end{array}\]...

  13. Chapter 9 Energy and the Environment
    (pp. 213-242)

    How much electrical power does one American or European family (or household) use (on average)?

    ANSWER: There are two ways to estimate the average power we use. We can work from the bottom up by adding up the contributions from individual appliances or we can work from the top down, using our electric bill to estimate the total electric energy we use in a month.

    Let’s start from the bottom up. Consider the appliances that are on for a significant fraction of the day. Since we are writing this book in August, we will consider air conditioners, stoves and ovens,...

  14. Chapter 10 The Atmosphere
    (pp. 243-272)

    What is the mass of the atmosphere?

    ANSWER: Atmospheric pressure is measured in too many different ways. It is 15 pounds per square inch or 10⁵ newtons per square meter or (shudder) 760mm (30 in.) of mercury or 10m of water. These last two measures just indicate that the weight of the air over a certain area is the same as the weight of an amount of mercury sufficient to cover the same area to a depth of 760mm (or enough water to cover the same area to a depth of 10 m).

    We can use any of these measures...

  15. Chapter 11 Risk
    (pp. 273-284)

    What is the risk (in the US) of dying per mile traveled in an automobile? What fraction of American deaths are caused by automobiles?

    ANSWER: We need to estimate the total number of miles traveled and the total number of deaths on the road. In question 5.1 we estimated the total distance that Americans drive each year to be about 2 × 1012mi. About 4 × 10⁴ Americans die each year in car crashes. Thus, the risk of death is

    \[R = \frac{{4 \times {{10}^4}\ {\text{deaths}}/{\text{yr}}}}{{2 \times {{10}^{12}}\ {\text{mi}}/{\text{yr}}}} = 2 \times {10^{ - 8}}\ {\text{deaths}}/{\text{mi}}\]

    Wow, there are only two deaths per 100 million miles. That sounds pretty safe.

    Let’s look at this...

  16. Chapter 12 Unanswered Questions
    (pp. 285-288)

    1. How many 1-gal (4-L) buckets of water are needed to empty Loch Ness (or Lake Erie)?

    2. How many cigarettes are smoked annually in the US? If you place them end-to-end, how far will they stretch?

    3. How many video rental stores are there in the US (or Europe)?

    4. How many people are talking on their cell phones at this instant?

    5. How many people are eating lunch at this instant?

    6. How fast does human hair grow (in m/s or mph)?

    7. How many grains of sand are there in all the beaches of the world?

    8. How many blades of grass are there on...

  17. Appendix A Needed Numbers and Formulas
    (pp. 289-290)
  18. Appendix B Pegs to Hang Things On
    (pp. 291-294)
  19. Bibliography
    (pp. 295-298)
  20. Index
    (pp. 299-301)