Fall 2013

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## The Numbers Game

Statistics are an important part of economics, and even we economists who love them have to admit they can sometimes be...well, boring. Crunching through the numbers of gross domestic product (GDP), the consumer price index, and interest rates, or calculating percentages and the difference between real and nominal values, students may struggle with putting these numbers and their importance into perspective. Consider just a few of the common economic statistics that might come up in your macroeconomics class (figures are current as of this writing).

U.S. civilian labor force: 155.8 million
First-quarter 2013 U.S. real GDP: \$13.7 trillion

And how much is a trillion anyway?

Below are a few tips, pointers, and links to help you make some common figures used in economics more real to your students—and a few of these tips are just plain fun!

What's the difference between 9 and 12 zeros? Hint: It's not 3!
Many of us grew up remembering the days when a million dollars could provide a comfortable living for a lifetime. Now Gen Y musicians Bruno Mars and Travie McCoy sing of wanting to be billionaires. What really is the difference? One mnemonic device that always impressed my students and that is a favorite with student tour groups here at the Atlanta Fed is this little factoid: it takes about 11 days for a million seconds to pass by, yet none of your high schoolers have yet seen a billion seconds elapse, since that takes about 32 years. And a trillion seconds? That would be 32,000 years!

The website pagetutor.com has a Google Sketchup graphic that shows exactly what a trillion dollars looks like. The MegaPenny Project web page helps you visualize the space you would need to store a trillion or even a quadrillion pennies. And for the classroom doodlers, a "Lots of Dots" tool lets you work with a million dots to grasp the numbers.

Stuck on what number comes after quadrillion? The University of North Carolina hosts a page that gives the names for all the large numbers, from quadrillion (10 to the 15th power) to duotrigintillion (10 to the 99th power). Among the interesting information on that page is the fact that in Europe, they count numbers differently: what we Americans call trillion, they call billion. In computer science, the difference between a million and a billion is denoted by the prefixes giga and tera.

Hands-on ideas
Another way for students to get a better grasp on these large numbers is to do some calculations. If one million dollars was divided throughout the U.S. population, everyone would get less than a third of a penny. A billion dollars would give us just over \$3. How much would we each get from a trillion dollars? That would be over \$3,000 each. How many years would it take your students to be the benefactor that could give this type of gift if they earned a yearly salary of \$25,000? \$50,000?  \$100,000?

The salaries of famous sports stars or celebrities, or the richest man in the world (Carlos Slim Helu, with a 2013 net worth of \$73 billion) are also topical ways to gauge the differences between a million and a billion or a billion and a trillion. And consider this: if Bruno Mars got his \$1 billion and had only a year to spend it, he would have to spend more than \$2.7 million dollars a day.

Seeing is believing
While online visuals are impressive, seeing really is believing when it comes to big numbers. That can be done in several ways, including counting grains of rice or candies such as M&Ms or pennies. Students can calculate not only the volume (how many containers it would take, for example) of these items, but also the weight. One million pennies, for example, weighs more than 6,000 pounds. If stacked in cubes, these pennies would make a wall four feet wide by five feet tall! How many pennies would you need to pay the school budget? How much would they weigh? What would you need to transport them in?

Another idea to express large numbers (as well as teach students the power of compounding) is to take a chessboard and have students start with a penny, paperclip, popcorn kernel, or other small object. Tell them that their task is to double the amount in each square. For instance, one penny in the first square, two in the second, then four in the third square, eight in the fourth square, and so forth. How many squares until they reach one million items in a stack? Of course, the students will run out of room on the squares before they complete their task—and there's the visual. If students try to guess beforehand how many squares, they'll probably be pretty far off on when they would reach a million. Even if they could fit everything on the squares, it won't take even half the board to get that far!

A picture tells the story
To test your students' ability to recognize large numbers, there are numerous neat visuals that you can use that also qualify as "artifacts," or primary sources, to meet Common Core standards. To help students really interact with the visuals, a very effective technique is to uncover only part of the picture (perhaps starting with the number) at a time, having the class try to guess what the item is before they put that number into context. Internet searches will reveal many good sources such as the 100 trillion dollar note from Zimbabwe, an excellent example of hyperinflation, or the \$9 billion dollar check (probably the largest ever written and an interesting story) written from Mitsubishi to Morgan Stanley during the financial crisis. Or you could start with the largest note of U.S. currency ever printed, the \$100,000 bill. How many of each of these would you need to reach a quadrillion?

A really, really big number
Here is one of the biggest numbers your students have probably ever encountered: \$16,900,000,000,000. That number represents the level of the national debt at the time this article was written. Just writing that number on the board will spark discussion. Students may ask, "Is that number real?" The U.S. National Debt Clock, though overwhelming, shows in real time the level of the national debt. As the numbers continue to move on the clock, it is not uncommon for students to ask, "How do we make it stop?"

The Concord Coalition has a number of good resources to help understand what these numbers mean, including an exercise in which students try their own hand at balancing the federal budget. From a Federal Reserve perspective, this exercise would be a good place to dispel a common myth about our central bank: the Federal Reserve Banks are not funded by the United States government. The Federal Reserve funds itself primarily from the interest on the U.S. Treasury securities it holds (currently about three trillion dollars, another big number!) and receives additional funding from the fees it charges depository institutions for services it provides, such as check clearing, funds transfers, automatic clearinghouse operations, and interest on loans. In contrast to adding to the federal debt, each year the Federal Reserve returns to the U.S. Treasury all funds exceeding its operating expenses. In 2012, this amount was \$88.4 billion.

To sum it all up (forgive the pun), macroeconomics deals with some very big numbers, and when students gain an appreciation of how big some of these numbers really are, they can better analyze the economy and the tradeoffs that occur when policymakers make economic policy decisions. They can also more easily compare economic conditions across time, regions, and the world.

By the way, here's one more number for you: this article contains 6,247 characters (without spaces). How long would this web page be if it had a million characters? A billion?