Teaching Physics with the Physics Suite Edward F. Redish |
In 2004 the US Federal Budget was deeply in deficit, i.e., they were spending more money providing services than they were taking in taxes. In one year, the deficit was approximately $500 Billion ($5.0 x 10^{11}).
About $2000 apiece.
or about 75 square miles. Using the first digit of my thumb (1 inch) and a dollar bill, I find its dimensions to be 6 inches by 2.5 inches. So it has an area of (6 in) x (2.5 in) = 15 in^{2}.
We can do our calculation in a number of ways. We can ask: How many $1 bills does it take to cover DC and see if we have enough, or we could calculate the area of the deficit laid out in $1 bills and divide by the area of DC. I'll do the first. To cover DC by $1 bills we would have to divide its area up into $1 size pieces. The number of those pieces will be (75 mi^{2}) / (15 in^{2}). This is a pure number with no dimensions since we have dimensions of L^{2} on top and L^{2} on bottom. But to get to that number we have to make our units cancel. This means changing units to get them the same. The easiest way to do this is to multiply by "1" appropriately. Don't forget that mi^{2} means mi x mi so we need to cancel miles twice.
All the units cancel. In the last part, I have estimated 12 x 12 as 150 (a bit too big) and 5280 x 5280 as 5000 x 5000 or 25 million (a bit too small). The result is easier to calculate and pretty accurate. Since 5 times 150 is 750, the result is 7.5 x 0.25 x 10^{10} or about 2 x 10^{10}. Just 20 billion. Since we have 500 billion, we could cover DC 25 times over!
For making it easier to work with we have grouped the number parts together, the powers of 10 parts together, and the units parts together. The units all cancel except "y" (years). The number part is about 1/6, the power of 10 are 10^{(10-3-1-2)} = 10^{4} so our result is 10^{4}/6 y = 10,000/6 y = about 1600 years.
Page last modified August 22, 2004: G18