Question

Determine how dollar bills, placed end to end, are required to go around Earth at the equator. You will need to measure the length of a dollar bill.
** Must use unit analysis for all problems **

Answer 1

I didn't have a dollar bill handy.  So I conducted an extensive, exhaustive, in-depth, 2-minute internet search to determine the length of one.  (I lived in Boston for 6 years and it had a profound effect on me. All during the 2 minutes of my research, I kept mumbling "dorla bill" to myself.)  Anyway, the length of a US dorla bill is 6.14 inches. We want to find out HOW MANY dorla bills it would take.  We don't know that number yet, but we need to use it in our math, so we have to use something to put in its place until we find out the actual number.  Most people would use 'x'.  I'm going to use ' M '. Length of 1 bill . . . . . 6.14 inches Length of ' M ' bills . . . . . (6.14 M) inches Circumference of the Earth at the equator . . . . .  40,075 km inches in 1 foot . . . . . 12 feet in 1 meter . . . . . 3.28084 meters in 1 km . . . . . 1,000 This is all the outside information we need.  The rest is all arithmetic. ========================================== length of 1 bill, in inches . . . . . 6.14 inches length of ' M ' bills, in inches . . . . . (6.14 M inches) length of ' M ' bills, in feet . . . . .(6.14 M inches) x (1 foot/12 inches) length of ' M ' bills, in meters . . . . . (6.14 M inches) x (1 foot/12 inches) x (1 meter/3.28084 foots) length of ' M ' bills, in km . . . . .  (6.14 M inches) x(1 foot/12 inches) x(1 meter/3.28084 foots) x(1 km/1,000 m) . . . . . . . . . . ^ these numbers are equal \/ . . . . . . . . . . Circumference of the equator . . . . . 40,075 km ============================================== Gather all the numbers together, and all the units together: (6.14M x 1 x 1 x 1)/(12 x 3.28084 x 1,000) x (inch-foot-meter-km/inch-foot-meter) = 40,075 km Do the arithmetic, and cancel out units that appear on both top and bottom: (0.000155956 M) x (km) = 40,075 km Divide each side by 0.000155956 km, and you'll have: M = (40,075 / 0.000155956) M = 256.96 million bills ============================================ Quick check, just to see if it makes sense: Round each dorla bill to 6 inches even: (256.96 million x 6 inches) x (1 ft/12 inch) x (1 mile/5280 ft) = 24,333 miles Well,  the same internet says the equator's circumference is  24,901 miles.  YAY ! ! !  As an engineer, I'd say the two numbers match perfectly.  So the answer to the question is confirmed to be 256.96 million bills (2.57 x 10⁸ bills)