What would be the value of expressing something like the national debt in scientific notation? What information would be lost in such a usage? Is that important? Explain why or why not.
The US national debt as of 4/15/13 at 1:21:51 GMT is:
You might write this as `1.682"x"10^13` in scientific notation.
(In scientific notation, a number is generally written as `a"x"10^b` with 0<a<10, and a a real number. The number of digits that a is given depends on the number of digits that are "significant".
The actual number as written may not give as much meaning as telling someone that the debt is 16 with 12 zeroes behind it. The actual number (taken from the national debt clock website) is too precise as no one knows the precise moment each government check is cashed or payments to the government received. Thus losing the smaller value digits is probably not a handicap.
And when you are talking about trillions of dollars, a few billion here are there really don't make much of a difference. (If you are hundreds of thousands of dollars in debt, picking up a penny doesn't really help your situation.)