Tuesday, June 14, 2011

Large Numbers

I saw this video a while back and was impressed with how well it conveyed how large a trillion dollars is.

Most of us have difficulty performing math involving large numbers in our heads. However, it's an ability that anyone can learn and may be useful to enable the average person how to evaluate policies and make decisions.  People fail to make calculations when it involves large numbers; consequently, they may make decisions based on "gut feeling" rather than facts.  However, there are shortcuts to making calculations involving large numbers:

One method involves the power of 10 and exponents. To multiply (or divide) large numbers and get a ball-park answer, one can add (or subtract) the exponents.  The number of digits in a number equals the exponent.  If the first digit is over 3, add one half.  If you want to divide 22 billion by 45 million, then convert to 10 to the 10 (1 billion = 9 zeros; 22 billion adds another digit) and 10 to the 7.5 (45 million = 1.5 digits plus 6 zeros). Subtracting, we get 10 to the 2.5, which is about 500 (the exact answer is 488.89).

Students might also find such methods useful on exams where the multiple choice answers differ by orders of magnitude.

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