Scientific Notation

    When my visual learning daughter was in high school, she had trouble learning scientific notation.  This is the conversion of LARGE NUMBERS to smaller numbers with exponents.  She could never remember which way to move the decimal and whether the exponent was a positive or negative.

     So I explained it to her using lollipops and rats.  The word lollipop starts with an l as does the word LEFT.  Lollipops are also a positive thing. The word rat starts with an r as does the word RIGHT.  Rats are usually a negative thing.  (Don't be fooled with the cute picture above.  He was just a cute image to get to this blog about MATH). 

    So, I told her the story about how a scientist is taking notes in shorthand to count MILLIONS of cells.  He was driving to the lab one day on the highway.  He noticed that the exit signs were placed on the road name signs on either the left (for a left hand exit) or on the right (for a right hand exit).  He compared this idea to exponents and was excited about explaining this to his class of future scientists.                                 

     So the next day in class, he used the number 7,854,000,000. as and example.  He told them that to convert this number to scientific notation, you must first recognize this number is a POSITIVE number. " Pretend that it is money," he told them.  They practiced and practiced just recognizing that the decimal at the end of the number made the number positive.  Next, he told them that to convert the number, they would have to place or move the decimal between the front or first two digits.  They were to pretend that they were turning LEFT off of the highway.  On the way to their destination, they saw a LOLLIPOP store.  Since this was such a POSITIVE idea, the exponents would also be positive.  Hence, the catch phrase, "LEFT IS FOR LOLLIPOPS."  So, the result of this conversion is:                  7.8 x 10⁹  

^{The exponent is nine because we moved the decimal point nine places.  It is positive because we went left past the lollipop store.}

  ^{The following day, he used the number  .000034  as an example.  He reminded them that they must recognize this number as a NEGATIVE number in exponents because it is smaller than 1.  In order to convert this number, they had to turn RIGHT off of the highway.  On the way to their destination this time, they saw a RAT.  Since this was such a NEGATIVE idea, the exponents would also be negative.  Hence, the catch phrase, "RIGHT IS FOR RATS."  So, the result of this conversion is:}

                                

                         3.4 x 10^-5

^{The exponent is -5 because we moved the decimal point five places to the right.  It is also negative because we went RIGHT past a RAT.}