Powers of Tenor exponential notation on a scientific calculator. 

In science, we deal with numbers that are sometimes extremely large or extremely small. It helps to have a calculator around when doing math with such large numbers but you have to know how to use one. There are 602,000,000,000,000,000,000,000 molecules in 18 grams of water. A shorter way of writing the same number is by using exponential notation to show all those zeros as a number to the power of ten: 6.02 x 10^{23} is the shorter way of representing all those molecules. Such a number can be read "Six point zero two times ten to the twenty third." A small number such as 0.0000000057 can be written as 5.7 x 10^{9}. Such a number can be read "Five point seven times ten to the minus nine." How do you convert from one way of writing to another? Well, it's all in how you move the decimal point. Writing 10^{4}, for example, means that you are writing a one and then moving the decimal point four places. Since the exponent (the 4) is a positive number, we move the decimal place to the right. The animation below shows how it is done: Notice that the animation starts by reminding us that when we write "1", we are really writing "1." but we usually do not put the decimal point. At the end of the animation, the decimal point is in its new place, but again, we do not write it. Notice, also that there is a total of four zeroes. This is one way of checking if you did it correctly. (10^{4}, gives 4 zeroes). Now let's try the opposite. What if the exponent is a negative number? With the number 10^{4}, the technique starts out the same  we write a number 1, remembering that there is a decimal point after it. But then instead of moving the decimal point to the right, we move it to the left. To remember which way to move (left or right), remember that negative exponents (like 4 in the example) represent very small numbers  numbers that are less than one. As a result, they will always start with zero. Positive exponents (like 4 in the example), give numbers bigger than one. On scientific calculators, it is sometimes a bit of a trick to type these numbers in.
But there is a quicker way, using a special button which has been designed especially for exponential notation.




Have fun with your number crunching! 

© A.W. Damon 2011


Last modification: 20110301 