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| Appendix A. Tutorial 6. Scientific Notation. At this time I would like to say a little bit about what is called scientific notation. Let’s look at some numbers: 1,000 1,000,000 100,000,000,000,000,000 What do we call the first number? It is one thousand. It has 3 zeroes. How about the second number? It is a million. It has six zeroes. How about the last number? It is one hundred quadrillion. It has 17 zeroes. How about this number? 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. I do not know its name, maybe someone does. Actually, I don’t want to know it even if someone does. It has 45 zeros. Sometimes in dealing with numbers in science we get so many zeros that it becomes very awkward to write them out. In fact, the first thing you need to do when you see such a number is to count the zeros. Wouldn’t it be nice to have some one count the zeros for you and tell you how many there are? That’s all scientific notation is. It is telling you how many zeros there are. So, we can also write 1,000 as the number 10^3, or sometimes as 1 x 10^3. Since in our number system a zero is a place holder for a ten times multiplier, in this symbol 10^3 the "10" indicates the multiplier and the "3" tells us how many multipliers or zeros there are. The ^ sign is used in spreadsheets to indicate an exponent, which is what the number in the position occupied by the 3 is called. So, since one million has six zeros, we can write it as 10^6. So, how about our big number? It has 45 zeros. So, we can write it as 10^45. And, if you are the reader, it is a lot nicer to have the author count the zeros for you instead of you yourself counting them. Suppose you want to write 2 million in scientific notation? In this case, you simply write it is two times one million, or 2 x 10^6. That is it. Scientific notation is nothing more than having someone else count all the zeroes for you and then telling you how many there are, so that you do not need to do it for yourself. |