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Multiplying and dividing powers of 10

  Now, maybe you're not convinced that it's nice being able to write numbers in powers of ten. Well, it turns out that powers of ten are nice for doing math, as well. Let's say I ask you ``what is 10 times 1,000?'' Not a big deal, right -- it's just 10,000. OK, but what if I asked you ``what is one trillion times one quadrillion?'' First, you'd probably say, ``who cares?!'' And you'd probably be right.

But it turns out that multiplication of numbers that big is really really easy with powers of 10. All you have to do is add up the exponents, and you're done. Let's use the example I just gave you. What is one trillion times one quadrillion? First, using Table 1, you can see one trillion is tex2html_wrap_inline537 and one quadrillion is tex2html_wrap_inline539 . So I can tell you that the answer is tex2html_wrap_inline541 , which is a really big number -- and I can tell you that almost immediately, without needing a calculator or a piece of paper to do it longhand. Here are some more examples:


Division works similarly, except that you subtract the exponents. What is one trillion divided by one quadrillion? Well, it is tex2html_wrap_inline543 , so the answer is tex2html_wrap_inline545 , or one thousandth. Here are some more examples:


Again, while this may not seem useful for small numbers, imagine dividing one trillion trillion trillion (which is tex2html_wrap_inline547 ) by one thousand million billion (which is tex2html_wrap_inline549 ) longhand. Yuck. (By the way, the answer is tex2html_wrap_inline549 .)

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Greg Anderson
Tue Jan 14 10:38:34 PST 1997