## 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 and one quadrillion is . So I can tell you that the answer is , 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 , so the answer is , 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 ) by one thousand million billion (which is ) longhand. Yuck. (By the way, the answer is .)

Greg Anderson
ganderson@ucsd.edu
Tue Jan 14 10:38:34 PST 1997