fraction exponents

[Meredith92]

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Does anyone know an easy way to handle fraction exponents (ones that dont have 2 or three in the denominator)? TBR had a problem where it expected us to know how to solve 10^.3

 

[milski]

If you want to be precise, it's best to go through logs. http://forums.studentdoctor.net/showthread.php?t=980006 this is fairly detailed but a bit of overkill, if you ask me. Look at post (http://forums.studentdoctor.net/showpost.php?p=13617494&postcount=8) for a simpler and more reasonable way.

I doubt that we'll have to deal with anything but 1/2 and 1/3. As for 0.3 - that's pretty much 1/3 and 10^0.3 should be about 2.1 or so.

 

[gettheleadout]

Using the premise behind this trick in the case of positive exponents, you can estimate this pretty closely. Given this trend:

10^3 = 1 x 10^3
10^3.5 = ~3 x 10^3
10^4 = 1 x 10^4
10^4.5 = ~3 x 10^4

Since the decimal 3 in 10^.3 is less than 5, we know the mantissa will be less than three, with an exponent of 10^0.

We can therefore estimate 10^.3 to be <3 x 10^0 so some value less than 3. That should be close enough.