I keep getting the same answer?

[jajrussel]

I have entered this into my calculator several times and I keep getting the same answer could someone tell me why?

 

 

c^2-(1/c)^2 = 8.987551787e16

 

Then I enter

 

c^2-(1/c^2)^2 = 8.987551787e16

 

c is the speed of light 299792458

 

I am hitting the enter key at the = sign

 

I was expecting the second calculation to have a different result.

[uncool]

Because the difference between the two is too small to be displayed (or may even have been rounded off).

=Uncool-

[Bignose]

uncool has it.

 

(1/c)^2 = 1.112 x 10^-17

 

(1/c)^4 = 1.237 x 10^-34

 

Considering c^2 is on the order of 10^16, you are looking for a different more than 30 orders of magnitude difference. There are not many calculations or measurements that truly have 30 significant digits.

[jajrussel]

My thoughts were in agreement with uncool before I asked the question, but then I was afraid that maybe the way I was writing the equation somehow canceled itself out in both cases.

 

You may have noticed that the result for both equations is c^2. I was hoping for an answer however minuscule of slightly less than c^2.

 

At the moment I am not feeling very happy thinking about the amount of money I paid for this calculator, considering that I got the same results using a calculator that cost much less.

 

Still I can see by your equations that my thinking was flawed in that I initially thought the second equation would actually widen the gap giving me a better chance of getting an answer that was not c^2.

 

I guess I am going to have to get my book out and learn how to think this through in long hand.

 

Thank you both...

[Bignose]

I do want to say that both equations are meaningless dimensionally. c^s has units of length^2/time^2. 1/c^2 is, obviously, time^2/length^2.

 

You cannot add or subtract unlike units.

 

This like asking: what is 15 bananas minus 8 automobiles? you can compute 15-8, but the different units make the question meaningless.

 

You have the same thing with c^2 - (1/c^2). The different units on the subtraction make it a nonsense statement.

 

Just something you will have to remedy if you want your calculation to mean something.

 

edited to change a 'can' to a 'cannot' -- kinda fixes the whole post, really.

Edited May 22, 2013 by Bignose

[jajrussel]

Yes! You are right...

I am pretty much getting that idea. I am one of those people who likes to see exactly why he is wrong. Sometimes, it takes a long time for me to figure out that I am wrong. Usually, someone telling me that I am wrong sends me into automatic quarry mode, but I have been trying to figure this out long enough now, to see that what I am trying to do doesn’t actually make sense.

When I was a kid I was shown a formula that for me seemed to be magical. I spent a week trying to make it do different things. That is pretty much a long time to keep doing the same equation over and over again from as many different angles as I could think of; sometimes getting an answer that is close to being right, but only getting a consistently correct answer when the formula was used for what it was designed.

Sometimes I long to remember what that formula was so I can try it again.

Thank you for your help.