Powers and Error Overflow

[Sarah Bauguss]

I have a student who is entering a math competition. Part of the
competition is intended to be completed on a calculator, and a
question is 527 to the power of 527. If you enter this on the TI-
Nspire, you get and Error: Overflow. I've tried various alternatives,
settings...but still can't get around the overflow. I need the
student to be able to get the answer in scientific notation. Any
ideas?

[mjs]

thats a big number.

 

Doesnt compute on my CAS version either, but on a calculator that was able to solve it the answer was:

 

2.4785302115077919944770094215491e+1434

 

mshideler

---

From: Sarah Bauguss <sbau...@gmail.com>
To: tinspire <tins...@googlegroups.com>
Sent: Thu, April 7, 2011 1:19:32 PM
Subject: [tinspire] Powers and Error Overflow

--
To post to this group, send email to tins...@googlegroups.com
To unsubscribe send email to tinspire+unsub...@googlegroups.com
For more options, visit this group at
http://groups.google.com.au/group/tinspire?hl=en-GB?hl=en-GB
The tns documents shared by group members are archived at
http://lafacroft.com/archive/nspire.php

[Andy Kemp]

I'm not aware of any calculator that can do 527^527 directly as the answer is around 2.47x10^1434, and the Nspire only goes up to 10^999...

--
To post to this group, send email to tins...@googlegroups.com

To unsubscribe send email to tinspire+u...@googlegroups.com

[Marc Garneau]

That is not intended to be a calculator question directly.  The number needs to be re-represented in such a way that a calculator could handle, and then you can reason to the power.  I'd have to give some thought to what that would be - I'm sure there are others on this list who might know at a glance of a strategy.  Is the question multiple choice?  If so then some patterning is probably the key to it.

[SBauguss]

Hmm...there has to be a way.  Other students were able to answer the question, but I don't know if they had a different calculator or if they were just using another strategy along with use of the calculator.  It was a calculator test competition, which would imply that it can be done.  I just can't figure out how.  :(  Thanks for your thoughts.

[Andy Kemp]

A very rough and ready method would be to calculate 527^100 = 1.51727x10^272 and 527^27 = 3.08238x10^73

So 527^527 = (1.51727x10^272)(1.51727x10^272)(1.51727x10^272)(1.51727x10^272)(1.51727x10^272)(3.08238x10^73)

Taking the 1.51727^5*3.08238 gives 24.7857

taking the powers of 10 you get 272+272+272+272+272+73

Which gives: 10^1433

so final answer is 24.7857x10^1433 or in standard form 2.47x10^1434

You need to watch you don't loose digits because of accuracy...

On Thu, Apr 7, 2011 at 8:32 PM, SBauguss <sbau...@gmail.com> wrote:

Hmm...there has to be a way.  Other students were able to answer the question, but I don't know if they had a different calculator or if they were just using another strategy along with use of the calculator.  It was a calculator test competition, which would imply that it can be done.  I just can't figure out how.  :(  Thanks for your thoughts.

--

[mjs]

Just playing around with the CAS, if the test was multiple choice, a student could have simple used: 5.27^527 for the input which gives you 2.47853...^380. If the only right answer had 2.47853... in it then those that answered it correcly may have just used logic knowing that their power would be off but the digits would be correct.

---

From: Andy Kemp <an...@kemp.co>
To: tins...@googlegroups.com
Sent: Thu, April 7, 2011 1:38:49 PM
Subject: Re: [tinspire] Powers and Error Overflow

[Neville Windsor]

This can be easily solved using logarithms.
Log(527^527)=527*log527
Calculate 527*log527 and get 1434.394194.
Note the integer part (1434) and calculate 10^0.394194. The latter is 2.47853, and so the answer is 2.47853*10^1434.
Neville Windsor
Hellyer College
Burnie, Tasmania

--

To post to this group, send email to tins...@googlegroups.com To unsubscribe send email to tinspire+u...@googlegroups.com
For more options, visit this group at
http://groups.google.com.au/group/tinspire?hl=en-GB?hl=en-GB
The tns documents shared by group members are archived at http://lafacroft.com/archive/nspire.php

________________________________

Please consider the environment before printing this, or any other e-mail or document

________________________________________
CONFIDENTIALITY NOTICE AND DISCLAIMER

Information in this transmission is intended only for the person(s) to whom it is addressed and may contain privileged and/or confidential information. If you are not the intended recipient, any disclosure, copying or dissemination of the information is unauthorised and you should delete/destroy all copies and notify the sender. No liability is accepted for any unauthorised use of the information contained in this transmission.

This disclaimer has been automatically added.

[Andy Kemp]

Nice approach!

[Travis Bower]

[Neville Windsor]

Logarithms can be handy!  Some years back I challenged my students (these were very able grade 12s) to find the largest number they could using the digits of the year and any operations or non-integral numbers on a standard (scientific) calculator – with the condition that any operation or number could be used once only.  The problem I had was that some of the numbers they came up with are just so large it is hard to tell which is largest - things like (19^99)! (that’s factorial).  Large factorials can be approximated by n! approaches (n^n)*(e^(-n))*sqrt(2*pi*n), but in the end I had to use logarithms of logarithms.

Once the year 2000 arrived, I gave up!

Neville Windsor

Hellyer College

Burnie, Tasmania

 

[kwee]

all those ans given are approximation only. i dont know how to find
the exact ans, but suspect that the q did not require exact ans.
reasons:
1. i use 527*log(527), get :1434.394194217, so i know it is 10^1434:
so many digits!
2. the one digit of 7 rise to different power has a period of 4: one
digit of 7^1=7, that of 7^2=9,..7^3=3, 7^4=1, so 527^527 has a one
digit as 3, and has 1435 digits.so i dont think the q asked for exact
ans.
the closer i can get is:
10^(fpart(527log527)=2.478530211439, so the closer i can get is
2.478530211439*10^1434