How accurate is the TI-89 for extremely large numbers

[mathlover987]

I had my calculator factor the expression 2^47-1; however, it said that 2 was a factor of this number (which is incorrect). Does the calculator become innacurate when dealing with extremely large numbers? Also, is there any way to fix this problem?

[mellamokb]

Hi mathlover987,

The calculator should not be inaccurate unless it cannot represent the entire number. This can be caused by using a decimal approximation of the result. What display mode is your calculator using (MODE -> Scroll down to Exact/Approx)?

In "Auto" mode, it will decide automatically whether to use exact numbers or approximations. In "Exact" mode, it will always use the whole number. In "Approx" mode it will use rough approximations using only the first 1-12 significant digits, depending on your MODE -> Display Digits setting.

For example, in exact mode, when I type 2^47-1 I get: 140737488355327
In approximate mode I get: 1.40737E14

The second case gives 2 as a factor, but the first case does not.

Hope this helps!

Regards,
~ mellamokb

[mathlover987]

Thanks, it helped.