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Rational or not? (Posted on 2015-05-29) Difficulty: 2 of 5
If I enter the expression


into my graphing calculator and then ask it for the fractional (rational) equivalent it cannot do so. Since the number is irrational it displays the first few decimal digits:


However, if I enter the expression


into the same graphing calculator and then ask it for the fractional equivalent it displays:
But this second number I entered is clearly not rational either.

What's going on?

No Solution Yet Submitted by Jer    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: solution | Comment 2 of 5 |
(In reply to solution by Charlie)

Incidentally I can only get TI-84 Plus Silver edition graphing calculators to do this.  Not the TI-83 or 84+, just the more expensive Silver Edition.

Several of my students have other brands of non-graphing scientific calculator: TI-30, Casio, Sharp.
I tried this on all of the calculators that have a rationalize key and none of them made this error.

Add that to the criticism of the over-priced TI graphing calculators.

I'm just finding out this goes further than I thought:
You can actually fool the calculator with A+B√2 with many values of A,B even if it doesn't exceed 100.

Edited on May 29, 2015, 12:31 pm
  Posted by Jer on 2015-05-29 12:26:22

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