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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.)
Some Thoughts This issue causes troubles. Comment 5 of 5 |
The problem Isosceles Leg Length
uses the very similar number 85+42√2
which my calculator thinks is 47651/330

What is it about 42√2?
which implies the excellent approximation
√2 ≈ 19601/13860
1.414213562 ≈ 1.414213564

The fraction is actually one of the convergents to √2

  Posted by Jer on 2016-06-11 12:22:47
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