Think Carefully Part 1

Number Theory Level 1

What is the last digit of π \pi ?

See Part 2 , and Part 3 .

2 1 3 5 This question is flawed 4

Chung Kevin by Chung Kevin , 45, Australia

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3 solutions

π \pi is an irrational number, and hence has a non terminating non repeating decimal expansion. So, there does not exist the last digit of π \pi .

For the ones interested in proof of irrationality of π \pi , check this out ! (I had tried to prove the irrationality myself, but was unsuccessful. This page contains a lot of details, not just the proof but it's insights too).

12 Helpful 1 Interesting 0 Brilliant 0 Confused

Moderator note:

Well done!

Wwt Manahan
May 17, 2015

π \pi is irrational, which means that there exists no whole-numbered base in which the expansion of π \pi has a finite number of digits. Therefore, there is no last digit of π \pi , no matter which base you are working in.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

That's right!

Chung Kevin - 6 years ago
Avinash Kamath
Dec 1, 2015

π \pi is an irrational number and does not have an ending number

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Yes exactly. Another way to think of it is "If π \pi has a last digit, then it must be rational." which is wrong.

Thank you for your solution!

Chung Kevin - 5 years, 6 months ago

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