Proof Using Euler's Theorem: Rational Implies Recurring
Автор: Dr Barker
Загружено: 2023-08-31
Просмотров: 4086
Описание:
We prove, using Euler's theorem, that every rational number has a recurring (repeating) or terminating decimal expansion.
Euler's theorem:
https://en.wikipedia.org/wiki/Euler%2...
00:00 Intro
00:16 Recurring implies rational
01:26 Form of the denominator
02:03 Proof outline
02:29 Getting 10^m
04:26 Terminating case
05:31 Euler's theorem
06:24 Getting 10^n - 1
08:28 Why is it recurring?
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