Is there any irrational number in decimal with a rational binary expansion?

Salvador Bush

Salvador Bush

Answered

2022-07-02

Is there any irrational number in decimal with a rational binary expansion?

Answer & Explanation

Shawn Castaneda

Shawn Castaneda

Expert

2022-07-03Added 17 answers

No. If a number is rational, then the expansion in any numeral system will repeat, and if it is irrational, then it will not repeat in any system.
Blericker74

Blericker74

Expert

2022-07-04Added 5 answers

The concept of irrational number is independent of the way we choose of representing them. So, if a number is irrational, its expression in any base will be non-terminating and non-repeating.

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