radix solution

[Commaster]

(36382.219) in radix 10 = (?) in radix 0.1

(5432.175)in radix 10 = (?)in radix 0.3

 

[Dr.Peterson]

(36382.219) in radix 10 = (?) in radix 0.1

(5432.175)in radix 10 = (?)in radix 0.3

How are you defining representations in bases less than 1? What digits do you allow? Have you been taught something about it, or are you just imagining possibilities?

The first is easy enough to answer, and provides some ideas; the second is a little harder to get my mind around.

 

[HallsofIvy]

"(36382.219) in radix 10" is 3.6382219 x 10^5
0.1= 10^{-1} so that is 3.632219 x 0.1^{-5}

 

[Dr.Peterson]

My assumption is that "radix 10" here means what it means in https://en.wikipedia.org/wiki/Radix, which we commonly call a "base".

There is a standard meaning for bases greater than 1: https://en.wikipedia.org/wiki/Non-integer_base_of_numeration

There are also negative bases: https://en.wikipedia.org/wiki/Negative_base

But for positive base (radix) less than 1, everything is questionable: https://math.stackexchange.com/ques...le-to-write-a-number-in-a-base-of-less-than-1