I attach photos of the text I refer to below.

Regarding Ex. 13. I understand that the answers can be found by multiplying successively by 2 and taking the whole unit at each stage as 1 and 0 where there is none.

My question is, is there another way?

Given the preceding narrative on expressing decimals as quotients of two rationals I thought it may be possible to do so and convert both numerator and denominator to binary and go from there.

Second, why does this multiplication by 2 method work?

Regarding Ex.14 my answer is that $0.\dot{9} = 1$ base 10 and $0.\dot{1} = 1$ base 2. Is that correct. It seems "strange"

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