Converting decimal to bicimal and other things

Feb 2011
86
1
Hi all

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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Debsta

MHF Helper
Oct 2009
1,312
597
Brisbane
Hi all

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"


Sent from my iPhone using Tapatalk
0.111... (bicimal)) = 1/2 + 1/4 + 1/8 + 1/16 + …. = 1


1(decimal) = 1(bicimal)
 
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topsquark

Forum Staff
Jan 2006
11,568
3,453
Wellsville, NY
0.111... (bicimal)) = 1/2 + 1/4 + 1/8 + 1/16 + …. = 1


1(decimal) = 1(bicimal)
Good grief! Don't go onto MMF and talk to zylo about this one...

-Dan
 
Feb 2011
86
1
Good grief! Don't go onto MMF and talk to zylo about this one...

-Dan
Lease elaborate!

@Debsta, sorry, is your Rey an answer to all the questions (granted, they are multifarious) in my post? If so, I am not seeing how!


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Debsta

MHF Helper
Oct 2009
1,312
597
Brisbane
Lease elaborate!

@Debsta, sorry, is your Rey an answer to all the questions (granted, they are multifarious) in my post? If so, I am not seeing how!


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Rey? No, just second part of Q14.
 

Debsta

MHF Helper
Oct 2009
1,312
597
Brisbane
Can you please show how you approach Ex 13 for 3.75? The example above Ex 13 refers back to Ex 1 which you have not included.

"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."
I don't understand what that is saying.


The way I would approach it is 3.75 = 2 + 1 + 0.5 + 0.25 = 1x2^1 +1x2^0 + 1x2^-1 +1x2^-2 = 11.11 (bicimal)