# Thread: Converting decimal to bicimal and other things

1. ## Converting decimal to bicimal and other things

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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2. ## Re: Converting decimal to bicimal and other things

Originally Posted by flashylightsmeow
I attach photos of the text I refer to below.
Where?

-Dan

3. ## Re: Converting decimal to bicimal and other things

Originally Posted by topsquark
Where?

-Dan
Apologies. Cc

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4. ## Re: Converting decimal to bicimal and other things

Originally Posted by flashylightsmeow
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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0.111... (bicimal)) = 1/2 + 1/4 + 1/8 + 1/16 + …. = 1

1(decimal) = 1(bicimal)

5. ## Re: Converting decimal to bicimal and other things

Originally Posted by Debsta
0.111... (bicimal)) = 1/2 + 1/4 + 1/8 + 1/16 + …. = 1

1(decimal) = 1(bicimal)

-Dan

6. ## Re: Converting decimal to bicimal and other things

Originally Posted by topsquark

-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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7. ## Re: Converting decimal to bicimal and other things

Originally Posted by flashylightsmeow
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.

8. ## Re: Converting decimal to bicimal and other things

Originally Posted by topsquark

-Dan
MMF?

9. ## Re: Converting decimal to bicimal and other things

Originally Posted by Debsta
Rey? No, just second part of Q14.

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10. ## Re: Converting decimal to bicimal and other things

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)

11. ## Re: Converting decimal to bicimal and other things

Originally Posted by Debsta
MMF?
My Math Forum. Are you also a member there?

12. ## Re: Converting decimal to bicimal and other things

Originally Posted by Monoxdifly
My Math Forum. Are you also a member there?
Thanks. Don't think so. Certainly not an active one. I'll check it out.

13. ## Re: Converting decimal to bicimal and other things

Originally Posted by Debsta
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)
Thanks Debsta. Please see the page below.
I used the same method to convert 3.75, but when it comes to 0.703125 it's not as straightforward.

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14. ## Re: Converting decimal to bicimal and other things

You say: "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."

Can you please show me how you do this for 3.75 (ie using the hint given) and then I can try the next one. I'm still unsure how this process works.

15. ## Re: Converting decimal to bicimal and other things

Originally Posted by Debsta
You say: "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."

Can you please show me how you do this for 3.75 (ie using the hint given) and then I can try the next one. I'm still unsure how this process works.
Sure

Here we go

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