# Converting decimal to bicimal and other things

#### 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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Forum Staff

#### Debsta

MHF Helper
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)

1 person

#### topsquark

Forum Staff
0.111... (bicimal)) = 1/2 + 1/4 + 1/8 + 1/16 + …. = 1

1(decimal) = 1(bicimal)

-Dan

#### flashylightsmeow

-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
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.

MHF Helper

-Dan
MMF?

#### flashylightsmeow

Rey? No, just second part of Q14.

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#### Debsta

MHF Helper
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)