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# Help! Thanks :)!

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For each part of this problem, convert the fraction to a "decimal" in the specified base.

(a) What is 1/2 in base 3?

(b) What is 1/7 in base 8?

(c) What is 1/(b-1) in base b?

Thanks!   Apr 9, 2018

### 3+0 Answers

#1
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(1/2)  to base 3

(1/2) * 3   =  3/2     ⇒  1  + 1/2

(1/2) * 3  =   3/2     ⇒  1  + 1/2

(1/2) * 3  =  3/2    ⇒   1  +  1/2

........

Read  the numbers  in red from bottom to top =  .111...3

(1/7) base  8

(1/7) * 8  =  8/7   =  1  +  1/7

(1/7) * 8  = 8/7    =  1  + 1/7

(1/7) * 8  = 8/7   =    1 + 1/7

........

Read the red numbers from bottom to top  =  .111...8

So  it appears  that   1  / (b - 1)  in  base b  is  .111.....b   Apr 9, 2018
#2
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1/2)  to base 3

(1/2) * 3   =  3/2     ⇒  1  + 1/2

(1/2) * 3  =   3/2     ⇒  1  + 1/2

(1/2) * 3  =  3/2    ⇒   1  +  1/2

........

Read  the numbers  in red from bottom to top =  .111...3

(1/7) base  8

(1/7) * 8  =  8/7   =  1  +  1/7

(1/7) * 8  = 8/7    =  1  + 1/7

(1/7) * 8  = 8/7   =    1 + 1/7

........

Read the red numbers from bottom to top  =  .111...8

So  it appears  that   1  / (b - 1)  in  base b  is  .111.....b

see im samt Apr 9, 2018
#3
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(1/2) * 3   =  3/2     ⇒  1  + 1/2

(1/2) * 3  =   3/2     ⇒  1  + 1/2

(1/2) * 3  =  3/2    ⇒   1  +  1/2

........

Read  the numbers  in red from bottom to top =  .111...3

(1/7) base  8

(1/7) * 8  =  8/7   =  1  +  1/7

(1/7) * 8  = 8/7    =  1  + 1/7

(1/7) * 8  = 8/7   =    1 + 1/7

........

Read the red numbers from bottom to top  =  .111...8

So  it appears  that   1  / (b - 1)  in  base b  is  .111.....b

Apr 9, 2018