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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! smileycoolsmiley

 Apr 9, 2018
 #1
avatar+100456 
+2

(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

 

 

 

cool cool cool

 Apr 9, 2018
 #2
avatar+8 
0

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 samtcheeky

 Apr 9, 2018
 #3
avatar+428 
0

(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

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