repeating decimals for prime numbers

[pedram]

hi guys!
i have a question about length of repeating decimals for prime number
if p is prime , for wich numbers length of repeat decimal 1/p is p-1?

 

[Steven G]

hi guys!
i have a question about length of repeating decimals for prime number
if p is prime , for wich numbers length of repeat decimal 1/p is p-1?

I think you are asking what is the length of repeat decimal 1/(p-1)?

p=2: 0

p=3: 1

p=5: 2

p=7: \(\displaystyle \infty\)

p=11: 1

p=13: \(\displaystyle \infty\)

I do not think that you can have a formula to get your result.

 

[lookagain]

hi guys!
i have a question about length of repeating decimals for prime number
if p is prime , for wich numbers length of repeat decimal 1/p is p-1?

No, I think it is asking for which prime numbers p, does its reciprocal have a (primitive) repeating block in the decimal expansion equal to (p - 1)?

1/7 --> 0.142857 (repeats) . . . . . . . . . . . . . . . . . . . . 6-digit long block

1/17 --> 0.0588235294117647 (repeats) . . . . . . . . . . . 16-digit long block

 

[pedram]

No, I think it is asking for which prime numbers p, does its reciprocal have a (primitive) repeating block in the decimal expansion equal to (p - 1)?

1/7 --> 0.142857 (repeats) . . . . . . . . . . . . . . . . . . . . 6-digit long block

1/17 --> 0.0588235294117647 (repeats) . . . . . . . . . . . 16-digit long block

yeah of course my question is it