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Post Closed as "Not suitable for this site" by Qiaochu Yuan, Daniel Loughran, Yemon Choi, Stefan Kohl♦, Felipe Voloch
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user9934
user9934
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Is there a way to calculate the number of non-repeating digits that precede the periodic repeating portion of a decimal expansion? For example:

1/6 = 0.1666.... (there is 1 non repeating digit) **(Correction) 1/1112 = 0.08333... (there are 2 non repeating digits) 7/12 = 0.58333....(there are 2 non repeating digits) 1/96 = 0.01041666..(there are 5 non repeating digits)

Do any forumulas exist for predicting the maximum length n, of the number of non repeating digits preceding the repeating portion?

I know that if the denominator of a fraction is n, the maximum length of the repeating periodic portion is n-1. Must also the length of the preceding portion before the cycle be n-1?

Thank you!

Is there a way to calculate the number of non-repeating digits that precede the periodic repeating portion of a decimal expansion? For example:

1/6 = 0.1666.... (there is 1 non repeating digit) **(Correction) 1/11 = 0.08333... (there are 2 non repeating digits) 7/12 = 0.58333....(there are 2 non repeating digits) 1/96 = 0.01041666..(there are 5 non repeating digits)

Do any forumulas exist for predicting the maximum length n, of the number of non repeating digits preceding the repeating portion?

I know that if the denominator of a fraction is n, the maximum length of the repeating periodic portion is n-1. Must also the length of the preceding portion before the cycle be n-1?

Thank you!

Is there a way to calculate the number of non-repeating digits that precede the periodic repeating portion of a decimal expansion? For example:

1/6 = 0.1666.... (there is 1 non repeating digit) **(Correction) 1/12 = 0.08333... (there are 2 non repeating digits) 7/12 = 0.58333....(there are 2 non repeating digits) 1/96 = 0.01041666..(there are 5 non repeating digits)

Do any forumulas exist for predicting the maximum length n, of the number of non repeating digits preceding the repeating portion?

I know that if the denominator of a fraction is n, the maximum length of the repeating periodic portion is n-1. Must also the length of the preceding portion before the cycle be n-1?

Thank you!

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user9934
user9934
  • 3
  • 3

Is there a way to calculate the number of non-repeating digits that precede the periodic repeating portion of a decimal expansion? For example:

1/76 = 0.1666.... (there is 1 non repeating digit) **(Correction) 1/11 = 0.08333... (there are 2 non repeating digits) 7/12 = 0.58333....(there are 2 non repeating digits) 1/96 = 0.01041666..(there are 5 non repeating digits)

Do any forumulas exist for predicting the maximum length n, of the number of non repeating digits preceding the repeating portion?

I know that if the denominator of a fraction is n, the maximum length of the repeating periodic portion is n-1. Must also the length of the preceding portion before the cycle be n-1?

Thank you!

Is there a way to calculate the number of non-repeating digits that precede the periodic repeating portion of a decimal expansion? For example:

1/7 = 0.1666.... (there is 1 non repeating digit) 1/11 = 0.08333... (there are 2 non repeating digits) 7/12 = 0.58333....(there are 2 non repeating digits) 1/96 = 0.01041666..(there are 5 non repeating digits)

Do any forumulas exist for predicting the maximum length n, of the number of non repeating digits preceding the repeating portion?

I know that if the denominator of a fraction is n, the maximum length of the repeating periodic portion is n-1. Must also the length of the preceding portion before the cycle be n-1?

Thank you!

Is there a way to calculate the number of non-repeating digits that precede the periodic repeating portion of a decimal expansion? For example:

1/6 = 0.1666.... (there is 1 non repeating digit) **(Correction) 1/11 = 0.08333... (there are 2 non repeating digits) 7/12 = 0.58333....(there are 2 non repeating digits) 1/96 = 0.01041666..(there are 5 non repeating digits)

Do any forumulas exist for predicting the maximum length n, of the number of non repeating digits preceding the repeating portion?

I know that if the denominator of a fraction is n, the maximum length of the repeating periodic portion is n-1. Must also the length of the preceding portion before the cycle be n-1?

Thank you!

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user9934
user9934
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How do you calculate/prove the length of n, the number of non-repeating digits preceeding a periodic sequence of a fractional repeating decimal

Is there a way to calculate the number of non-repeating digits that precede the periodic repeating portion of a decimal expansion? For example:

1/7 = 0.1666.... (there is 1 non repeating digit) 1/11 = 0.08333... (there are 2 non repeating digits) 7/12 = 0.58333....(there are 2 non repeating digits) 1/96 = 0.01041666..(there are 5 non repeating digits)

Do any forumulas exist for predicting the maximum length n, of the number of non repeating digits preceding the repeating portion?

I know that if the denominator of a fraction is n, the maximum length of the repeating periodic portion is n-1. Must also the length of the preceding portion before the cycle be n-1?

Thank you!