How to predict how long the repeating decimal and the non-repeating part are going to be?

With a repeating decimal (recurring decimal), how can we envision how prolonged a a repeating decimal as well as a non-repeating partial have been starting to be?

Like, with 0,0142857142857 a repeating partial is 6 digits prolonged (142857) as well as a nonrepeating partial 1 series prolonged (the 0 at a back of a ,).

I usually know how to envision a repeating partial of a intermittent number.

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Suggestions:


1. Since you know how to predict the repeating part of a repeating decimal:

   For the non-repeating part, look at the powers of 2 and 5 in the denominator. The larger of theses exponents will tell you how long the non-repeating part of the decimal is. (Why 2 and 5? They are factors of 10, which is the base for the decimal system.)

   Example: 1/720
   720 = 2^4 * 3^2 * 5.

   Since there are four 2’s and 1 5, there must be 4 nonrepeating decimal places in the decimal expansion.

   Double check: 0.001388888…

   I hope this helps!