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How to predict how long the repeating decimal and the non-repeating part are going to be?
With the repeating decimal (recurring decimal), how can we envision how prolonged the a repeating decimal as well as the non-repeating partial have been starting to be?
Like, with 0,0142857142857 the repeating partial is 6 digits prolonged (142857) as well as the nonrepeating partial 1 series prolonged (the 0 at the back of the ,).
I usually know how to envision the repeating partial of the intermittent number.
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!
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