Comments on: How to predict how long the repeating decimal and the non-repeating part are going to be? http://www.howto.com.my/2009/answer-this-if-you-can/how-to-predict-how-long-the-repeating-decimal-and-the-non-repeating-part-are-going-to-be/ Your How To Solution For Just About Everything Fri, 20 Jan 2012 12:43:10 +0000 hourly 1 http://wordpress.org/?v=3.3.1 By: kbhttp://www.howto.com.my/2009/answer-this-if-you-can/how-to-predict-how-long-the-repeating-decimal-and-the-non-repeating-part-are-going-to-be/comment-page-1/#comment-19481 kb Tue, 27 Oct 2009 16:32:32 +0000 http://www.howto.com.my/2009/answer-this-if-you-can/how-to-predict-how-long-the-repeating-decimal-and-the-non-repeating-part-are-going-to-be/#comment-19481 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! 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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