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The sum of a rational number and an irrational number is irrational.. By definition, an irrational number in decimal form goes on forever without repeating (a non-repeating, non-terminating decimal). By definition, a rational number in decimal form either terminates or repeats. If you add a non-repeating, non-terminating decimal to a terminating decimal, you still have a non-repeating, non-terminating decimal.
Date: 11/12/97 at 13:50:25 From: Beh Auge Subject: Irrational numbers I teach an advanced 7th grade math class and we are discussing rational vs irrational numbers. The text states that .6 repeating is considered a rational number because it can be expressed a/b by using 2/3. But if you try to express .6 repeating over ten, or 100, or 1000, etc., it is impossible because you never know exactly what power of ten will be in your denominator. Please explain to us how .6 repeating can be a rational number when expressing it over 10's, 100's, etc.