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3.407640764076407640764076(not repeating) is rational. Rational numbers are numbers that can be written as a fraction. Irrational numbers cannot be expressed as a fraction.
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3.407640764076407640764076 = 3407640764076407640764076/1000000000000000000000000
Which is of the form of one_integer/another_integer so it a rational number.
3.4076... (where the 4076 repeats forever):
3.4076... = 34076/9999
= 34073/9999
Again of the form of one_integer/another_integer so it a rational number.
Either way, 3.4076...4076 is a rational number.
Decimal numbers that terminate, or go on forever with repeating a sequence of digits are rational.
Decimal numbers that go on forever without repeating a sequence of digits are irrational, eg √2.
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