Is 3.40764076407640764076 rational or irrational

Answer 1

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.