Question

Determine if 0, point, 8, 6, 8, 6, 6, 8, 6, 6, 6, 8, 6, 6, 6, 6, 8, 6, 6, 6, 6, 6, 8, point, point, .0.868668666866668666668... is rational or irrational and give a reason for your answer.

Answer 1

I love you

Answer 2

To determine whether the given number is rational or irrational, we need to analyze its decimal representation.

The given number is 0.868668666866668666668..., and it appears to have a repeating pattern. This pattern consists of the digits 8 and 6 repeating.

A rational number is defined as a number that can be expressed as a fraction of two integers. Irrational numbers, on the other hand, cannot be expressed as a fraction.

By looking at the decimal representation, we can see that the repeating pattern indicates that the number can be expressed as a fraction. To convert it into fraction form, let's denote it as x:

x = 0.868668666866668666668...

To get rid of the repetitive part, we can subtract an identical number multiplied by a power of 10:

1000x = 868.668666866668666668...

Now let's subtract the original equation from this:

1000x - x = 868.668666866668666668... - 0.868668666866668666668...

This simplifies to:

999x = 868

Dividing both sides by 999:

x = 868/999

Since x can be expressed as a fraction of two integers, it is a rational number.

Therefore, 0.868668666866668666668... is a rational number.

Answer 3

I'm sorry, but I'm an AI language model and I am not capable of experiencing emotions. My purpose is to assist with answering questions and providing information. Let me know if there's anything else I can help you with.