Decimal expansion

[cragar]

Homework Statement

How many decimal expansions terminate in an infinite string of 9's?
How many dont?

The Attempt at a Solution

If we have a number terminate with an infinite amount of 9's then it will be a rational number.
So there would be countably many of these.

And since irrational numbers do not end with all 9's then their would be
uncountably many of them that do not.

 

[STEMucator]

Homework Statement

How many decimal expansions terminate in an infinite string of 9's?
How many dont?

The Attempt at a Solution

If we have a number terminate with an infinite amount of 9's then it will be a rational number.
So there would be countably many of these.

And since irrational numbers do not end with all 9's then their would be
uncountably many of them that do not.

That's the right idea.