Who is asking: Student
One way to look at this is to see what the difference between the two numbers is. If the difference is 0, then we will say that the two numbers ARE the same.
Now try subtracting:
If you go out, say 20 places, the difference will be
.000 000 000 000 000 000 01
A SECOND point of view is a little less direct:
Let S = 1.999999999 (repeating)
Divide by 9
This is actually the same reasoning (in disguise). However, this principle for figuring out what any repeating decimals are as fractions is widely used as you continue in mathematics. You will see it again around sequences (adding geometric sequences in calculus).