Divide 7 by 18 on your calculator. You get 0.38888888888888888888888888888889, which really means that it is 0.38 followed by repeated 8s forever. Since writing that many digits is not only impractical but impossible, we have a shorthand notation.
is only approximate (very, very close, but still approximate)
But if you say
which means zero point three followed by an infinity of eights, we now have a manageable and exact representation.
If you have a decimal fraction that has a group of digits that repeat, you run the line over the entire group that repeats. For example:
but we can write:
Again, notice the assertion of exactness.
John
My calculator said it, I believe it, that settles it
