Fun Fact of the Day #1
The repeating decimal 0.99999... is equal to the number 1.
It is not
nearly
equal to or
almost
exactly 1; it
is
1.
Let us use a simple proof to demonstrate this, representing the repeating decimal with three decimal places for the sake of simplicity. Let
x
= 0.999...
x
= 0.999...
10
x
= 9.999...
10
x
-
x
= 9.999 - 0.999
9
x
= 9
x
= 1
Thus,
x
= 0.999... = 1.
Similarly, for example, 241.777777 = 241.78. Cool, right?