Can "one third" be represented accurately in decimal?
No. Its representation continues indefinitely: 0.3333333....
The problem with "one tenth" is not a special flaw of binary. With all bases there are fractions that cannot be represented exactly.
Here is a program fragment in Java. (It could also be in C or C++). Is there something in this program that you should worry about?
float x; for ( x = 0.0; x != 10.0; x += 0.1 ) { System.out.println("Crimson and Clover"); }
How many times will "Crimson and Clover" be printed?