A rational number is any number that can be written as a ratio between two numbers (hence rational). For example, 1/8 is a rational number, which makes 0.125. Also, 1/3 is a rational number which makes 0.333333. The difference between 1/8 and 1/3 is that the number of digits of 1/8 is finite (0.125), while the number of digits of 1/3 is infinite. You can write as many "3" as you like after the decimal point up to infinity.

Another example of rational number is the 4/7. The result of this division is 0.571428571428571428571428... Again, it has infinite digits after the decimal point, BUT notice that there is a pattern. The digits "571428" are repeated.

Now you can understand the difference between rational and irrational numbers. An irrational number is a number that simply cannot be represented with a ration between numbers - an irrational number has infinite digits after the decimal point, but these digits do not appear any repeated pattern whatsoever. The most famous irrational number is the Pi...