I am not an expert, but I know a little. A rational number can be written as a ratio of two numbers, in other words it can be written as a fraction. When you long divide the two numbers in a fraction the list of remainders will eventually repeat, so its decimal expansion will also repeat. A irrational number is one who's decimal expansion never repeats itself, it goes on forever, so it cannot be written as a fraction. The number pi and the square root of 2 are examples of irrational numbers.