irrational numbers, like 0.01020304...., can be written as a fraction

No, irrational numbers cannot be written as fractions because fractions represent rational numbers, which are numbers that can be expressed as the ratio of two integers. Irrational numbers, on the other hand, cannot be expressed as a ratio of integers and have non-repeating decimal expansions. Therefore, numbers like 0.01020304... are not rational numbers and cannot be written as fractions.