Research study on students' conceptions of irrational numbers before entering university is of importance in order that the construction of the real number field introduced at the university level will have the desired effect. The aim of the present study is to analyze the way students approach the question of the existence of irrational numbers. 91 10th graders and 97 11th and 12th graders participated in the research study. The analysis focuses first on students' conceptions of irrational numbers by using their representation as non-repeating infinite decimals. Then, the analysis focuses on students' conceptions of irrational numbers on the number line. In spite of the fact that around 80% of the students claimed that they had learned about irrational numbers, only a small percentage of students (19%) showed awareness of the existence of irrational numbers as non-repeating infinite decimals. The same percentage of students (20%) showed awareness of the existence of irrational numbers on the real number line. I also observe some students' answers that expressed their awareness of the existence of irrational numbers as non-repeating infinite decimals but the same students wrote that there are only rational numbers on the number line. Analyzing students' conceptions of irrational numbers using both representations, as non-repeating infinite decimals and as points on the number line, I observe the incoherence of some of their conceptions.