Answer: A. 0.874387438743.. is a rational number.
Step-by-step explanation:
Since Any number that can be written in fraction form is a rational number if it can be in the form of p/q where p and q are integers and q≠0
Since we can write 0.874387438743... = [tex]\frac{8743}{9999}[/tex]
Where, 8743 and 9999 are integers and 9999≠0
Thus, 0.874387438743... is a rational number.
But, 0.0000100020003... , 5.891420975..... and 10.07401259... can not be written in the form of p/q therefore they are not the rational number.
Therefore, Only Option A is correct.
