Answer:
Correct option is D.
Step-by-step explanation:
we have to choose the option for which number produces a rational number when added to 0.6
A rational number is an algebraic term expressed as a fraction. The fraction can also be in decimals but only if the decimal places are not repeating or finite(infinite then repeating). If they aren't, then these are called irrational numbers.
Let's try each of the choices:
A. The term 0.5050050005... is irrational number. Now, when 0.6 is added to it, the sum would be irrational.
B. √2 is an irrational number because its exact value is 1.4142135.. Even if you add 0.3 to it, the answer would still be irrational
C. Obviously, π is an irrational number and addition of rational to irrational always results in irrational.
D. The term [tex]\frac{5}{7}[/tex] is a rational number. Now, when 0.6 or [tex]\frac{6}{10}[/tex] is added to it, the sum would be [tex]\frac{92}{70}[/tex] This is a rational number.
Therefore, the answer is D.
