1. 4.2040404...
a. I, N
b. Q
The number 4.2040404... belongs to the sets of irrational numbers (I) and natural numbers (N). This is because the decimal representation of the number does not terminate or repeat, making it irrational. Additionally, it can be considered a natural number since it is positive and a whole number.
Furthermore, since the number can be expressed as a ratio of two integers (e.g., 42040404/10000000), it is also a rational number (Q). However, it is important to note that although it is rational, it is not a whole number or an integer since it has a decimal component.
2. 3.581818181...
a. I
b. Q, W
c. I
d. Z
e. Q
f. I, N
The number 3.581818181... is an irrational number (I) because its decimal representation neither terminates nor repeats. It cannot be expressed as a simple fraction.
However, it is also a rational number (Q) because it can be expressed as a repeating decimal. The pattern "81" repeats indefinitely.
Additionally, it can be considered a whole number (W) because it is positive and does not have a fractional or decimal component. However, it is not an integer (Z) since it has a decimal component.
Moreover, since it is a positive number without a fractional or decimal component, it can be considered a natural number (N).
In summary, the number 3.581818181... belongs to the sets of irrational numbers (I), rational numbers (Q), whole numbers (W), integers (Z), and natural numbers (N).