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Question: Name the subset(s) of the real numbers to which 0.444444.... belongs.


A ) whole numbers, rational numbers, real numbers
B ) rational numbers, real numbers
C ) irrational numbers, real numbers
D ) integers, rational numbers, real numbers

Steps to derive

1 Let N = 0.44444...
 [First equation.]

2 100 N = 44.444...
 [Second equation.]

3 99 N = 44
 [Subtract the first equation from the second equation.]

4 N = 4499 = 49

5 If a number can be expressed as a quotient of two integers, then it is a rational number. So, N = 0.44444. . . is a rational number.

6 The set of rational numbers is a subset of the real numbers.


7 Therefore the subsets to which 0.44444. . . belongs to are: the rational numbers and the real numbers.



Hence the right answer is Option B

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