Final answer:
The number 11.0 belongs to the subsets of rational numbers, whole numbers, integer numbers, and counting numbers, but it is not an irrational number.
Step-by-step explanation:
The number 11.0 belongs to several subsets of the real number system. As a number composed of digits and can be expressed with a decimal point, 11.0 is a rational number because it can be written as a fraction (11/1). Additionally, it is a whole number and an integer number, as whole numbers and integers include all non-negative numbers without a fractional or decimal part, and 11.0 has no fractional part. Since counting numbers are defined as whole numbers starting from 1, 11.0 is also a counting number. However, 11.0 is not an irrational number since it does not have a non-repeating, non-terminating decimal expansion; therefore, the correct answer does not include option C.
To determine the subsets of the real number system to which the number 11.0 belongs, we need to understand the different types of numbers in the real number system.
1) Rational numbers are numbers that can be expressed as a fraction of two integers. Since 11.0 can be written as the fraction 11/1, it belongs to the subset of rational numbers.
2) Whole numbers are non-negative integers. Since 11.0 is a positive integer, it does not belong to the subset of whole numbers.
3) Irrational numbers are numbers that cannot be expressed as a fraction. Since 11.0 can be expressed as a fraction, it does not belong to the subset of irrational numbers.
4) Counting numbers are positive integers. Since 11.0 is a positive integer, it does belong to the subset of counting numbers.
5) Integer numbers are positive and negative whole numbers. Since 11.0 is a positive integer, it does belong to the subset of integer numbers.