Students are not expected to know the names of the subsets of the real numbers until grade eight.
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The set of rational numbers includes the set of all numbers that can be expressed as fractions in the form 𝑎/𝑏 where 𝑎 and 𝑏 are integers and b does not equal zero. The decimal form of a rational number can be expressed as a terminating or repeating decimal. A few examples of rational numbers are √25, 1/4, -2.3, 75%, and 4.59̅ [.59 repeating].
Rational numbers may be expressed as positive and negative fractions or mixed numbers, positive and negative decimals, integers and percents.
Some numbers can belong to more than one subset of the real numbers (e.g., 4 is a natural number, a whole number, an integer, and a rational number). The attributes of one subset can be contained in whole or in part in another subset. The relationships between the subsets of the real number system can be illustrated using graphic organizers (that may include, but not be limited to, Venn diagrams), number lines, and other representations.
Illustrate the relationships among the subsets of the real number system by using graphic organizers such as Venn diagrams. Subsets include rational numbers, irrational numbers, integers, whole numbers, and natural or counting numbers.
Classify a given number as a member of a particular subset or subsets of the real number system, and explain why.