Q. Which lists contain only rational numbers? Select all that apply.Multi-select Choices:(A) −6, −7, −9, −11, 61(B) 6, 12, 18, 24, 30(C) −70, −71, −72, −73, −74(D) −75, −76, −77, −78(E) −79, −90, −91, −92
Analyze Integers: Step 1: Analyze list A−6,−7,−9,−11,61. All numbers in this list are integers. Integers are rational numbers because they can be expressed as a fraction where the denominator is 1 (e.g., −6 can be written as −16).
Analyze Square Roots: Step 2: Analyze list (B) 6, 12, 18, 24, 30. Square roots of non-perfect squares are irrational numbers. None of 6, 12, 18, 24, 30 are perfect squares, so their square roots are irrational.
Analyze Fractions: Step 3: Analyze list (C) 36, 74, 9911, 13−6, 37−13. All elements are fractions of integers. Fractions of integers are rational numbers as they can be expressed as a ratio of two integers.
Analyze Decimals: Step 4: Analyze list (D) 0.865, 0.4444, −6.37, −11.11. All numbers are decimals. 0.865 and −6.37 are terminating decimals; 0.4444 and −11.11 are repeating decimals. Both terminating and repeating decimals are rational numbers.
Analyze Repeating Decimals: Step 5: Analyze list (E) 7.{3}, 4.1{5}, −6.{26}, −9.{1}. These are non-terminating, repeating decimals (indicated by the notation {}). Non-terminating, repeating decimals are rational numbers.
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