Question

rational and irrational number sort
directions: sort the numbers and words into 2 groups - rational or irrational. write the answers in the appropriate group.

• whole numbers
• non-perfect square roots
• integers
• non-repeating decimals
• π
• √121
• 2.389746...
• 3.77
• -√400
• non-terminating decimals
• terminating decimals
• perfect square roots
• repeating decimals
• √32
• 0
• -17
• 2.75
• 6 ½

rational
irrational

Explanation:

Step1: Recall Rational/Irrational Definitions

Rational numbers can be expressed as $\frac{p}{q}$ ($p,q$ integers, $q
eq0$), including whole numbers, integers, terminating/repeating decimals, perfect square roots. Irrational numbers are non - repeating, non - terminating decimals, non - perfect square roots, $\pi$, etc.

Step2: Classify Each Item

- **Rational Group**:
- Whole Numbers: 0 (whole number, rational).
- Integers: - 17 (integer, rational).
- Perfect Square Roots: $\sqrt{121}=11$ (perfect square, rational); $-\sqrt{400}=-20$ (perfect square, rational).
- Terminating Decimals: 3.77 (terminating, rational); 2.75 (terminating, rational); $6\frac{1}{2}=\frac{13}{2}$ (fraction, rational).
- Repeating Decimals: (any repeating decimals, but here the labeled repeating decimals group is rational). Also, the categories "Whole Numbers", "Integers", "Perfect Square Roots", "Terminating Decimals", "Repeating Decimals" are rational by definition. So items: Whole Numbers, Integers, Perfect Square Roots, Terminating Decimals, Repeating Decimals, $\sqrt{121}$, $-\sqrt{400}$, 0, - 17, 3.77, 2.75, $6\frac{1}{2}$.
- **Irrational Group**:
- Non - Perfect Square Roots: $\sqrt{32}$ (non - perfect square, irrational).
- Non - Repeating Decimals: 2.389746... (non - repeating, non - terminating, irrational).
- $\pi$ (irrational, non - repeating non - terminating).
- Non - Terminating Decimals (non - repeating ones): and the category "Non - Perfect Square Roots", "Non - Repeating Decimals", "Non - Terminating Decimals" (non - repeating), $\pi$, $\sqrt{32}$, 2.389746...

Answer:

Rational Group:

Whole Numbers, Integers, Perfect Square Roots, Terminating Decimals, Repeating Decimals, $\sqrt{121}$, $-\sqrt{400}$, 0, - 17, 3.77, 2.75, $6\frac{1}{2}$

Irrational Group:

Non - Perfect Square Roots, Non - Repeating Decimals, Non - Terminating Decimals, $\pi$, $\sqrt{32}$, 2.389746...