Classifying & Ordering Real Numbers-Part 1 interactive worksheet ... - Free Printable

Problem Analysis:

The task involves classifying real numbers into different categories based on their properties. The categories are:
- Natural Numbers: Positive integers starting from 1 (e.g., 1, 2, 3, ...).
- Whole Numbers: Non-negative integers starting from 0 (e.g., 0, 1, 2, 3, ...).
- Integers: All whole numbers and their negatives (e.g., ..., -2, -1, 0, 1, 2, ...).
- Rational Numbers: Numbers that can be expressed as a ratio of two integers \( \frac{p}{q} \) where \( q \neq 0 \). This includes all integers, fractions, and terminating or repeating decimals.
- Irrational Numbers: Numbers that cannot be expressed as a ratio of two integers. They have non-terminating, non-repeating decimal expansions (e.g., \( \sqrt{2}, \pi \)).
- Real Numbers: All rational and irrational numbers combined.

Step-by-Step Solution:

#### Part 1: Drag each number into the Venn Diagram
We need to classify each number into the appropriate category in the Venn Diagram.

1. -19: Integer (negative), Rational.
2. 1.\(\overline{2}\): Repeating decimal, Rational.
3. 0: Whole Number, Integer, Rational.
4. 3: Natural Number, Whole Number, Integer, Rational.
5. \(\sqrt{10}\): Irrational (since \( \sqrt{10} \) is not a perfect square).
6. -\(\sqrt{81}\): Simplifies to -9, which is an Integer, Rational.
7. 3.456: Terminating decimal, Rational.
8. -\(\frac{6}{11}\): Fraction, Rational.
9. -1.4828...: Non-repeating, non-terminating decimal, Irrational.
10. -44: Integer (negative), Rational.
11. \(\pi\): Irrational (well-known constant).

#### Part 2: Indicate which grouping each real number belongs to
We need to fill in the table for the given numbers (\( \sqrt{81}, 1.2, 0, 13 \)).

1. a) \(\sqrt{81}\):
- Simplifies to 9.
- Natural: Yes
- Whole: Yes
- Integer: Yes
- Rational: Yes
- Irrational: No
- Real: Yes

2. b) 1.2:
- Repeating decimal (1.2 = \( \frac{6}{5} \)).
- Natural: No
- Whole: No
- Integer: No
- Rational: Yes
- Irrational: No
- Real: Yes

3. c) 0:
- Natural: No
- Whole: Yes
- Integer: Yes
- Rational: Yes
- Irrational: No
- Real: Yes

4. d) 13:
- Natural: Yes
- Whole: Yes
- Integer: Yes
- Rational: Yes
- Irrational: No
- Real: Yes

#### Part 3: Select a number that is an integer, but not a whole number
- An integer that is not a whole number must be negative.
- From the given numbers, -19 and -44 are integers but not whole numbers.
- Answer: \(-19\) or \(-44\)

#### Part 4: Select a Rational number that is not an Integer
- A rational number that is not an integer must be a fraction or a terminating/repeating decimal.
- From the given numbers, 1.\(\overline{2}\), 3.456, and -\(\frac{6}{11}\) are rational but not integers.
- Answer: \(1.\overline{2}\) or \(3.456\) or \(-\frac{6}{11}\)

Final Answers:

1. Venn Diagram Classification:
- Rational: \(-19, 1.\overline{2}, 0, 3, -\sqrt{81}, 3.456, -\frac{6}{11}, -44\)
- Irrational: \(\sqrt{10}, -1.4828..., \pi\)

2. Table Filling:
- a) \(\sqrt{81}\): Natural (Yes), Whole (Yes), Integer (Yes), Rational (Yes), Irrational (No), Real (Yes)
- b) 1.2: Natural (No), Whole (No), Integer (No), Rational (Yes), Irrational (No), Real (Yes)
- c) 0: Natural (No), Whole (Yes), Integer (Yes), Rational (Yes), Irrational (No), Real (Yes)
- d) 13: Natural (Yes), Whole (Yes), Integer (Yes), Rational (Yes), Irrational (No), Real (Yes)

3. Integer but not Whole: \(\boxed{-19}\)

4. Rational but not Integer: \(\boxed{1.\overline{2}}\)