Question

Classify each number into it's lowest possible category(5 points)

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Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers

Answer 1

[AI-generated answer — Bot GPT 3.5]

To classify each number into its lowest possible category, we need to understand the definitions of each category:

1. Natural Numbers: These are positive counting numbers, including 1, 2, 3, 4, 5, and so on.

2. Whole Numbers: Whole numbers include zero along with all the natural numbers. It includes 0, 1, 2, 3, 4, 5, and so on.

3. Integers: Integers are the whole numbers (including zero) along with their negatives. It includes ..., -3, -2, -1, 0, 1, 2, 3, ... and so on.

4. Rational Numbers: Rational numbers are any numbers that can be written as a fraction, where the numerator and denominator are integers and the denominator is not zero. Examples include 1/2, -3/4, 0.5, etc.

5. Irrational Numbers: Irrational numbers are numbers that cannot be expressed as a fraction. They cannot be written as a terminating or repeating decimal. Examples include pi (π) and the square root of 2 (√2).

Now, let's classify each number:

-7: Integer.
56: Natural number, whole number, and integer.
0: Whole number, integer, and rational number.
3/4: Rational number.
-2.5: Rational number.
√9: Rational number.
π: Irrational number.

Answer 2

Classify each number into it's lowest possible category(5 points)

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Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers

3.14, 1.5, -52, 2, 0

Answer 3

[AI-generated answer — Bot GPT 3.5]

3.14: Irrational number (π is an irrational number and cannot be expressed as a fraction).

1.5: Rational number (can be expressed as 3/2, a fraction).
-52: Integer (a whole number with a negative sign).
2: Natural number, whole number, integer, rational number (positive counting number).
0: Whole number, integer, rational number (includes zero).

Answer 4

Classify each number as rational or irrational(6 points)

Rational Number Irrational Number

-23.5, 5.732... 0/0.3333, 3/4, 2.12123412345, √7

Answer 5

[AI-generated answer — Bot GPT 3.5]

Rational Number: -23.5, 0/0.3333, 3/4

Irrational Number: 5.732..., 2.12123412345, √7

Answer 6

Fractions can be part of the whole number system

true or false

Answer 7

[AI-generated answer — Bot GPT 3.5]

True. Fractions are part of the whole number system.

Answer 8

Match each vocabulary word with it's definition

Irrational Number
Rational Number
Real Number
Whole Number
Natural Number
Integer

a number that can be expressed as a quotient of an integer divided by another integer (example: 10/5)
a number from the number set that includes all natural numbers and zero
a number that is a whole number of it's opposite (example 1 and -1)
a number from the largest number set, which includes rational and irrational numbers
a number that cannot be obtained by the division of 2 integers (cant be a fration)

Answer 9

[AI-generated answer — Bot GPT 3.5]

Irrational Number - a number that cannot be obtained by the division of two integers (can't be a fraction)

Rational Number - a number that can be expressed as a quotient of an integer divided by another integer (example: 10/5)

Real Number - a number from the largest number set, which includes rational and irrational numbers

Whole Number - a number that is a whole number or its opposite (example: 1 and -1)

Natural Number - a number from the number set that includes all natural numbers and zero

Integer - a number that is a whole number or its negative (example: -2, -1, 0, 1, 2)

Answer 10

[AI-generated answer — Explain Bot]

To classify numbers into their lowest possible category, you need to understand the different types of numbers and their relationships.

1. Natural Numbers:
- Natural numbers are positive integers (whole numbers) starting from 1 and going infinitely.
- For example: 1, 2, 3, 4, 5, ...

2. Whole Numbers:
- Whole numbers include all the natural numbers and also include 0.
- For example: 0, 1, 2, 3, 4, 5, ...

3. Integers:
- Integers consist of all natural numbers (positive integers), their opposites (negative integers), and zero.
- For example: -3, -2, -1, 0, 1, 2, 3, ...

4. Rational Numbers:
- Rational numbers are numbers that can be expressed as a fraction (ratio) of two integers.
- They can be either terminating or repeating decimals or whole numbers.
- For example: 1/2, 0.75, 2, -5/8, 7.9

5. Irrational Numbers:
- Irrational numbers are numbers that cannot be expressed as a fraction or a ratio.
- They are non-terminating, non-repeating decimals and cannot be written as whole numbers or fractions.
- Examples include √2, π (pi), e.

Now, let's classify some numbers into their lowest possible categories:

1. 5
- Natural Number
- Whole Number
- Integer
- Rational Number (since it can be written as 5/1)

2. -3
- Integer
- Rational Number (since it can be written as -3/1)

3. 0
- Whole Number
- Integer
- Rational Number (since it can be written as 0/1)

4. 1/2
- Rational Number (since it can be expressed as a fraction)

5. π (pi)
- Irrational Number (cannot be expressed as a fraction or ratio)

By understanding the definitions and relationships between different types of numbers, you can classify numbers into their lowest possible categories.