# Classification Of Numbers Worksheet

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There are several Classification of numbers in math:

• Natural Numbers: Whole numbers (1, 2, 3,...).
• Whole Numbers: Zero added to natural numbers (0, 1, 2,...).
• Integers: Positive and negative whole numbers (-2, -1, 0, 1, 2,...).
• Rational Numbers: Those that have a fractional expression \frac{a}{b} (where $$a$$ and $$b$$ are integers, $$b \neq 0$$).
• Irrational Numbers: Those that cannot be stated as non-repeating, non-terminating decimals ($$\sqrt{2}, \pi$$) or as simple fractions.
Algebra 1
Algebra Foundations

## How Will This Worksheets on "Classification of Numbers" Benefit Your Students' Learning?

• Assist students in comprehending various numerical forms.
• Give practice recognizing and classifying numbers.
• Develop their capacity to resolve mathematical puzzles involving different kinds of numbers.
• With consistent work, hone their arithmetic abilities.
• Create a solid basis for more complex mathematical ideas.

## How to Find Classification of Numbers?

Identify if the number is a natural number, whole number, integer, rational number, or irrational number.

• Natural Numbers: Positive integers starting from 1 (1, 2, 3, ...).
• Whole Numbers: Natural numbers including zero (0, 1, 2, ...).
• Integers: Whole numbers and their negatives (-3, -2, -1, 0, 1, 2, ...).
• Rational Numbers: Numbers that can be expressed as a fraction \frac{a}{b}, where $$a$$ and $$b$$ are integers and $$b \neq 0$$. They include terminating and repeating decimals.
• Irrational Numbers: Numbers that cannot be expressed as fractions. Their decimal expansions are non-terminating and non-repeating (e.g., $$\sqrt{2}, \pi$$).

## Solved Example

Q. Which of the following is a natural number?$\newline$Choices:$\newline$(A) $7$$\newline$(B) $\frac{3}{7}$$\newline$(C) $7.555\ldots$$\newline$(D) $\pi$
Solution:
1. Definition of Natural Numbers: Natural numbers are the set of positive integers starting from $1$. They do not include fractions, decimals that do not terminate or repeat, or irrational numbers. Let's evaluate each choice to see which one is a natural number.
2. Evaluation of Choice (A): Choice (A) is $7$. Since $7$ is a positive integer and it is a whole number without any fractional or decimal part, it is a natural number.
3. Evaluation of Choice (B): Choice (B) is $\frac{3}{7}$. This is a fraction and not a whole number, so it is not a natural number.
4. Evaluation of Choice (C): Choice (C) is $7.555\ldots$ This is a decimal number that does not terminate or repeat, so it is not a natural number.
5. Evaluation of Choice (D): Choice (D) is $\pi$ (pi). Pi is an irrational number, which means it cannot be expressed as a fraction of two integers and its decimal representation is non-terminating and non-repeating. Therefore, it is not a natural number.
6. Final Conclusion: Based on the above evaluations, the only choice that is a natural number is $(A) 7$.

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