Classification Of Numbers Worksheets [PDF]: Algebra 1 Math

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.

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?

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Choices:

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(A)

7

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(B)

\frac{3}{7}

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(C)

7.555\ldots

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(D)

\pi

Solution:

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.
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.
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.
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.
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.
Final Conclusion: Based on the above evaluations, the only choice that is a natural number is $(A) 7$ .