Classification of Numbers

Imagine a life without the means to express ages, weight, birthdays, times, scores, bank accounts, or telephone numbers. These quantities are defined and communicated through ten mathematical digits ranging from 0 to 9.

Numbers, essentially strings of digits, serve as representations of quantities. They indicate the magnitude, conveying the size of a given quantity, whether vast or minute. Numbers manifest in various forms, from simple integers like 3 or 999 to decimals like 0.351 and fractions like 2/5.

Numbers can be classified into different categories based on their properties and characteristics.

The following diagram demonstrates the number system:

Common Classification of Numbers

Here are some common classifications of numbers:

Natural Numbers (N)

These are the counting numbers starting from 1 and going on infinitely (1, 2, 3, …).

Whole Numbers (W)

Similar to natural numbers but includes zero (0, 1, 2, 3, …).

Integers (Z)

These include all positive and negative whole numbers and zero (…, -3, -2, -1, 0, 1, 2, 3, …).

Rational Numbers (Q)

These numbers can be expressed as the quotient or fraction of two integers, where the denominator is not zero. This includes integers and fractions (e.g., 1/2, -3, 4/5).

Irrational Numbers

These are numbers that cannot be expressed as fractions and have non-terminating, non-repeating decimal expansions. Examples include the square root of 2 (√2) or π (pi).

Real Numbers (R)

The set of all rational and irrational numbers combined.

Complex Numbers (C)

These are numbers in the form a + bi, where “a” and “b” are real numbers, and “i” is the imaginary unit (i.e., the square root of -1).

Prime Numbers

Numbers greater than 1 that have no positive divisors other than 1 and itself. Examples include 2, 3, 5, 7, 11, and so on.

Composite Numbers

Numbers greater than 1 that are not prime and can be factored into smaller positive integers. For example, 4, 6, 8, and 9 are composite numbers.

Even and Odd Numbers

Even numbers are integers divisible by 2 (e.g., 2, 4, 6), while odd numbers are not divisible by 2 (e.g., 1, 3, 5).

Cardinal Numbers

These represent the size or “count” of a set, for example, 1, 2, 3, …

Question 2

Determine the classification of the number -15.

Solution:

Integer: -15 is an integer because it is a whole number that can be negative.

Odd Number: -15 is an odd number because it is not divisible by 2.

Negative Number: -15 is a negative number because it is less than zero.

Integer but not a Natural Number: -15 is an integer, but it is not a natural number because natural numbers are positive.

Question 3

Classify the number 0.75 into its different types.

Solution: 

Rational Number: 0.75 is a rational number because it can be expressed as the fraction 3/4.

Decimal Number: 0.75 is a decimal number.

Real Number: 0.75 is a real number because it can be located on the number line.

Non-Integer: 0.75 is a non-integer because it is not a whole number.

Question 4

Categorize the number √9.

Solution:

Integer: √9 is an integer because it equals 3.

Rational Number: √9 is a rational number because it can be expressed as the fraction 3/1.

Whole Number: √9 is a whole number because it is both positive and an integer.

Natural Number: √9 is a natural number because it is a positive integer.

Question 5

Classify the number 22/7.

Solution:

Rational Number: 22/7 is a rational number because it can be expressed as a fraction.

Fractional Number: 22/7 is a fractional number because it is a ratio of two integers.

Irrational Number: 22/7 is irrational because the decimal expansion is non-repeating and non-terminating.

Non-Integer: 22/7 is a non-integer because it is not a whole number.

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