Number Types in Math: Natural, Rational, Real and More Explained

By Pankaj Kumar|Last Updated: July 12, 2026|

Key Takeaways

Natural numbers start at 1; whole numbers add zero to that set.
Integers include all whole numbers and their negative counterparts.
Rational numbers can be expressed as a fraction m/n where n≠0.
Irrational numbers like √2 and π cannot be written as fractions.
Imaginary numbers are square roots of negative numbers, forming complex numbers.

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Natural Numbers

These are the numbers we got introduced to while learning counting as young children. They start from 1 and go all the way to infinity, i.e., 1, 2, 3, 4, 5, 6, etc. They are also called positive integers.

Whole Numbers

If you add ‘0’, i.e., 0, 1, 2, 3, 4, 5, 6, and so on, then this set is called the set of Whole Numbers.

Integers

The next important number type is Integers. If you write all the whole numbers and their negative counterparts, i.e., -∞, …, -3, -2, -1, 0, 1, 2, 3, …∞, then all these numbers are called integers. We can say that all whole numbers and natural numbers are integers, but not vice versa.

Fractions

A fraction represents parts of a whole number. It can be written in the form m/n, where both m and n are whole numbers, and n cannot be 0. Once again, all fractions are rational numbers, but not vice versa.

Those fractions are termed as proper that have the numerator smaller than the denominator. If, on the other hand, the numerator is greater than the denominator, then the fraction is termed as the improper one. Example: 2/3 is a proper fraction, and 3/2 is an improper fraction.

All terminating decimal numbers and some repeating decimals can be written as fractions. You can write the terminating decimal 1.28 as 128/100 = 32/25. While repeating decimal 0.333333… can be written as 1/3, but 0.4444444… does not yield that elegant an answer though you can still express it as 1/2.2500002250000.

Rational Numbers

Rational Numbers are those numbers that can be represented in the form of m/n, where n≠0. The number m/n can be further simplified and represented in decimal form. The set of rational numbers includes positive, negative numbers, and zero.

Some examples of rational numbers are 10/2 (=5), 1/100 (=0.01), and 60/10 (=6). Understanding how rational numbers relate to other number types is a core skill in MATLAB and numerical computing courses.

Irrational Numbers

Irrational Numbers are those numbers that cannot be written in fraction form or the ratio of two integers. A few examples of irrational numbers are √2, √3, √5, and π. Students studying engineering mathematics encounter irrational numbers frequently in applied problem sets.

Real Numbers

The set of rational and irrational numbers is called the set of Real Numbers. This concept also appears in biostatistics, where real-valued data underpins most statistical models.

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Imaginary Numbers

Numbers other than real numbers are imaginary or complex numbers. When we take the square of an imaginary number, it gives a negative result, which means it is a square root of a negative number — for example, √-2 and √-3. When we square these numbers, the results are -2 and -3.

The square root of -1 is represented by the letter i, which means i = √-1. When a real number gets combined with an imaginary number, a Complex Number is expressed as m + ni or m + n√-1.

For a more detailed list, check the Wikipedia page on Number types in Math. Before choosing a math tutor, it also helps to know which questions reveal tutor quality, and whether a calculus tutor is worth the investment.