What type of number is defined as any number that cannot be expressed as a simple fraction?

The type of number that cannot be expressed as a simple fraction is known as an irrational number. Irrational numbers are numbers that cannot be exactly expressed as the quotient of two integers, meaning they cannot be written in the form ( \frac{a}{b} ) where ( a ) and ( b ) are whole numbers and ( b ) is not zero.

Examples of irrational numbers include (\pi) (pi), which represents the ratio of the circumference of a circle to its diameter, and the square root of 2, which cannot be precisely represented as a simple fraction. These numbers have non-repeating and non-terminating decimal expansions, which distinguishes them from rational numbers.

In contrast, whole numbers, integers, and rational numbers can all be represented as fractions or whole number values. Whole numbers encompass all non-negative integers (0, 1, 2, 3, etc.), integers include all whole numbers both positive and negative, and rational numbers cover any numbers that can be expressed as a fraction including whole numbers and integers. This is why the identification of irrational numbers as those that cannot be expressed as simple fractions is crucial in understanding different number sets in mathematics.