FTCE General Knowledge Math Practice Test

Which type of numbers cannot be expressed as the ratio of two integers?

1. Irrational numbers

2. Rational numbers

3. Natural numbers

4. Whole numbers

The correct answer is: Irrational numbers

Irrational numbers cannot be expressed as the ratio of two integers. This type of number includes those that have non-repeating, non-terminating decimal expansions. Examples include numbers like the square root of 2 or pi. These cannot be accurately represented as a fraction of two integers and thus fall outside the category of rational numbers. On the other hand, rational numbers are defined as numbers that can indeed be expressed as a ratio of two integers. Natural numbers and whole numbers are also types of rational numbers since they can be represented as a fraction (e.g., the natural number 5 can be written as 5/1). Hence, the defining characteristic of irrational numbers is what distinguishes them from the other options provided.