FTCE General Knowledge Math Practice Test

What do rational numbers encompass?

1. Only whole numbers

2. Fractions, decimals, and positive integers

3. All numbers expressed as fractions or decimals

4. Only negative fractions

The correct answer is: All numbers expressed as fractions or decimals

Rational numbers encompass all numbers that can be expressed in the form of a fraction \( \frac{a}{b} \), where \( a \) is an integer and \( b \) is a non-zero integer. This definition includes all integers, fractions, and terminating or repeating decimals, as they can all be converted into fractional form. For instance, the number 0 can be represented as \( \frac{0}{1} \), and the decimal 0.75 can be expressed as \( \frac{3}{4} \), which illustrates that both decimals and whole numbers fall under the category of rational numbers. Additionally, numbers like \( \frac{1}{3} \) or -2 (which can be written as \( \frac{-2}{1} \)) further demonstrate that both positive and negative values are included in this set. The presence of integers and the ability to express decimals and fractions reinforces the comprehensive nature of rational numbers, confirming that they include every kind of number that meets the fraction criterion.