Rational numbers

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A rational number is any number that can be expressed as a fraction, or ratio, of two integers. This means it can be written in the form , where p (the numerator) is an integer and q (the denominator) is a non-zero integer.

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What Counts as a Rational Number?

The name “rational” comes from the word “ratio.” If you can write a number as a ratio of two integers, it’s a rational number. This includes several types of numbers you use every day. 🤓

• Integers: All whole numbers (like 5 or -3) are rational because they can be written as a fraction with a denominator of 1. For example, 5 can be written as .
• Fractions: Any number that is already written as a fraction, such as or , is a rational number.
• Terminating Decimals: Decimals that end are rational. For instance, 0.75 is rational because it can be written as .
• Repeating Decimals: Decimals that have a pattern that repeats forever are also rational. For example, 0.333… (often written as ) is rational because it’s equal to .

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What Isn’t a Rational Number?

Numbers that cannot be written as a simple fraction are called irrational numbers. Their decimal representations go on forever without repeating.

The most famous example is Pi (), which starts as 3.14159… and continues infinitely with no pattern. Other examples include the square root of 2 () and the golden ratio ().