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Is 0 a Rational Number? Yes — Here’s Why

is 0 a rational number: Measuring tape on top of a keyboard

Is 0 a rational number? In short, yes! But before we explain why, let's discuss what rational and irrational numbers are.

What Are Rational Numbers?

When a rational number is written as the fraction, a/b, both a and b are integers and b is a non-zero denominator. To clarify, integers are non-fractional whole numbers. They can be negative or positive integers that don’t have decimal points.

Let’s explain the difference between rational and irrational numbers.

When expressed in the rational expression form of a/b, neither a and b can have decimal points. However, the fraction of a rational number can be a number that, when not expressed in the form of a/b, has decimal points. It can even have an exponential amount of decimal points. Here are some examples of rational and irrational numbers:

is 0 a rational number: Example of rational numbers

is 0 a rational number: Example of irrational numbers

Even though 2.5 is a decimal and is 0 a rational number: Decimal with exponentially repeating numbers is a decimal with exponentially repeating numbers, they are rational numbers because both of them can be converted to rational expressions in the form of a fraction:

is 0 a rational number: Rational expression in the form of a fraction

Rational expression in the form of a fraction

Pi and the square root of 2 are irrational numbers because there is no possible way to convert them into a fraction. There are no two integers that can be used in ratio, or fraction form, to express an irrational number.

Why Is 0 a Rational Number?

In a rational expression, you can’t divide by zero. The denominator must be a non-zero integer. This is because any quotient divided by 0 results in a non-integer. The number doing the dividing, however, can be zero. See the below fraction p/q:

Rational expression

Rational expression

This rational expression proves that 0 is a rational number because any number can be divided by 0 and equal 0.

Irrational expression

Irrational expression

Fraction r/s shows that when 0 is divided by a whole number, it results in infinity. Infinity is not an integer because it cannot be expressed in fraction form. Thus, it's an irrational number:

How You’ll Use the Answer To ‘Is 0 a Rational Number?’

Understanding why 0 is a rational number helps you know how integers work and distinguish between rational and irrational numbers. It also makes it easier to learn similar math concepts like irrational numbers, natural numbers, and real numbers.

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