Is 0 a Rational Number? Why Zero Is Rational?

Yes, 0 is a rational number. But what does that mean? A rational number is any number that can be expressed as a fraction (p/q) where p and q are integers, and q ≠ 0. Since 0 can be written as 0/1, 0/5, or 0/n (as long as the denominator is not zero), it meets all the criteria to be considered rational.

Is 0 Rational or Irrational?

Some may wonder: Is 0 a rational or irrational number?
To clarify:

• Irrational numbers (like √2 or π) cannot be expressed as a simple fraction.
• Rational numbers can be written as a fraction of two integers.

Since 0 = 0/1, it is clearly rational.

Answer: 0 is not irrational. It is a rational number.

Read Other Examples of Rational Numbers

Reasons Why Is 0 A Rational Number?

There are several reasons why 0 is classified as a rational number:

1. Expressible as a Fraction

We can write 0 as a fraction in multiple forms:

• 0/1: An integer divided by 1 is the integer itself — in this case, 0.
• 0/n: As long as n ≠ 0, the result is still 0.

Since 0/n (where n is a non-zero integer) gives a finite, well-defined result, 0 fits the definition of a rational number.

2. Consistency with Number Systems

Including 0 in the set of rational numbers keeps our mathematical systems consistent.

• When you add, subtract, or multiply 0 with any rational number, the result remains rational.
• For example:
  r + 0 = r (where r is any rational number)

If 0 weren’t rational, this rule wouldn’t work

3. Properties of Rational Numbers

Zero exhibits core properties of rational numbers:

• Closed operations:
  • 0 + rational = rational
  • 0 × rational = 0 (also rational)
  • 0 ÷ rational = 0 (if the rational ≠ 0)
• Position on the number line:
  • 0 sits between -1 and 1
  • It preserves the order and symmetry of rational numbers

These traits confirm that 0 behaves exactly like a rational number should.

Examples of 0 as a Rational Number

Here’s how 0 compares with other rational numbers:

Number	Fraction Form
0	0/1, 0/5, 0/100
1/2	1/2
-3	-3/1
4/5	4/5
7	7/1

All these are rational — and so is zero.

How 0 Fits into the Number System

Zero isn’t just rational — it’s also:

• An integer
• A whole number
• A real number
• A neutral element in addition: a + 0 = a
• The midpoint of the number line between negatives and positives

It plays a central role in math, from basic arithmetic to algebra and calculus. In algebra, 0 is the additive identity.