Is Zero a Rational Number

Q: Is Zero a Rational Number? Justify Your Answer.

Yes, zero is a rational number.

A rational no. is a number represented as p/q, where q and p are integers and q ≠ 0.

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

x/y= 0/6

x/y= 0

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

 a/b= 4/0

a/b= infinity

Fraction a/b shows that dividing 0  by integer results in infinity. Infinity is not an integer because it cannot be represented in fractional form. Therefore, this is an irrational number.

 The properties of rational numbers are: 

1. Closure property 

2. Commutative property 

3. Combined real estate 

4. Dispersion property 

5. Identity Attribute 

6. Inverse property 

7. Close property 

Closure Property 

We can say that rational numbers are closed by addition, subtraction and multiplication. 

The division is not closure or property because division by zero is undefined. We can also say that except `0`, all numbers are closed by division. 

Commutative Properties

For rational numbers, addition and multiplication are commutative.

 Commutative law of addition: a + b = b + a 

 Commutative law  (multiplication):a × b = b × a 

Distributive Property

The distributive property says if a, b and c are three rational numbers, then; 

 A x (b + c) = (a x b) + (a x c) 

Identity and Reciprocal Properties of Rational Numbers

Identity: 0 is added, and 1 is multiplication for rational numbers.

Understanding why 0 is a rational number helps you understand how integers work and distinguish between rational and irrational numbers. You can also easily learn similar mathematical concepts such as irrational numbers, natural numbers, and real numbers.