0/1is a rational number hence 0 is a rational number it can written as p/q where q is not equal to 0

Is zero a rational number?

Yes, zero is indeed a rational number. A rational number is defined as any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. Since zero can be expressed as the quotient of two integers, it meets the criteria of a rational number.

Representing zero as p/q:

To represent zero in the form of p/q where p and q are integers, we can choose any non-zero integer for p and set the denominator q to zero. However, it is important to note that dividing any non-zero number by zero is undefined in mathematics, as it leads to contradictions and inconsistencies.

Explanation:

When we consider the fraction p/q, where p is an integer and q is zero, the result is undefined. This is due to the fact that division by zero is not defined in mathematics. Dividing any non-zero number by zero yields an infinite result or undefined value.

For example, if we take p = 1 and q = 0, the fraction 1/0 is undefined. Similarly, if we take any non-zero integer for p and set q to zero, the resulting fraction would also be undefined.

Zero as a unique case:

Zero is a unique case because it is the only number that does not have an associated multiplicative inverse. In other words, there is no non-zero number that can be multiplied by zero to give a result of 1. This distinguishes zero from other rational numbers, as they all have a well-defined inverse.

Conclusion:

Zero is indeed a rational number as it can be expressed as the quotient of two integers. However, when attempting to represent zero in the form of p/q where q is zero, the result is undefined. This is due to the fact that division by zero is undefined in mathematics. Zero's unique properties make it stand out among other rational numbers.