**What is number zero?**

Zero is a number which is **neither positive nor negative**.

It is a number with** no value**.

In number line, zero is represented as:

You can see that** 0 is the interface between positive and negative number**.

On the **right of zero, the positive number starts** and **on the left there are negative numbers**.

**Is 0 an integer?**

**Yes!!**

Number 0 is a part of integer.

**But what are integers?**

**Integers** are numbers that can be positive, negative or zero. But they can’t be decimal or fraction numbers.

Number 0 is neither fraction nor decimal, hence are part of integer.

**Is 0 a natural number?**

**NO!!**

**Natural numbers** are counting numbers starting from 1. They are also said to be positive integers.

As natural number starts from 1, the number 0 is not part of the group

**Is 0 a whole number?**

**Yes!!**

**Whole numbers** are positive integers starting from zero.

Since whole number includes 0, the number 0 is part of the group

**Is 0 a rational number?**

**Yes!!**

A **rational number** is the one which can be represented in the form of p/q {q should not be 0}

Examples of rational number are:

\mathtt{\frac{2}{3} ,\ \frac{4}{1} ,\ \frac{6}{4} \ \ }

0 is also rational number & can be expressed in the form of p/q as follows:

\mathtt{\frac{0}{5} ,\ \frac{0}{2} ,\ \frac{0}{4} \ }

**Is 0 an even number or odd number?**

**Yes !!**

Number 0 is considered as even number.

Let us understand what are even numbers?

Any number which is divisible by 2 is known as even number.

Even number is represented by expression ⟹ 2k { k = 1, 2, 3 . . .}

So even numbers are: 0, 2, 4, 6, 8, 10, . . .

In short, any number whose end digits are 0, 2, 4, 6, 8 are even numbers.

**Property of number 0**

In this section we will understand property of zero which will be useful for algebra calculation

**Zero Addition Property**

It says that if any number is added with number 0, the output of the addition will yield same number

**Number + 0 = Number**

**Examples**

2 + 0 = 2

17 + 0 = 0

899 + 0 = 0

Hence, addition of any number with zero have no effect on the given number.

**Zero Subtraction Property**

It says that any number subtracted with 0 will result in the same number

**Number – 0 = Number**

**Examples**

10 – 0 = 10

98 – 0 = 98

763 – 0 = 763

Hence, subtraction of number with 0 results in same number.

But what will happen when you **subtract number from 0**

**0 – Number = – Number**

**Example**

0 – 23 = -23

0 – 167 = – 167

0 – 9012 = – 9012

Subtracting number from 0 yield negative number

**Multiplication with 0**

When we multiply any number with zero we get zero

**Number x 0 = 0**

Let us understand the concept below.

First we have nothing (aka. 0)

When we multiply nothing multiple times we still have nothing.

That’s why multiplication with 0 returns 0

**Example**

4 x 0 = 0

121 x 0 = 0

9999 x 0 = 0

**Zero Product Property**

The property says that if the multiplication of two items returns zero then either one of the item value is zero or both the values are zero.

**A x B = 0**

Here A & B are two objects whose multiplication returns zero.

**According to zero product property**

Either A = 0 or B = 0

Or

Both A & B = 0

**Example 01**

Let A = 2 & B = 0

The multiplication of A & B is:

A x B ⟹ 2 x 0 ⟹ 0

**This property is helpful to solve algebraic equation**

**Example** **02**

\mathtt{( x-\ 3) \times \ ( x\ -5\ ) \ =\ 0}\\\ \\ \mathtt{By\ zero\ product\ property,\ we\ can\ say\ that:}\\\ \\ \mathtt{( x\ -\ 3) \ =\ 0\ \ or\ ( x\ -\ 5) \ =\ 0}\\\ \\ \mathtt{x\ =\ 3\ \ \ \ \ or\ \ x\ =\ 5}

Hence using multiplication property we found the value of x

**Zero Exponent** **Property**

Zero exponent is basically **number with the power zero**

The property states that any **number with power zero results in number 1**

**For example**

\mathtt{2^{0} \ =\ 1}\\\ \\ \mathtt{9^{0} \ =\ 1}\\\ \\ \mathtt{( -6)^{0} =1}

**But zero to the power of zero is undefined**

\mathtt{0^{0} \ =\ undefined}