# Number Zero || Property of number 0

## 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 ExponentProperty

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}

## Features of Number 0 – Summary

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