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

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}