Numbers and Whole Numbers in Grade III

Hello friends,Previously we have discussed about real numbers definition and in today's session we all are going to discuss about one of the most interesting topic of mathematics, number system. In grade II of maharashtra board we learn counting of numbers(1,2,3,4,5,6,7…….) in mathematics, but we have not learnt about type of numbers. So in grade III we are going to learn What are numbers and  definition of whole numbers and how to solve math problems related to it.
First of all, we discuss what is numbers? Numbers are mathematical object which is used to count and measure different things. In mathematics there are so many numbers between    positive numbers (1,2,3,4………), negative numbers(-1,-2,-3………).
………………-9 -8 -7 -6 -5 -4 -3 – 2 -1 0 1 2 3 4 5 6 7 8 9………………………
But from algebra point of view, all numbers are defined in a set which is called as a real numbers and we divide real numbers into two types of numbers

• rational numbers
• irrational numbers

So, first of all we discuss about rational numbers  :(want to Learn more about Whole Numbers ,click here),
We know rational numbers are represented as (a/b) where a and b are integers and b is not equal to zero, but when b is equal to 1 then all numbers are represented as rational numbers . There are following numbers which is a part of rational number set (Q)  -

• Whole Numbers (W) - In algebra, whole numbers can be represented by a set of numbers which is starting from 0 to infinity .

W = ( 0 , 1 , 2 , 3 , 4 , 5 , 6 ………………………………….)
here W shows Whole Numbers set .

• Natural Numbers (N) - From algebraic number system, natural number is a set of number which include all whole numbers except 0.

N = ( 1, 2 , 3 , 4 , 5 , 6 , 7 ………………………………………)
here N is natural number set.

• Integer Numbers (I) - From algebraic definition, integer numbers are set of numbers which include all negative, positive and zero number except decimal numbers.

                 I = ( ……… -7 -6 -5 -4 -3 – 2 -1 0 1 2 3 4 5 6 7  ………)
                 here I represent set of integer number
Now further we are going to discuss our second type of real numbers irrational numbers.
Those numbers which are not part of rational numbers are part of irrational numbers or we can say that those numbers which are not represent in (a/b) form are called as a  irrational numbers like sqrt(2),  sqrt(5) etc.
At last, this picture represents whole story about Numbers
  
So, my friends this all about our Grade III mathematic topic Number System. I hope guys you enjoyed today's session and if anyone want to know about Models for multiplication then they can refer to internet and text books for understanding it more precisely.Read more maths topics of different grades such as Multiplication and division situations in the next session here.

Place Value for Grade III

Hello friends, today we are going to learn about place value and whole numbers. Here I am going to tell you the best way of understanding place value and whole numbers which comes under the cbse board syllabus.
First we discuss about the Place value to calculate math answers. In our Decimal numbers system, the value of digit depends on its place. In the number each place has a value of 10 times the place to its right. A number in standard form is separated into group of three digit using commas. Each of these group is called period. Place value of digit is determined by its position in a number, the name of the place or location of a digit in a numbers. Place value is positional system of notation in which the position of a number with respect to a point determines its value. In the decimal system, the value of the digit is based on the number ten. Each position in a decimal number has a value that is a power of 10. A decimal point separates the non-negative power of 10 (10⁰=1 , 10²=100, 10³=1000). The idea of the place value is at the heart of our numbers system, First however, a symbol for nothing or zero had to be invented. Zero holds the place of particular value.  When no other digit goes in that position. For example the number “100” in words means one hundred. No one’s without a symbol for nothing our decimal number system wouldn’t work.To get more information about it click here:

Beginning with one place at the right, each place value is multiplied by increasing power of 10, the value of the first place on the right is “one ” the value  place to the left of it is ten which is 10 times 1. The place to the left of the ten place is hundred, which is 10 time 10. Place value number can be represented in many ways. But standard form is usually the shortest and easiest. Here are some numbers expressed in different form with their standard form show alongside.
We take one number 145, have three digits. Each digit is a different value in this value “1” refer to the hundredth place the “4” refers to the ten place and the “5” refers to the one place is succeeded.
Place value is an important concept that is often misunderstood and misplaced. Place value the particular power of the base of continue system that is represented by a particular position in a place value Notation for example: - unit, ten, hundred, etc. The definition correctly places the concept of place value as an attribute of positional system not solely the decimal one.  Place value the value given to a digit by virtue of the places it occupies in the number relative to units place. Importance of place value has been emphasized in the NCTM standards.  The place value is important to understand numeration system.

In above article we discuss about the place value and whole number and if you want to know about Properties of numbers in Grade III and Place value whole numbers then you can refer to the various sites available on Internet.