6TH GRADE || KNOWING OUR NUMBERS || INTRODUCTION

 Introduction

1. Ancient method of counting.
2. Why numbers are required.

Ancient method of counting :

• Facts clearly state that counting sense in humans emerged long before the names of the numbers 1,2,3,4......
• In ancient times,the method of counting was based on distinct,uniform objects like fingers,stones,knots and lines.

For Example :



Kharosthi Numerals : Indian writing found in third century B.C.

Here, 1 is represented by I line,2 is represented by II,3 is represented by III and so on.... this is more of a symbolic representation to counting rather than a numerical representation.

Why numbers are required :

• Numbers are required to count concrete objects.
• Numbers help to create sequence by arranging smaller to bigger and bigger to smaller.
• Helps in creating order.

Shifting digits

Definition : Shifting given set of numbers from one place to another.

Let us consider set of certain numbers :

Examples :



Exchange digit at hundreds place to the digit at ones place



1.2.3.Introducing 10000

As we all know that 99 is the largest two digit number,1 added to 99 gives us the smallest 3 digit number.

99+1 =100 ( smallest three digit number )

Similarly,

999+1 =1000 (smallest four digit number )
Largest 3 digit number + 1 = smallest 4 digit number.

9999+1 =10000 (smallest five digit number )
Largest 4 digit number + 1 = smallest 5 digit number.

10	→	1×10
100	→	10×10
1000	→	10×100
10000	→	10×1000
10000 is actually 10 times 1000.so it is 10000

So,we concluded that

Greatest single digit number+1=Smallest 2 digit number

Greatest 2 digit number  +1=Smallest 3 digit number

Greatest 3 digit number  +1=Smallest 4 digit number

Greatest 4 digit number  +1=Smallest 5 digit number

1.2.4 :Revisiting place value

Let us consider few examples.

• 28 = 20 + 8 = 2 × 10 + 8
• 528 = 500 + 20 + 8 = 5 × 100 + 2 × 10 + 8 × 1
• 4528 = 4000 + 500 + 20 + 8 = 4 × 1000 + 5 × 100 + 2 × 10 + 8 × 1
• 64528 = 60000 + 4000 + 500 + 20 + 8 = 6 × 10000 + 4 × 1000 + 5 × 100 +2 × 10 + 8 × 1.

Let us illustrate above example using a table :

Number	Ten Thousand	Thousand	Hundreds	Tens	Ones
28				2	8
528			5	2	8
4528		4	5	2	8
64528	6	4	5	2	8

Expansion of numbers:

Example :

Number	Number Name	Expansion
50000	Fifty Thousand	5 × 10000
28000	Twenty Eight Thousand	2 × 10000 + 8 × 1000
68250	Sixty Eight Thousand Two Fifty	6 × 10000 + 8 × 1000 + 2 × 100 + 5 × 10
89264	Eighty Nine Thousand Two Hundred and Sixty Four	8 × 10000 + 9 × 1000 + 2 × 100 + 6 × 10 + 4 × 1

1.2.5 Introducing 100000:

Greatest 5 digit number.
Adding 1 to the greatest 5 digit number gives the smallest 6 digit number.

Example :

99,999 + 1 =100000 ( This number is one lakh )

10 × 10000 = 100000

Let us consider 6 digit number in the expanded form for example.

8,56,243 = 8 × 100000 + 5 × 10000 + 6 × 1000 + 2 × 100 + 4 × 10 + 3 × 1.

This number has 3 in one's place,4 in ten's place,2 in hundred's place,6 in thousand's place,5 in ten thousands place and 8 in lakhs place and the number is "eight lakhs fifty six thousand two hundred and forty three".

Few more examples of expansion :

Number	Number Name	Expansion
500000	Five Lakh	5 × 100000
450000	Four Lakh Fifty Thousand	4 × 100000 + 5 × 10000
398029	Three Lakh Ninety Eight Thousand and Twenty Nine	3 × 100000 + 9 × 10000 + 8 × 1000 + 2 × 10 + 9 × 1