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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 :

    knowingournumbers1

    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 :

    knowingournumbers4

    Exchange digit at hundreds place to the digit at ones place

    knowingournumbers5

    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.

    101×10
    10010×10
    100010×100
    1000010×1000
    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 :

    NumberTen ThousandThousandHundredsTensOnes
    2828
    528528
    45284528
    6452864528

    Expansion of numbers:

    Example :

    NumberNumber NameExpansion
    50000Fifty Thousand5 × 10000
    28000Twenty Eight Thousand2 × 10000 + 8 × 1000
    68250Sixty Eight Thousand Two Fifty6 × 10000 + 8 × 1000 + 2 × 100 + 5 × 10
    89264Eighty 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 :

    NumberNumber NameExpansion
    500000Five Lakh5 × 100000
    450000Four Lakh Fifty Thousand4 × 100000 + 5 × 10000
    398029Three Lakh Ninety Eight
    Thousand and Twenty Nine
    3 × 100000 + 9 × 10000 + 8 × 1000 + 2 × 10 + 9 × 1

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