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TET Syllabus - Mathematics Study Materials in Number System (part I)

 

      Teachers Eligibility Test - Paper 2

 

Class – VI Mathematics

 

                                       NUMBER SYSTEM

 

Successor:

          

          When 1 is added to a number we get its Successor.

 E.g.:

The Successor of 2453 is ------------.

Answer: 2454

 

Predecessor:

            When 1 is subtracted from a number we get its Predecessor.

E.g.:

The Predecessor of 7469 is ------------.

Answer: 7468

 

Formation of large numbers:

 

 

Greatest number

Add

Equals

Smallest number

Number Name

Greatest 1 digit number

9

+ 1

=

Smallest 2 digit number

10

Ten

Greatest 2 digit number

99

+ 1

=

Smallest 3 digit number

100

Hundred

Greatest 3 digit number

999

+ 1

=

Smallest 4 digit number

Thousand

Greatest 4 digit number

+ 1

=

Smallest 5 digit number

10000

Ten Thousand

Greatest 5 digit number

+ 1

=

Smallest 6 digit number

Lakh

Greatest 6 digit number

+ 1

=

Smallest 7 digit number

Ten Lakh

Greatest 7 digit number

9999999

+ 1

=

Smallest 8 digit number

10000000

Crore

 

Place value chart:

   TC

   C

   TL

  L

  T Th

  Th

     H

    T

     O

 

Ten

Crores

 

Crores

 

Ten Lakh

 

Lakhs

 

Ten Thousands

 

Thousands

 

Hundreds

 

Tens

 

Ones

 

 

Try to read the number 359468421. Is it difficult? Yes. It is not easy. But by using the indicators or the periods, it is easy to read and write 359468421 as under.

Periods

Crores

Lakhs

Thousands

Ones

Place Value

TC

C

TL

L

TTh

Th

H

T

O

Number

3

5

9

4

6

8

4

2

1

Number Name

Thirty five crore ninety four lakh sixty eight thousand four hundred twenty one.

 

 

Example: 1

           How many thousands are there in 1 lakh?

Solution:

 

Place value

       L

   T Th

   Th

     H

     T

      O

 

1 Lakh

 

 

   1

 

     0

 

     0

 

    0

 

   0

 

     0

 

1 Thousand

 

 

 

 

     1

 

      0

 

    0

 

      0

 

                                   

 

Lakh is 2 places to the left of thousand.

So, it is 10 × 10 = 100 times thousand.

Hence, 1 lakh = 100 thousand.

 

Example: 2

Read and expand the number 50000

Number: 50,000

Expanded form: 5 × 10000

Read as             : Fifty Thousand

 

Example: 3

Read and expand the number 676097

Number             : 676097

Expanded form: 6 × 100000 + 7 × 10000 + 6 × 1000 + 0 × 100 + 9 × 10 + 7 × 1

Read as             : Six Lakh Seventy Six Thousand Ninety Seven

 

Place Value of digits in Large Numbers:

Every digit of a number has a place value which gives the value of the digit.

Finding the place value of all the digits in 9847056

v The Place value of 6 is 6 × 1 = 6 (Six)

v The Place value of 5 is 5 × 10 = 50 (Fifty)

v The Place value of 0 is 0 × 100 = 0 (Zero)

v The Place value of 7 is 7 × 1000 = 7000 (Seven Thousand)

v The Place value of 4 is 4 × 10000 = 40000 (Forty Thousand)

v The Place value of 8 is 8 × 100000 = 800000 (Eight Lakh)

v The Place value of 9 is 9 × 1000000 = 9000000 (Ninety Lakh)

Hence, the number 9847056 is read as Ninety Eight Lakh Forty Seven Thousand Fifty Six.

Use of commas and Comparison of Number Systems

v In our Indian System of Numeration, we use commas from the right. The first comma comes before Hundreds place (3 digits from the right). The second comma comes before Ten Thousands place (5 digits from the right). The third comma comes before Ten Lakh place (7 digits from the right) and represents Crore.

v In the International System of Numeration, we use Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, Millions and Billions. Commas are used to mark Thousands, Millions and Billions.

v We can easily understand both the Indian and the International Number Systems from the following table.

 

 

 

Indian Number System

 

 

International Number System

Period

Name

Numeral

Name

Numeral

Period

Ones

One

1

One

1

Ones

Ten

10

Ten

 

10

 

    

 

       Ones

Hundred

100

Hundred

 

 

100

Thousands

Thousand

1,000

Thousand

 

 

1,000

 

 

 

 

Thousands

 

 

 

 

Ten thousand

10,000

Ten thousand

 

 

10,000

Lakhs

Lakh

1,00,000

Hundred thousand

 

 

100,000

Ten Lakh

10,00,000

Million

 

 

1,000,000

 

 

 

 

Millions

 

Crores

Crore

1,00,00,000

Ten Million

10,000,000

Ten crore

10,00,00,000

Hundred Million

100,000,000

Hundred crore

100,00,00,000

Billion

1,000,000,000

 

  Billions

Thousand crore

1000,00,00,000

Ten Billion

10,000,000,000

 

 

                With the help of the above table, we can read the number 57340000 as 5,73,40,000 (five crore seventy three lakh forty thousand) in the Indian System and as 57,340,000 (fifty seven million, three hundred forty thousand) in the International System.

Example: 4

        The distance between the Sun and the Earth is about 92900000 miles. Read and write the number in the Indian and the International System by using commas.

Solution:

Indian System

Crores

Ten lakhs

Lakhs

Ten thousands

Thousands

Hundreds

Tens

Ones

9

2

9

0

0

0

0

0

 

i.e., 9,29,00,000

This is read as Nine Crore Twenty Nine Lakh.

 

International System

Ten Millions

Millions

Hundred thousands

Ten thousands

Thousands

Hundreds

Tens

Ones

9

2

9

0

0

0

0

0

 

i.e., 92,900,000

This is read as Ninety Two Million Nine Hundred Thousand.

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