## Tuesday

### 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 ------------.

Predecessor:

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

E.g.:

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

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

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.