5th Class Mathematics Number System and its Operations System of Numeration

   System of Numeration

Mathematical notation of numbers is called numeration. We are aware of the symbols which are used to write any numbers. In this chapter we will study about the following two system of numeration:

(a) Indian system of numeration

(b) International system of numeration  

Indian System of Numeration

Indian system of numeration is also called Hindu-Arabic number system. It is a positional decimal number system. Look at the following place value chart:  

This system is based on periods and places. Units, thousands, lakhs, crores, arabsetc. are periods. Each period has been divided into places. The first period, units, has been divided into three places ones, tens, and hundreds. Other periods have been divided into two places. Like thousands has been divided into two places thousands and ten-thousands.    

Sixty five thousand six hundred and eighty nine is written as:

Six in place of "Ten thousands"

Five in place of "Thousands"

Six in place of "Hundreds"

Eight in place of "Tens" and

Nine in place of "units"

Now the expanded form of the number = 6 x \[=6\times 10000+5\times 1000+6\times 100+8\times 10+9=65689\]  

Forty two crores seventy two lakhs ninety six thousand two hundred and fifteen is written as:

Four in place of "ten crores"

Two in place of "crores"

Seven in place of "Ten lakhs"

Two in place of "lakhs"

Nine in place of "Ten thousands"

Six in place of "Thousands"

Two in place of "Hundred-s"

One in place of "Tens"

Five in place of "Units or ones"

Now expanded form of the number \[=4\times 100000000+2\times 10000000+7\times 1000000+2\times 100000+\]\[9\times 10000+6\times 1000+2\times 100+5\times 10+5=427296215\]  

Two lakhs Eight thousand and four is written as:

Two in place of "Lakhs"

Zero in place of "Ten thousands"

Eight in place of "Thousands"

Zero in place of "Hundreds"

Zero in place of "Tens"

Four in place of "units or ones"

Now expanded form of the number \[=2\times 100000+0\times 10000+8\times 1000+0\times 100\] \[+0\times 10+4=208004\]  

Name the number indicated in the place value chart.

Solution:

Fourteen kharab seventy two arab ninety six crore eighty three, lakh fifty thousand eight hundred sixty two  

Relation

Between Different Periods 10 ones = 1 tens              

100 lakshs =1 crores

10 tens  =1 hundreds     

100 crores = 1 arabs

10 hundreds = 1 thousands

100 arabs = 1kharabs                

100 thousands = 1 laks      

International System of Numeration

This system is applied in whole world. The following place value chart shows the international system of numeration:  

International Place Value Chart  

This system is also based on periods and places. Ones, thousands millions, billionsetc. are periods. In this system each period have been divided into three places. Like thousands has been divided into three places, thousands, ten-thousands, and hundred-thousands.   Name the number indicated in the place value chart

Solution:

Six hundred eight trillions one hundred sixty four billions eight hundred seventy millions nine hundred twenty nine thousand six hundred thirty five.  

Punctuate the following as per international system.

(a) 24365968                                      

(b) 115632865

(c) 56268708005                               

(d) 52012

Solution:

(a) 24365968 Twenty four million three hundred sixty five thousand nine hundred sixty eight.

(b) 115632865 One hundred fifteen million six hundred thirty two thousand and eight hundred sixty five.

(c) 56268708005 Fifty six billion two hundred sixty eight million seven hundred eight thousand and five.

(d) 52012 Fifty two thousand and twelve.  

Relation Between Indian and International Number System