What is the International Place Value System?

What is the International Place Value System?

​The International Place Value System 

In this system, we start grouping the number from right in group of 3 called period.  

 

  • Starting from the right, the first period is ones, consisting of three place values i.e. ones, tens and hundreds.  

 

  • The next period is thousands, consisting of three places i.e. thousands, ten-thousands and hundred-thousands. 

 

  • The third period is millions consisting of three places i.e. millions, ten-millions and hundred million and then billions, trillions and so on. 

 

 

Reading and writing a number 

  • While reading a number in the International system, all of the digits in the same period are read together and the name of the period (except the ones) is read along with them. 

  • While writing a number in the International system, we put a comma after every period to separate the period and making it easier to read. 

 

Example 1: Write the following in words: 

  1. 227,842  

  1. 36,479,111  

  1. 508,541,360 

 

Solution: Let us arrange the digits in International place value chart as follows: 

 

  1. Two hundred twenty-seven thousand eight hundred forty two 

  1. Thirty-six million four hundred seventy-nine thousand one hundred eleven 

  1. Five hundred eight million five hundred forty-one thousand three hundred sixty 

 

Example 2 : Write the following in figures : 

  1. Three hundred five million thirty-seven thousand sixty three 

  1. Eighty-nine million one hundred twenty-six thousand ninety 

  1. Two million twenty 

Solution: Let us make the International place value chart and write the digits in the respective places from the number name. 

 

 

The required number is- 

  1. 305,037,063 

  1. 89,126,090 

  1. 2,000,020 

 

Expanded Form 

  • A number when expressed with its place value denotes its expanded form. 

 

  • Suppose we write a number 619, here we actually mean that we have a total of 600 + 10 + 9. This expansion shows the value of each of its digit and hence represents the expanded form. 

 

  • The expanded form varies in the Indian and International structure as per their defined period. 

 

International Place Value System 

Examples:   

Expand the following numbers as per International Place Value System: 

  1. 81,664 

  1. 1,697,832  

We can expand any given number in three ways: 

  1. 81,664 

      = 8 ten thousand + 1 thousand + 6 hundred + 6 ten +  
    4 one 

Or = 8 x 10,000 + 1 x 1,000 + 6 x 100 + 6 x 10 + 4 x 1 

Or = 80,000 + 1,000 + 600 + 60 + 4 

 

  1. 1,697,832 

     = 1 million + 6 hundred thousand + 9 ten thousand +  
    7 thousand + 8 hundred + 3 ten + 2 one 

Or = 1 x 1,000,000 + 6 x 100,000 + 9 x 10,000 + 7 x 
    1,000 + 8 x 100 + 3 x 10 + 2 x 1 

Or = 1,000,000 + 600,000 + 90,000 + 7,000 + 800 + 30 + 
   2 

 

 

 

Did you know?? 

  • Zero was invented by Aryabhata. India invented the Number System. 

  • The place value system and the decimal system were developed in India in 100 BC. 

  • The largest numbers used by the Greeks and the Romans were 10^6 whereas Hindus used numbers as big as 10^53 with specific names as early as 5000 BC during the Vedic period.  

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