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.  

    • Related Articles

    • What are the Place Value Systems for India and the International Number System?

      Introduction: Place Value System, India and International According to our number system, the value of a digit depends upon the place it holds in the number. The TRUE and ACTUAL value of a number depends on two factors: (1) Face value of a digit in a ...

    • What is the Place Value System?

      Introduction: Place Value System, India and International According to our number system, the value of a digitdepends upon the place it holds in the number. The TRUE and ACTUAL value of a number depends on two factors: Face value of a digit in a ...

    • What is Expanded Form in the International and Indian Place Value Systems?

      Expanded Form: International Place Value System The expanded form varies in the Indian and International structure as per their defined period. We just learned how to expand a number per the Indian Place Value System, now let us go through some ...

    • What is the Indian Place Value System?

      The Indian Place Value System Using the same concepts as we had learned in the introduction, the Indian Place Value System is also a Base -10 number system, with following key rules: We start grouping the number from the right, first in group of 3 ...

    • 5th Grade, Module 1: What are Large Numbers?

      Large Numbers How far is moon from earth? What is the speed of light? How many cells are there in the human body? The answers to these questions are numbers that go way beyond 10’s or 100’s. This chapter gives us an idea about numbers beyond 1000. In ...