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.