International Numeration System: Rules, Examples

International Numeration System: It is difficult to your brain from the grip of numbers once you have learned them. They appear to be natural, innate, and something that every individual is born with. Consider a time when the invention of numbers was almost unthinkable to early man. Counting was done using actual objects like sticks, pebbles, and bones. Lines and marks on rocks, bones, and pottery remained after then. After that, there were the numbers. As a result, a consistent way of counting, known as the numeral system, was developed.

A numeral system is used to express numbers using digits and symbols in a consistent manner. In the International System, different periods are formed for the easier reading of numbers. The first comma is placed after the hundreds place, and then commas are placed after every third digit. In this article, we would discuss the International system of numeration.

International System of Numeration

The International number system is another method of representing numbers. In the International numbering system, different periods are formed to read large numbers. The periods used here are ones, thousands, millions, billions, etc.

The number names in International system of numeration are provided in the chart below:

International Number System Table

In the International and Indian number system, the places are separated into groups or periods. In the International system, we start grouping the number from right in a group of \(3,\) called a period. We place a comma or space after each period to read the number easily. In the International number system chart, the groups are made with periods as shown below:

Counting from the right-hand towards the left-hand side, we have,

• One’s period: First \(3\) digits, i.e., hundreds, tens and ones
• Thousand’s period: Next \(3\) digits, i.e., Hundred-thousands, Ten-thousands and Thousands
• Million’s period: Next \(3\) digits, i.e., Hundred-millions, Ten-millions and Millions
• Billion’s period: Next \(3\) digits, i.e., Hundred-billions, Ten-billions and Billions

Let us understand this by taking a couple of examples.

While writing a number in the International System, we separate the periods by adding commas \(\left( , \right).\)

For example, \(209,450,123\) and \(34,235,987.\)

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

For example, \(23450968\) is written as \(23,460,968\) and read as twenty-three million four hundred sixty thousand nine hundred sixty-eight.

\(998239659\) is written as \(998,239,659\) and read as nine hundred ninety-eight million two hundred thirty-nine thousand six hundred fifty-nine.

Indian System of Numeration (Hindu-Arabic)

The Indian system of numeration is, in fact, the decimal system in use worldwide. The ancient Hindu mathematicians developed this system and were carried to the west by the Arabs. For this reason, it is called the Hindu-Arabic (Indian) system of numeration.

For example, the number \(7789430\) can be written as \(77,89,430\) and read as seventy-seven lakh eighty-nine thousand four hundred thirty.

International vs Indian Number Systems (Place Value)

The following table compares the International number system and Indian number system:

In comparing the International number system and Indian number system, we find these systems differ in the numbers of digits contained in each of their periods.

In the Indian number system, starting from the right, only the first period has \(3\) digits and all other periods have \(2\) digits each. However, in the International number system, all the periods contain \(3\) digits each.

Both the International and Indian number system have the same names and same writing styles for the first \(5\) digits from the right. But after the ten thousand places, the digits in the Indian system are called Lakhs, Ten lakhs, Crores and so on. In comparison, they are called Hundred thousands, Millions, Ten million and so on in the International System.

The following table shows the differences in the names and writing styles of the digits after ten thousand places:

In the generalised form, we can represent it as,

Thus, the smallest \(6\)-digit number \(1,00,000\) in the Indian system is read as one lakh, whereas it is read as one hundred thousand in the International system.

In the International number system, place values can be extended to the left to include numbers having more than \(9\) digits. These place values come under the billions period that follows the millions period.
A digit placed after the hundred million places has the place value of thousand millions or one billion, which is equal to hundred crores in the Indian System.

International Number System Examples

As of now, we are thorough with the representation of numbers according to the International System. Let us become more proficient in the same by solving some more problems based on the International System.

Example 1: Write the following numbers in words.
a) \(700,217\)
b) \(824,220,306\)
Solution: a) \(700,217 = \) Seven hundred thousand two hundred seventeen
b) \(824,220,306 = \) Eight hundred twenty-four million two hundred twenty thousand three hundred six.

Example 2: Write the following words in numbers.
a) Sixty-six million two hundred thousand one hundred one
b) One hundred eleven million one hundred eleven thousand one hundred twenty-three
Solution: a) Sixty-six million two hundred thousand one hundred twenty-three \( = 66,200,123\)
b) One hundred eleven million one hundred eleven thousand one hundred one \( = 111,111,101\)

Example 3: Put commas between periods in the following numbers according to the International Number System.
a) \(6425678\)
b) \(199911990\)
Solution: In the International System, we start grouping the number from right in a group of \(3,\) called a period, and place a comma or space after each period.
Hence, a) \(6425678 = 6,425,678\) b) \(199911990 = 199,911,990\)

Note

1. Do not write the periods in the plural form. Never write \(789,987\) as seven hundred eighty-nine thousand nine hundred eighty-seven; instead, write it as seven hundred eighty-nine thousand nine hundred eighty-seven.
2. Do not use the word “and” before tens and ones. Do not read \(2323\) as two thousand three hundred and twenty-three; instead, read it as two thousand three hundred twenty-three.
3. Do not place commas when writing the numeral. Never write \(2323\) as two thousand, three hundred, twenty-three; instead, write it as two thousand three hundred twenty-three.

International Number System Solved Examples

Q.1: Write the number and the number name that the abacus represents in the International Number System.

Ans: Number: \(64,952,373.\)
Number name: Sixty-four million nine hundred fifty-two thousand three hundred seventy-three

Q.2: Put commas between periods in the following numbers according to the International number system.
a) \({\text{89404798 }}\) b) \(123321890\)
Ans: In the International System, we start grouping the number from right in a group of \(3,\) called a period, and place a comma or space after each period.
Thus, a) \(89,404,798\) b) \(123,321,890\)

Q.3: Write in figures. One hundred ten million nine hundred thousand five hundred fifty.
Ans: One hundred ten million nine hundred thousand five hundred fifty \( = 110,900,550\)

Q.4: Write in words.
a) \(101,100,001\)
b) \(99,999,999\)
Ans: a) \(101,100,001 = \) One hundred one million one hundred thousand one. b) \(99,999,999 = \) Ninety-nine million nine hundred ninety-nine thousand nine hundred ninety-nine.

Q.5: Write the place value of \(4\) in \(564,500,500\) according to the International system of numeration.
Ans: According to the International System of Numeration, the place value of \(4\) in \(564,500,500\) is \(4,000,000,\) i.e., \(4\) million.

Summary

In this article, we learned the concept of the International system of numbers. We also learned the difference between the Indian system and the International system and the representation of numbers in both systems. We now know that both the Indian system and the International system have the same name and writing styles for the first five digits from the right, but after that, the notation changes.

FAQs on International Numeration System