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**International System Of Numeration: **Counting things on a daily basis is as natural as the process of breathing. we use numbers and counting a lot in our daily lives. but have you ever wondered what the standard way of Counting is? and how it emerged. what are the basic rules of numbers? this article will introduce you to the **Number system** and briefly discuss the International System of Numeration.

The **International System of Numeration**, commonly used worldwide, simplifies the representation of numbers by dividing them into groups or periods. This system is different from the Indian numeral system, primarily used in India among Hindus. Let’s explore the International System of Numeration in this article and understand its structure and rules.

## The Numeral System

In **Mathematics**, a numeral system is a way of expressing numbers consistently. The Hindu Arabic numeral system, originating in India, is the most commonly used. It is a positional base 10 system, meaning the position of each digit in a number is crucial, and a place value chart helps explain this.

## What is the International System of Numeration?

The International System of Numeration organises numbers into periods such as ones, thousands, millions, etc., facilitating the accurate reading of large numbers. While the system shares similarities with the Indian numeral system, the placement of commas differs.

## Structure of the International System of Numeration

The International System of Numeration divides numbers into periods, each further grouped based on place values:

**One Period:**Comprising ones, tens, and hundreds, the first three digits of a number fall under this period.**Thousand Period:**Encompassing thousands, ten thousand, and hundred thousand, the next three digits form this period.**Million Period:**Grouping million, ten-million, and hundred million, the subsequent three digits fall under this period.**Billion Period:**Including billion, ten billion, and hundred billion, the next three digits constitute this period.

## Rules of the International System of Numeration

In the International System of Numeration, commas separate periods, and digits within the same period are spoken together while reading a number. For example, 78,921,092 is read as “Seventy-eight million nine hundred twenty-one thousand ninety-two.”

## International System of Numeration Chart

Below given figure explains the International System of Numeration. Save the International System of Numeration Chart for future reference. Also, download it in PDF format from the link below.

## Key Rules of the International System of Numeration

**Plural Forms**: Periods are not written in a plural form; for instance, 456,876 is read as “four hundred fifty-six thousand eight hundred seventy-six,” without adding an ‘s’ to thousand or hundred.

**‘And’ Usage:**The word ‘and’ is not used before tens and ones; for example, 3535 is read as “three thousand five hundred thirty-five,” not as “three thousand and five hundred thirty-five.”

**Comma Placement:**Commas are not used when writing the number in expanded form. For instance, 3535 is written as “three thousand five hundred thirty-five,” not as “three thousand, five hundred thirty-five.”

## International System of Numeration: Solved Examples

**Example 1. Rewrite the number 85694217 according to the International number system.**

**Solution:** In the International number system, commas are used to separate different periods, making large numbers easier to read. Therefore, as per the International numeral system, the given number 85694217 is written as 85,694,217.

**Example 2. Express the number 4532789614 in accordance with the International number system.**

**Solution:** In the International number system, commas play a crucial role in marking different periods within a large number. Therefore, adhering to the International numeral system, the number 4532789614 is expressed as 4,532,789,614.

## Indian Numeral System:

In the Indian system, the place values of digits progress in the sequence of Ones, Tens, Hundreds, Thousands, Ten Thousand, Lakhs, Ten Lakhs, Crores, and so on. For example, in the number 78921092:

2 represents Ones

9 represents Tens

0 represents Hundreds

1 represents Thousands

2 represents Ten Thousand

9 represents Lakhs

8 represents Ten Lakhs

7 represents Crores

The relationship between them is defined as 1 hundred, equaling 10 tens and so on.

## Difference Between Indian and International System of Numeration

The primary distinction lies in the grouping of digits. In the Indian system, the first period has 3 digits, and subsequent periods have 2 digits each. Conversely, the international system consistently groups 3 digits in all periods. After the ten thousand places, the Indian system uses terms like Lakhs, Ten lakhs, and Crores, while the international system uses terms like Hundred thousand, Millions, and Ten million.

Indian System of Numeration |
International System of Numeration |

Nine places grouped into four periods: ones, thousands, lakhs, and crores. | Nine places grouped into three periods: ones, thousands, millions, and further into billion and so on. |

Place Values: ones, tens, hundreds, thousands, ten thousand, lakhs, ten lakhs, crores, and ten crores. | Place Values: Ones, tens, hundreds, thousands, ten thousand, hundred thousand, millions, ten million, and hundred million. |

Lakhs and crores are Indian units. | Millions and billions are international units. |

## FAQs on International System of Numeration

### What is meant by place value?

Place value in Math refers to the value of any digit in a number based on its position. For example, in 345, the place value of 4 is 40 because it's in the ten's position.

### What is the difference between place value and face value?

The place value of a digit is determined by its position in a number, while the face value is the digit itself. For example, in 297, the place value of 2 is 200, and the face value is 2.

### What is the difference between the Indian and International numeral systems?

The main difference lies in the placement of commas. In the Indian system, lakhs are written after thousands, whereas in the International system, millions are written after thousands.