CLASS 6TH | UNIT 1: NUMBERS | NUMBERS IN INDIA AND INTERNATIONAL SYSTEM | REVISION NOTES

Hindu–Arabic numeral system 

Before the invention of numbers, counting was done using some sort of physical objects such as pebbles or sticks. The numbers came into existence, eventually and then the need for adapting to a standard system of counting. 

The Hindu–Arabic numeral system also known as the Arabic numeral system or Hindu numeral system, is a positional decimal numeral system. It is the most common system for the symbolic representation of numbers in the world. It was invented between the 1st and 4th centuries by Indian mathematicians. The system was adopted in Arabic mathematics by the 9th century.  The system later spread to medieval Europe.

The system is based on ten different symbols. The symbols in actual use are descended from Brahmi numerals and have split into various typographical variants.

Today, this numerical system is still used worldwide.

Hindu Arabic system of numeration:

• In Indian number system, ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are used to write numeral. Each of this number is called a digit.
• Values of the places in the Indian system of numeration are Ones, Tens, Hundreds, Thousands, Ten thousand, Lakhs, Ten Lakhs, Crores and so on.
  The following place value chart can be used to identify the digit in any place in the Indian system.
• Commas are placed to the numbers to help us read and write large numbers easily. As per Indian system of numeration, the first comma is placed after the hundreds place. Commas are then placed after every two digits.

Periods	Crores	lakhs	Thousands	Ones
Places	Tens	Ones	Tens	Ones	Tens	Ones	Hundreds	Tens	Ones

Example 1:

Using Hindu-Arabic system, read the number 850746

Solution:

850746 – Eighty Lakh Fifty Thousand Seven Hundred Forty Six. Place value chart is as shown in the picture below on the left:

Example 2:

Write four crores fifteen lakh fifty thousand five hundred twenty seven in the numeral form using the Hindu-Arabic system.

Solution:

Number – 4,15,50,527

The international system of numeration:

A numeral system (or system of numeration) is a system for expressing numbers; using digits or other symbols in a consistent manner. The number the numeral represents is called its value. The most commonly used system of numerals is the Hindu–Arabic numeral system which was invented by Indian mathematicians.

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

The international system of numeration:

As per the International numeration system, the first comma is placed after the hundreds place. Commas are then placed after every three digits.

The values of the places in the International system of numeration are Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, Millions, Ten millions and so on.
1 million = 1000 thousand,
1 billion = 1000 millions.

Shown on the left side is a chart with the International number system. Shown on the right side is a chart with a comparison between Indian and International system:

Let us consider some examples.

International system – table

Indian system –  table

Let us consider some examples:

Example 1: Using the International system, write the number; Six million, four hundred and eleven thousand, two hundred and sixty.

Solution:  6,411,260.

Example 2: Using the international system, read the number 7456123.

Solution: 7456123- Seven million Four Hundred Fifty six thousand one hundred twenty three.

Example 3:  Write the number in words: 12,367,169.

Solution:  Twelve million, three hundred and sixty-seven thousand, one hundred and sixty-nine.

Example 4: Write seven hundred forty three million eight hundred thirteen thousand two hundred fifty six in the numeral form using the international system.

Solution: 743,813,256.

Similarly, 48670002 can be read as

48,670,002 – Forty eight million, six hundred and seventy thousand and two.