CBSE Class 5 Mathematics Large Numbers International Place Value Notes Set 01

Why two systems?

Large numbers are written in two ways. In India we group digits as ones, thousands, lakhs and crores. Many other countries use the International system, which groups digits as ones, thousands and millions. Knowing both lets you read numbers in newspapers, atlases and science books from anywhere.

The International place value chart

In this system every period has three places: ones, tens and hundreds. The periods, from the right, are:

1. Ones period: Ones, Tens, Hundreds
2. Thousands period: Thousands, Ten Thousands, Hundred Thousands
3. Millions period: Millions, Ten Millions, Hundred Millions

Commas are placed after every three digits, starting from the right. For example, 34527498 is written as 34,527,498.

Where the two systems agree and differ

Up to the ten thousands place both systems look the same: ones, tens, hundreds, thousands and ten thousands. They differ from the next place. In the Indian system the next place is lakhs, and in the International system it is hundred thousands.

Useful links between the systems:

1. 1 lakh = 100 thousand
2. 10 lakh = 1 million
3. 1 crore = 10 million
4. 10 crore = 100 million

So 100,000,000 in the International system is the same number as 10,00,00,000 in the Indian system.

Reading and writing numbers

To read a number, split it into periods and read each period followed by its name. The ones period is read without its name. The number 5,435,765 is read as five million four hundred thirty-five thousand seven hundred sixty-five.

To write a number from its name, write each named period as three digits and put zeros where nothing is said. Always remember that a period of three digits needs all three places filled.

Face value and place value

The face value of a digit is the digit itself. The place value is the digit multiplied by the value of the place it sits in. The face value and place value of a digit in the ones place are always the same.

Worked examples

Example 1. Write 62849031 using International commas and read it.
Group from the right: 62,849,031. It is read as sixty-two million eight hundred forty-nine thousand thirty-one.

Example 2. Write "Nineteen million nineteen" in figures.
Nineteen million is 19, then the thousands period is not mentioned so it is 000, and the ones period is 019. The number is 19,000,019.

Example 3. Convert 3,25,00,000 to the International system.
3 crore = 30 million and 25 lakh = 2.5 million, so the number is 32.5 million, written as 32,500,000.

Key points to remember

1. The International system has the periods ones, thousands and millions.
2. Every period has three places.
3. 10 lakh = 1 million and 1 crore = 10 million.
4. Place value = digit × value of its place.

Quick Check Questions