The number is an essential element in our daily life. Here students will learn about the large number in math in this learning concept. They will learn about large numbers with different digits.

In this learning concept, the students can

- classify the different digits in large numbers in class 5 with examples.
- Representation of large numbers.
- Application of reading and writing large numbers in the international system of numeration

Each concept is explained to class 5 maths students using illustrations, examples, and mind maps. Students can assess their learning by solving the two printable worksheets given at the page’s end.

Download the large numbers worksheet for class 5 and check the solutions for the concept of large numbers provided in PDF format.

**Different Types of Large Numbers**

We have learned:

Biggest 5-digit number = 99999. If we add 1 to 99999, we get ‘one hundred thousand’. We read it as ‘One lakh’.

- Smallest 6-digit number is 100000 (One lakh)
- Biggest 6-digit number is 999999 (Nine lakh ninety-nine thousand nine hundred and ninety-nine)

Biggest 6-digit number = 999999. If we add 1 to 999999, we get 1000000. We read it as ‘Ten lakh’.

- Smallest 7-digit number is 1000000 (Ten lakh)
- Biggest 7-digit number is 9999999 (Ninety-nine lakh ninety-nine thousand nine hundred and ninety-nine)

Biggest 7-digit number = 9999999. If we add 1 to 9999999, we get ‘Hundred Lakh’. We read it as ‘One Crore’.

- Smallest 8-digit number is 1000000 (One crore)
- Biggest 8-digit number is 99999999 (Ninety-nine crore ninety-nine lakh ninety-nine thousand nine hundred and ninety-nine)

**Representation of Large Numbers**

We generally use the following two numeration systems to read and write numbers.

**1.Indian and International Systems of Numeration**

**Use of commas:**

- Commas are used to mark each period like ones, thousands, lakhs, etc.
- The first comma comes after hundreds place. (After three digits from right). It marks thousands.
- The second comma comes after ten thousands place. (After five digits from right). It marks lakhs.
- The third comma comes after ten lakhs place. (After seven digits from right). It marks crores.
- In this way after two digits we can put commas.

By using these commas, we can easily interpret large numbers.

*493574637 → 49,35,74,637 80956234 → 8,09,56,234*

**Question 1: **Write the number 6,08,77,681 in words.

**Answer:**

*The given number can be written in words as ‘Six crore eight lakh seventy-seven thousand six hundred and eighty-one’.*

**Question 2: **Write ‘Five lakh two thousand four hundred and nine’ using numerals.

**Answer:**

- There are 5 lakhs in this number, so write 5 in the place of L.
- There are no ten thousand, so write 0 in the place of TTH.
- There are 2 thousand, so write 2 in the place of TH.
- There are 4 hundreds, so write 4 in the place of H.
- There are no tens, so write 0 in the place of T.
- There is nine, so write 9 in the ones place.

So, we write this number as ‘5,02,409’.

**2. International System of Numeration**

**Use of commas:**

- Commas are used to mark each period like ones, thousands, millions, billions etc.
- The first comma comes after hundreds place. (After three digits from right). It marks thousands.
- The second comma comes after hundred thousands place. (After six digits from right). It marks millions.
- The third comma comes after hundred million place. (After nine digits from right). It marks billions.
- In this way after three digits we can put commas.

By using this commas’, we can easily interpret the numbers.

324574810 → 324,574,810 70262625 → 70,262,625

**Read and Write Large Numbers in the International System of Numeration:**

In the following examples by using commas learn to read and write the numbers.

1. 58,634,521 (Write this number in words.)

Put this number in place value table of International system of numeration.

So, we write this number as **‘Fifty-eight million six hundred thirty-four thousand five hundred and twenty-one’.**

2. Six million seventy-four thousand four hundred and three (Write this number in figures.)

- There are 6 million in this number, so write 6 in the place of M.
- There are no hundred thousand, so write 0 in the place of HTH.
- There are 74 thousand, so write 7 in the place of TTH and 4 in place of TH.
- There are 4 hundred, so write 4 in the place of H.
- There are no tens, so write 0 in the place of T.
- There are 3, so write 3 in the ones place.

So, we write this number as 6,074,403

**Comparison Between the Indian System and International System of Numeration:**

**Place Value and Expanded Form of Number**

Learn place value with an example.

Put this number in the place value table.

{**Trick:** Count the digits after the number for which place value is to be found.

For example: 93,546

There are 4 digits after the number 9. So, write 4 zeroes after the number 9 and we get the place value of the number 9.

Place value of 9 = 90000}

**Expanded form:**

By writing place values of the digits in the form of addition, we get expanded form of the number.

Write the expanded form of the 67,09,402

We can write expanded form as:

67,09,402 = 6000000 + 700000 + 0 + 9000 + 400 + 0 + 2

Write the number by using expanded form.

700000 + 20000 + 8000 + 3

- 700000 is place value of lakh place.
- 20000 is place value of ten thousand place.
- 8000 is place value of thousand place.
- 3 is place value of ones place.
- Place values of hundred and tens place are missing. So, put 0 in these places. We get the number as:

700000 + 20000 + 8000 + 3 = 7,28,003

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