**Numbers**

**Large Numbers**

We have learned:

6-Digit Numbers

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)

7-Digit Numbers

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)

8-Digit Numbers

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 System 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.

**Example 1: **

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

**Example 2: **

**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.

**Example**

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

**Read and write large numbers in International system of numeration:**

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

**Example**

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 Indian system of numeration and International system of numeration:**

**Place value of digits and expanded form of number**

Learn place value with an example.

**Example: ** 67,09,402

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.

**Example: **Let’s take above example:

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

**Example:**

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