# Numbers up to 9-Digits

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 1 Introduction to Numbers up to 9-Digits 2 The Big Idea: What are 9-digit numbers? 3 How To Decompose 9 digit numbers 4 Smallest 9 Digit Number 5 Biggest 9 Digit Number 6 Solved Examples 7 Challenging Questions 8 Practice Questions 9 Important Notes 10 Maths Olympiad Sample Papers 11 Frequently Asked Questions (FAQs)

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## Introduction to Numbers up to 9-Digits

We have learnt numbers from 2-digit to 8- digit.

Let us extend our learning to a bigger number now - 9-digit numbers.

A 9 digit number has numbers from 0 to 9 in its 9 place value.

We learnt about the place values from Units, Tens, Hundreds, Thousands, Ten-thousands, Lakhs, Ten lakhs, and Crore.

Now we are going to learn about the 9th  place value i.e. Ten crores.

As discussed earlier, we can represent it using the Indian system and the International system  ## The Big Idea: What are 9-digit Numbers?

9 digit numbers have the numbers $$0,1,2,3,4,5,6,7,8,9$$ in its 9 place values except that 0 cannot be in the Ten Crores place.

Nine digit numbers can be expressed in both the Indian system of numbers and the International system of numbers.

Let us consider a random nine digit number, 324864701.

Let us look at the two ways we can write this number:

Indian: 32,48,64,701 (this can be read as Thirty-two crores, forty-eight lakhs, sixty-four thousand seven hundred and one)

International: 324,864,701 (this can be read as Three hundred twenty-four million, eight hundred sixty-four thousand, seven hundred and one)

## How To Decompose 9 – Digit Numbers

Any 9 digit number has place values up to 10 crores (or hundred million).

These are the names of the place values (starting from the right) in a 9-digit number in the Indian system and the International system:

• Digit 1 – Units
• Digit 2 – Tens
• Digit 3 – Hundreds
• Digit 4 – Thousands
• Digit 5 – Ten Thousands
• Digit 6 – Lakhs / Hundred Thousands
• Digit 7 – Ten Lakhs / Million
• Digit 8 – Crores / Ten Million
• Digit 9 – Ten Crores / Hundred Million

Let us take a random 9 digit number - 338652931, and see how it gets decomposed.

Here, PV = Place Value

 Digit 1 PV = 1 x 1                 = 1 Digit 2 PV = 3 x 10               = 30 Digit 3 PV = 9 x 100             = 900 Digit 4 PV = 2 x 1000           = 2000 Digit 5 PV = 5 x 10000         = 50000 Digit 6 PV = 6 x 100000       = 600000 Digit 7 PV = 8 x 1000000     = 8000000 Digit 8 PV = 3 x 10000000   = 30000000 Digit 9 PV = 3 x 100000000 = 300000000

### The Importance of a Comma

As mentioned above, the smallest 9 digit number is called a hundred million.

It is written as 1 followed by 8 zeroes.

But, just the placement of the comma in the two different number systems gives this number two different names.

The Indian system of numbers follows the 3:2:2 system of placing commas, so the smallest 9 digit number would be written as 10,00,00,000

The 8th digit from right denotes the start of a crore, thus, this number would be called 10 crores in the Indian number system.

Let us now look at the 3:3:3 system of comma placement in the International number system.

This number would be written as 100,000,000.

Since the second comma after the 6th digit from right denotes the start of a million, this number would be called a hundred million in the International number system.

## Smallest 9 Digit Number

We know that adding 1 to the greatest 8 digit number 9,99,99,999 gives us the first and smallest 10 digit number 10,00,00,000

We call this number Ten crores.

Can you place the comma for the smallest 9-digit number according to the International system?

## Biggest 9 Digit Number

The biggest 9 digit number is 99,99,99,999

In number names, we read it as ninety-nine crores, ninety-nine lakhs, ninety-nine thousand nine hundred and ninety-nine.

Can you place the comma for the largest 9-digit number according to the International system and write its number name?

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## Solved Examples

 Example 1

Write the number name for the number 19,32,35,372 according to the Indian system.

Solution:

The given number 19,32,35,372 is a 9 digit number.

The number name is Nineteen crores, thirty-two lakhs, thirty-five thousand, three hundred and seventy-two.

 $$\therefore$$ Nineteen crores, thirty-two lakhs, thirty-five thousand, three hundred and seventy-two
 Example 2

Write the following number in expanded form: 23,41,53,701

Solution:

It is a 9-digit number; it has place value up to ten crores.

The expanded form is:

$\begin{matrix} 23,41,53,701 = \\ 2 \times 100000000\:+ \\ 3 \times 10000000\:+ \\ 4 \times 1000000\:+ \\ 1 \times 100000\:+\\ 5 \times 10000\:+ \\ 3 \times 1000\:+ \\ 7\times 100 \:+\\ 0 \times 10 \:+\\ 1 \times 1 \end{matrix}$

 $$\therefore$$ The expanded form of the number is as above.
 Example 3

Write the number in the Indian and International system by placing the commas correctly.

$\begin{matrix} 3 \times 100000000\:+ \\ 3 \times 100000\:+ \\ 7 \times 1000\:+ \\ 1\times 100 \:+\\ 1 \times 1 \end{matrix}$

Solution:

The number in the Indian system is 30,03,07,101 and is written as thirty crores, three lakhs, seven thousand, one hundred and one.

The number in the International system is 300,307,101 and is written as three hundred million, three hundred and seven thousand, one hundred and one.

 $$\therefore$$ The number is 300307101
 Example 4

What is the predecessor and the successor of the difference of the biggest 9 digit number and the smallest 9 digit number?

Solution:

The smallest 9 digit number is 10,00,00,000 and the biggest 9 digit number is 99,99,99,999

Their difference is 99,99,99,999 - 10,00,00,000  = 89,99,99,999

Successor of 89,99,99,999 is 90,00,00,000

Predecessor of 89,99,99,999 is 89,99,99,998

 $$\therefore$$ Numbers are 90,00,00,000 and 89,99,99,998
 Example 5

Find the sum. Solution:

The first number is 12,23,11,123 and the second number is 10,11,12,345

Their sum is 12,23,11,123 + 10,11,12,345 = 22,34,23,468

 $$\therefore$$ Sum is 22,34,23,468 Challenging Questions
1. If there are nine hundred million different 9-digit numbers, represent the number of 9 digit numbers in the Indian system.
2. Arrange the following numbers in descending order 11,11,11,111 ; 10,10,10,111 ; 11,10,10,111 and 10,00,00,111

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## Practice Questions

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.

IMO (International Maths Olympiad) is a competitive exam in Mathematics conducted annually for school students. It encourages children to develop their math solving skills from a competition perspective.

## 1. What is a 9 digit number?

A 9 digit number has 9 digits.

It starts from ten crores to ninety-nine crores ninety-nine lakhs, ninety-nine thousand, nine hundred and ninety-nine.

## 2. How many 9 digit numbers are there in all?

There are nine hundred million different 9-digit numbers.

## 3. What is the smallest number of 9 digits?

The smallest 9-digit number is 10,00,00,000 and it is read as ten crores.

## 4. Which is the greatest 9 digit number?

The greatest 9 digit number is 99,99,99,999

In number names, we read it as ninety-nine crores, ninety-nine lakhs, ninety-nine thousand, nine hundred and ninety-nine.

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