Class 5 Exam  >  Class 5 Notes  >  Mathematics for Class 5  >  Chapter Notes: Operations on Large Numbers

Operations on Large Numbers Class 5 Notes Maths

Large Numbers

Have you ever wondered how we count things that are really big? Think about:

  • How many people live in your city?
  • How many stars are in the sky? 
    For such huge things, we need large numbers.
    Operations on Large Numbers Class 5 Notes MathsIn this Chapter, you’ll learn to read, write, compare, and play with large numbers so you can measure the big things all around us.

Indian Place Value Chart

Following is the table for the Indian Place Value System to let students understand how numbers are arranged and read.Operations on Large Numbers Class 5 Notes Maths

Example:  Write the numeral by separating periods of the following
1. 603274087 
Ans: 60,32,74,087

Sol: 
Step 1: Identify the periods(refer to the table given above):

Crore: 60
Lakh: 32
Thousand: 74
Ones: 087
Step 2: Put commas 
After putting commas according to the periods we get = 60,32,74,087

2. 37007690
Ans: 3,70,07,690

Sol: 
Step 1: Identify the periods(refer to the table given above):
Crore: 3
Lakh: 70
Thousand: 07
Ones: 690
Step 2: Put commas 
After putting commas according to the periods we get = 3,70,07,690

Number Names & Expanded Form

1. Number Names

To write number name for any given number, we must follow the following steps

Operations on Large Numbers Class 5 Notes Maths

We will refer to some solved examples for better clarity of the concept

Example 1: Write number name for the following
1. 76,23,45,809
Ans: Seventy-six crore twenty-three lakh forty-five thousand eight hundred nine.

Sol: 
Step 1: Break it down
Crore: 76
Lakh: 23
Thousand: 45
Ones: 809
Step 2: Arrange and combine
Seventy-six crore twenty-three lakh forty-five thousand eight hundred nine.

2. 1,05,08,406
Ans: One crore five lakh eight thousand four hundred six.

Sol:
Step 1: Break it down

Crore: 1
Lakh: 05
Thousand: 08
Ones: 406

Step 2: Arrange and combine
One crore five lakh eight thousand four hundred six.

2. Expanded Form

Refer to the following example to understand the concept of expanded form

Example 2: Write 45,76,90,213 in expanded form

Sol: 
Step 1: The given number is 45 crore 76 lakh 90 thousand 2 hundred thirteen.
The given number in the place value chart is as shown below.Operations on Large Numbers Class 5 Notes Maths

Step 2: Write the table into number name format
Thus, 45,76,90,213 = 4 ten crores + 5 crores + 7 ten lakhs + 6 lakhs+ 9 ten thousands + 0 thousands + 2 hundreds+ 1 ten + 3 ones

Step  3: Mathematically we can write it as

= 4 x 100000000 + 5 x 10000000 + 7 x 1000000 + 6 x 100000 + 9 x 10000 + 0 x 1000 + 2 x 100 + 1 x 10 + 3

= 400000000 + 50000000 + 7000000 + 600000 + 90000 + 0 + 200 + 10 + 3

Comparing & Ordering Large Numbers

In this section, we will  learn about the following three things

Operations on Large Numbers Class 5 Notes Maths

1. Comparing Large Numbers

For comparing large numbers , we have two cases:

Case 1: Unequal number of digits  
The number having more digits is greater than the number having fewer digits.

Example 1: Which is greater: 8,93,10,009 or 11,00,73,640? 

Sol: On counting both of the digits we found out that,
11,00,73,640 has 9 digits whereas 8,93,10,009 has 8 digits. 
and 9 is greater than 8.
therefore, 11,00,73,640 > 8,93,10,009.

Case 2: Equal number of digits
Start from the left and compare the digits until they differ. 

Example 2: Compare 8,31,46,205 and 8,31,57,610?

Sol: As we can see both of these numbers have same number of digits,
therefore we start comparing from the left until both of them differ.
Operations on Large Numbers Class 5 Notes Maths

The digits differ at the ten thousands place.
 5 > 4,
So, 8,31,57,610 > 8,31,46,205.

2. Ordering Large Numbers:

In this , we will arrange large numbers into ascending or descending order according to their values.
Example 3: Arrange the following numbers in descending order.

 8,36,04,295 ; 40,34,51,276 ; 3,04,63,500 ; 89,72,340 ; 99,00,32,941

Sol: 
Step 1: Line up the numbers by their place values
Operations on Large Numbers Class 5 Notes Maths

Step 2
There are two 9-digit numbers, two 8-digit numbers and one 7-digit number.
Comparing 9-digit numbers.
9 TC > 4 TC, 
So, 99,00,32,941 > 40,34,51,276
Comparing 8-digit numbers.
8 crore > 3 crore, ∴ 8,36,04,295 > 3,04,63,500 
7-digit number is the smallest.
Hence, the numbers written in descending order are:
99,00,32,941 > 40,34,51,276 > 8,36,04,295 > 3,04,63,500 > 89,72,340.

3. Formation of  Smallest & Greatest Numbers


For forming smallest and the greatest numbers from a given collection of numbers , we have following cases
Case 1: Repetition of Digits is not Allowed
When repetition of numbers is not allowed, 
1. Greatest Number :We place the greatest digit at the leftmost place and the other digits in descending order.
2. Smallest Number: We place the smallest at the leftmost place and the other digits in ascending order.
Example 4: Write the smallest and the greatest 7-digit number by using the digits 0, 2, 4, 6, 5, 8 and 9 only once.

Sol: 
1. Smallest Digit: 
For writing the smallest number, we place the smallest digit at the leftmost place and write the other digits in ascending order.
Here, 0 is the smallest digit but we cannot begin a number with 0.
So, we write the next higher digit which is 2 in this case.
So, the smallest 7-digit number is 2045689
2. Greatest Digit:
For writing the Greatest Number, We place the greatest digit at the leftmost place and the other digits in descending order.
Here, 9 is the greatest digit 
So, the greatest 7-digit number is 9865420

Case 2:  Repetition of Digits is Allowed
Example 5: Write the smallest and the greatest 7-digit number by using the digits 0, 1, 4, 6, 5, 8 and 9, where repetition is allowed.

Sol: Greatest Number: 9999999
Smallest number : 1000000

Question for Chapter Notes: Operations on Large Numbers
Try yourself:
Which of the following is the greatest 8-digit number formed using the digits 3, 7, 2, 5, 8, 9, 0, and 6, without repetition?
View Solution

Arithmetic Operations on Large Numbers

The arithmetic operations on the large numbers are given below 

  •  Addition of Large numbers
  • Subtraction of Large Numbers

Operations on Large Numbers Class 5 Notes Maths

1. Addition

In case of addition of  large numbers, we have to add the numbers of same place values.

Operations on Large Numbers Class 5 Notes MathsExample: The statistics on the Internet suggest that the estimated population of Russia and Mexico is 14,39,64,709 and 13,07,59,074, respectively. If the population of the USA is 32,67,66,748, find out whether the population of Russia and Mexico taken together is more than that of the USA or not.

Sol: 

Operations on Large Numbers Class 5 Notes Maths

  • The population of Russia and Mexico is 27,47,23,783
  • Population of USA = 32,67,66,748
  • Since, 3 ten crores > 2 ten crores, the population of the USA is more than the population of Russia and Mexico taken together.

Question for Chapter Notes: Operations on Large Numbers
Try yourself:Add 44,71,214 and 31,27,510
View Solution

2. Subtraction

In case of subtraction of large numbers, we have to subtract the numbers of same place values.

Operations on Large Numbers Class 5 Notes Maths

Example : The population of Greater Mumbai and Chennai as per the 2011 census was 1,63,68,084 and 64,24,624, respectively. How much more is Greater Mumbai’s population as compared to Chennai?

Sol: 
  • The population of Greater Mumbai = 1,63,68,084
  • Population of Chennai = 64,24,624
  • Population difference  = 1,63,68,084 – 64,24,624 =  99,43,460
  • Operations on Large Numbers Class 5 Notes Maths
  • Thus, the population of Greater Mumbai is 99,43,460 more than that of Chennai.
  • You can check subtraction by adding the subtrahend to the difference. If the sum is equal to the minuend, then the subtraction has been carried out correctly.
  • Operations on Large Numbers Class 5 Notes Maths

Question for Chapter Notes: Operations on Large Numbers
Try yourself:Subtract 65248907 from 86165281
View Solution

International System of Writing Numbers

In International system, the number 10 lakh is called a million and furthermore every bigger calculations is in millions.
Operations on Large Numbers Class 5 Notes Maths

The chart can be extended to its left to include more than 9 places. The period just to the left of the millions period is called the billions period. Then, we have the trillions period and so on. 
On comparing the two systems of numerations, we can observe the following relationships.

  • 10 lakh = 1 million
  • 1 crore = 100 lakh = 10 million
  • 10 crore = 100 million
  • 100 crore = 1,000 million = 1 billion
  • 1000 crore = 10,000 million = 10 billion

Operations on Large Numbers Class 5 Notes Maths

Did You Know
  • The Indian system, starting from the right after the first period of 3 digits all other periods are of 2 digits.
  • In the International system, each period consists of three digits. 
  • We place comma or leave space after every 3 digits.

Example 1: Write in numerals:
(a) 8 million 
(b) Eighty-five million three hundred five thousand nine hundred

Sol: 
(a) 8 million = 8,000,000 
(b) Step by step breakdown of the numbers

1. Eighty-five million = 85,000,000

2. Three hundred five thousand = 305,000

3. Nine hundred = 900
On adding we get, 85,305,900

Example 2: Number names in international system:

1. 23,450,789

Sol: Number Name for the same is given below
Number Name: Twenty-three million four hundred fifty thousand seven hundred eighty-nine

2. 105,067,092

Sol: Number Name for the same is given below
Number Name: One hundred five million sixty-seven thousand ninety-two

Example 3: Write ‘sixty-nine crore four lakh forty-one thousand six hundred twenty-seven’ in the International system.

Sol: The numeral in Indian system is 69 04 41 627. 
On writing it in International system, we get,
Numeral : 690,441,627
Number Name : Six hundred ninety million four hundred forty-one thousand six hundred twenty-seven.

Question for Chapter Notes: Operations on Large Numbers
Try yourself:
Which is the greatest number among the following: 76,89,23,450; 89,12,67,543; 54,34,21,987; 90,87,65,432?
View Solution

The document Operations on Large Numbers Class 5 Notes Maths is a part of the Class 5 Course Mathematics for Class 5.
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FAQs on Operations on Large Numbers Class 5 Notes Maths

1. What are large numbers and how do we write them in number names?
Ans.Large numbers are numbers that have many digits, typically over four digits. They can be written in number names by breaking them down into their place values. For instance, the number 1,234 can be written as "one thousand two hundred thirty-four."
2. How do you expand a large number into its expanded form?
Ans.To expand a large number into its expanded form, you break it down into the sum of each digit multiplied by its place value. For example, the number 4,567 can be expanded as 4,000 + 500 + 60 + 7.
3. How can we compare and order large numbers effectively?
Ans.To compare and order large numbers, start by looking at the number of digits; the number with more digits is larger. If they have the same number of digits, compare them digit by digit from left to right until you find a difference.
4. What are the basic arithmetic operations we can perform on large numbers?
Ans.The basic arithmetic operations that can be performed on large numbers include addition, subtraction, multiplication, and division. Each operation follows the same rules as with smaller numbers, but careful alignment and carrying may be needed due to the increased number of digits.
5. What is the International System of Writing Numbers?
Ans.The International System of Writing Numbers is a standardized way of writing numbers using digit grouping, often in sets of three separated by commas. For example, the number 1,000,000 is read as "one million," making it easier to read large numbers quickly and clearly.
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