Large Numbers (7-Digit and 8-Digit Numbers) - Class 5 Worksheet
What are Large Numbers?
In mathematics, numbers that are bigger than six digits are called large numbers. These numbers are used to represent very big quantities such as population, distances, money, and production.
The greatest 6-digit number is:
999,999
If we add 1 to this number:
999,999 + 1 = 1,000,000
This number has 7 digits, so it becomes a seven-digit number.
Similarly:
9,999,999 + 1 = 10,000,000
This becomes an eight-digit number.
Understanding large numbers helps students read, write, compare, and work with big values used in real life.
Students can practise these concepts regularly with worksheets and exercises available on CBSEClassWorksheets, which help strengthen number sense and confidence in working with large numbers.
Examples of Large Numbers
Some examples of 7-digit and 8-digit numbers are:
7-digit numbers
1,245,673
3,567,890
7,345,210
8-digit numbers
12,345,678
45,876,321
90,234,567
These numbers are commonly used to represent population, large money values, and distances.
Indian and International Systems of Numeration
To make large numbers easier to read and understand, mathematicians use numeration systems. The two commonly used systems are:
Indian System of Numeration
International System of Numeration
These systems group digits and assign place values to them.
Indian System of Numeration
In the Indian system, digits are grouped differently compared to the international system.
Example number:
1,23,45,678 read as One crore twenty-three lakh forty-five thousand six hundred seventy-eight
Place Value Chart (Indian System)
Use of Commas (Indian System)
In the Indian system:
The first comma comes after three digits from the right
After that, commas come after every two digits
Example:
12345678 → 1,23,45,678
This grouping helps us read large numbers easily.
International System of Numeration
In the international system, digits are grouped in sets of three digits.
Example number:
12,345,678 – read as Twelve million three hundred forty-five thousand six hundred seventy-eight
Place Value Chart (International System)
Face Value and Place Value
Every digit in a number has two types of values:
Face Value
Place Value
Face Value
The face value of a digit is the digit itself, regardless of where it appears in the number.
Examples of Face Value
In the number 5,47,326
Face value of 5 = 5
Face value of 4 = 4
Face value of 7 = 7
Face value of 3 = 3
The face value never changes.
Place Value
The place value of a digit depends on its position in the number.
Examples of Place Value
In the number 5,47,326
| Digit | Place | Place Value |
|---|---|---|
| 5 | Lakhs place | 5,00,000 |
| 4 | Ten thousands place | 40,000 |
| 7 | Thousands place | 7,000 |
| 3 | Hundreds place | 300 |
| 2 | Tens place | 20 |
| 6 | Ones place | 6 |
Difference Between Face Value and Place Value
| Face Value | Place Value |
|---|---|
| Digit itself | Value of digit based on position |
| Does not change | Changes depending on place |
| Example: In 352, face value of 5 = 5 | Place value of 5 = 50 |
Expanded Form of Large Numbers
Expanded form means writing a number as the sum of the place values of its digits.
Example:
5,47,326
Expanded form:
5,00,000 + 40,000 + 7,000 + 300 + 20 + 6
Example:
12,45,678
Expanded form:
10,00,000 + 2,00,000 + 40,000 + 5,000 + 600 + 70 + 8
Expanded form helps students understand the value of each digit clearly.
Comparing and Ordering Large Numbers
Large numbers can be compared to determine which number is greater or smaller.
Comparing Large Numbers
To compare numbers:
Compare the number of digits first.
If the number of digits is the same, compare digits from left to right.
Example:
45,67,890
34,56,789
Since 45 lakh is greater than 34 lakh, the first number is greater.
45,67,890 > 34,56,789
Examples of Comparison
Compare:
1,23,45,678 and 1,12,45,678
Compare lakhs place:
23 lakh > 12 lakh
So:
1,23,45,678 > 1,12,45,678
Ordering Numbers
Ordering numbers means arranging numbers in:
Ascending order (smallest to largest)
Descending order (largest to smallest)
Examples of Ordering
Numbers:
45,67,890
34,56,789
56,78,901
Ascending order: 34,56,789 45,67,890 56,78,901
Descending order: 56,78,901 45,67,890 34,56,789
Creating the Largest and Smallest Numbers
Sometimes students are asked to form numbers using given digits.
Steps to Create the Largest Number
Arrange the digits in descending order.
Place the largest digit first.
Continue arranging from largest to smallest.
Example
Digits: 7, 2, 9, 4, 5
Largest number:
9, 7, 5, 4, 2
Largest number = 97,542
Steps to Create the Smallest Number
Arrange digits in ascending order.
The smallest digit should come first.
If 0 is present, place the smallest non-zero digit first.
Example
Digits: 7, 2, 9, 4, 5
Smallest number:
2, 4, 5, 7, 9
Smallest number = 24,579