Chapter Notes: Large Numbers
Ria & Some Big Big Numbers!
- One day, Ria was reading the newspaper.
- She saw something interesting!
- The population of India is more than 100 crore.
- The population of Delhi is about 2 crore 50 lakh.
- Ria started thinking...
"What exactly is a crore? It sounds like a really BIG number!"
So she asked her teacher. Her teacher explained that crore is a very large number and it is connected to lakh and place value.
Ria wondered how much will a crore be?But before understanding crore, Ria first needed to understand lakh.
What is One Lakh?
- 100000 is the smallest 6-digit number.
- Below are the smallest numbers having 6, 4, 3, 2 and 1 digits (see the picture).
Try yourself: How many zeros are there in Ten Lakhs?
We learnt about One Lakh! Come on! Let's learn about 100 Lakh or One Crore now!
- The number 10000000 is read as 100 lakh or one crore.
- Thus, 100 lakh = 1 crore.
- For example,
Summary: One crore is the number 10000000 (that is, 100 lakh). One lakh is the number 100000 (one hundred thousand).
Do you know?
The moon is approximately 384400 km away from the Earth. This is a very large number too.
In the image Earth and Moon look very near but it in reality it isn't so.
Greatest Digit Numbers
Ria had now learned about lakh and crore. But her curiosity didn't stop there!
Her teacher asked the class:
"What is the greatest 5-digit number?"
Ria quickly remembered that digits go from 0 to 9.
So to make the largest number, we use 9 in every place.
Example:
So, the greatest 5-digit number is given in the picture below.
You might see numbers like this in prices of phones, bikes, or online shopping deals!
Example:
Some gadgets are priced at ₹99,999, which is almost one lakh.
Think and Tell!
Which is the greatest 8-digit number?
Let's follow the same rule:
Use 9 in all the places.
Without commas it is written as: 99999999
How do we read it?
From 8 Digits to 9 Digits:
Ria wondered something interesting:
"How do we get the smallest 9-digit number?"
The answer is very simple!
when we add 1 to the greatest 8-digit number, we get the smallest 9-digit number.
- Similarly,
- For example:
- Big cricket tournaments can have crores of viewers watching on TV.
- Popular movies sometimes earn hundreds of crores of rupees.
What are Place Values?
Have you ever wondered why the same digit can mean different things in different numbers?
For example:
- In 5, the digit 5 means five ones.
- In 50, the digit 5 means five tens.
This happens because of Place Value.
Place value tells us the value of a digit based on its position in the number.
Every digit in a number sits in a special place, and that place decides its value.
- When we write a number in full form, we expand positions from right to left.
- Let's look at this number:
7,231,468
This number is read as:
Seventy-two lakh thirty-one thousand four hundred sixty-eight
- Look at the place value chart for the first nine digits in the Indian system of numeration (see picture).
In the Indian System of Numeration, digits are grouped into periods.
Try yourself: Which of the following is the place value of 4 in the number 4,67,13,223?
How to Read Large Numbers?
Writing Large Numbers
- Earlier, numbers were written using commas.
- The modern way is to leave spaces between periods instead of commas.
When we read numbers in the Indian System, we:- Read the digits in the same period together
- Add the name of the period (except the units period)
EduRev Tips:
The population of Japan in 2018 was about 12,71,85,332.
The same number can be shown in different ways (see picture):
Example 1: Write the numeral for the following by separating the periods.
(a) 603274087
(b) 37007690
Solution:(a)
Start from the right, first group three digits, then make groups of two digits.
(b):
Example 2: Write the number names for each numeral.
(a) 5 78 22 506
(b) 7 00 05 624
(c) 82,10,00,050
(d) 60,00,00,066
Solution:
Arrange the digits of the given numbers in the place value chart and then write their number names.
How to Compare Large Numbers?
Comparing Large NumbersRules for Comparing Large Numbers
(a) Unequal number of digits: If two numbers have different numbers of digits, the number with more digits is greater.
Example 1: Which is greater: 8,93,10,009 or 11,00,73,640?
Solution:
Write both numbers by place values to count digits.
11,00,73,640 has 9 digits whereas 8,93,10,009 has 8 digits.
Since 9 > 8, we conclude 11,00,73,640 > 8,93,10,009.
(b) Equal number of digits: Start from the left and compare digits one by one until they differ. The number with the greater digit in the first place where they differ is the larger number.
Example 2: Compare 8,31,46,205 and 8,31,57,610.
Solution:
Line up the numbers by place value and compare digits from the leftmost place until they differ.
The digits are same up to the thousands period; they differ at the ten thousands place where 5 > 4.
Therefore 8,31,57,610 > 8,31,46,205.
Real Life Example
Imagine two cities:
Since 8,31,57,610 is larger, City B has more people.
Forming Smallest and Greatest Numbers
Smallest number from digits 4,1,0,2,8 is 10248The smallest number that can be formed with the digits 4, 1, 0, 2, 8 (using each digit only once) is 10248.
Step 1: Arrange digits in ascending order (smallest to largest)
0, 1, 2, 4, 8
But remember:
A number cannot start with 0.
Step 2: Place the smallest non-zero digit first
So we write:
Smallest number = 10,248
Case 1: When repetition of digits is not allowed
Example: Write the greatest 6-digit number using the digits 3, 2, 9, 5, 6 and 8 only once.
Solution: Place the greatest available digit at the leftmost place and then the remaining digits in descending order.
The greatest 6-digit number is 986532.
Case 2: When repetition of digits is allowed
Example: Form the greatest and the smallest 8-digit numbers using each of the digits 2, 8, 0 and 1 twice.
Solution:
The greatest 8-digit number is 88221100.
The smallest 8-digit number is 10012288.
Arrange digits in ascending order, but remember:
0 cannot come first
International System of Writing Numbers
You already learned how numbers are written in the Indian System using lakh and crore.
But many countries like the USA, UK, and most parts of the world use another system called the International System of Numeration.
Let's see how it works!
So we can say:
10 lakh = 1 million
Periods in the International System:
In the International System, numbers are grouped into periods of three digits each.
Example:
Important Difference Between the Two Systems:
Example: Same Number in Both Systems
Let's look at this number: 6,849,240
Did You Know?
Example 1: Write in numerals.
(a) 4 million
(b) 11 million
Solution:
(a) 4 million = 4 000 000 or 4,000,000
(b) 11 million = 11 000 000 or 11,000,000
Example 2: Using the International system of numeration, write the numeral for each of the following.
(a) Seventy-four million three hundred forty thousand two hundred fifty-six.
(b) Sixty-eight million two hundred thousand three hundred twenty-four.
(c) Five hundred nine million seven hundred seventy-six thousand two hundred thirty.
Solution:
Write the numbers in the place value chart and then read off the numerals.
So, the numerals are:
(a) 74 340 256
(b) 68 200 324
(c) 509 776 230
Try yourself: Which of the following is the greatest 8-digit number?
FAQs on Chapter Notes: Large Numbers
| 1. How do I read and write numbers in the Indian numbering system for Class 5? |  |
| 2. What's the difference between face value and place value in large numbers? | |
| 3. How do I write large numbers in expanded form and why is it important? | |
| 4. What are the place value columns used for large numbers up to crores? | |
| 5. How do I compare and arrange large numbers in ascending and descending order? | |
