Page 1
Counting things is easy for us now. We can count objects in large numbers,
for example, the number of students in the school, and represent them
through numerals. We can also communicate large numbers using suitable
number names.
It is not as if we always knew how to convey large quantities in conversation
or through symbols. Many thousands years ago, people knew only small
numbers. Gradually, they learnt how to handle larger numbers. They also learnt
how to express large numbers in symbols. All this came through collective
efforts of human beings. Their path was not easy, they struggled all along the
way. In fact, the development of whole of Mathematics can be understood
this way. As human beings progressed, there was greater need for development
of Mathematics and as a result Mathematics grew further and faster.
We use numbers and know many things about them. Numbers help us
count concrete objects. They help us to say which collection of objects
is bigger and arrange them in order e.g., first, second, etc. Numbers are
used in many different contexts and in many ways. Think about various
situations where we use numbers. List five distinct situations in which
numbers are used.
W e enjoyed working with numbers in our previous classes. W e have added,
subtracted, multiplied and divided them. We also looked for patterns in number
sequences and done many other interesting things with numbers. In this chapter,
we shall move forward on such interesting things with a bit of review and
revision as well.
1.1 Introduction
Chapter 1 Chapter 1 Chapter 1 Chapter 1 Chapter 1
Knowing our Knowing our
Knowing our Knowing our Knowing our
Numbers Numbers
Numbers Numbers Numbers
Rationalised 2023-24
Page 2
Counting things is easy for us now. We can count objects in large numbers,
for example, the number of students in the school, and represent them
through numerals. We can also communicate large numbers using suitable
number names.
It is not as if we always knew how to convey large quantities in conversation
or through symbols. Many thousands years ago, people knew only small
numbers. Gradually, they learnt how to handle larger numbers. They also learnt
how to express large numbers in symbols. All this came through collective
efforts of human beings. Their path was not easy, they struggled all along the
way. In fact, the development of whole of Mathematics can be understood
this way. As human beings progressed, there was greater need for development
of Mathematics and as a result Mathematics grew further and faster.
We use numbers and know many things about them. Numbers help us
count concrete objects. They help us to say which collection of objects
is bigger and arrange them in order e.g., first, second, etc. Numbers are
used in many different contexts and in many ways. Think about various
situations where we use numbers. List five distinct situations in which
numbers are used.
W e enjoyed working with numbers in our previous classes. W e have added,
subtracted, multiplied and divided them. We also looked for patterns in number
sequences and done many other interesting things with numbers. In this chapter,
we shall move forward on such interesting things with a bit of review and
revision as well.
1.1 Introduction
Chapter 1 Chapter 1 Chapter 1 Chapter 1 Chapter 1
Knowing our Knowing our
Knowing our Knowing our Knowing our
Numbers Numbers
Numbers Numbers Numbers
Rationalised 2023-24
MATHEMATICS
2
1.2 Comparing Numbers
As we have done quite a lot of this earlier, let us see if we remember which is
the greatest among these :
(i) 92, 392, 4456, 89742
(ii) 1902, 1920, 9201, 9021, 9210
So, we know the answers.
Discuss with your friends, how you find the number that is the greatest.
Can you instantly find the greatest and the smallest numbers in each row?
1. 382, 4972, 18, 59785, 750. Ans. 59785 is the greatest and
18 is the smallest.
2. 1473, 89423, 100, 5000, 310. Ans. ____________________
3. 1834, 75284, 111, 2333, 450 . Ans. ____________________
4. 2853, 7691, 9999, 12002, 124. Ans. ____________________
Was that easy? Why was it easy?
We just looked at the number of digits and found the answer.
The greatest number has the most thousands and the smallest is
only in hundreds or in tens.
Make five more problems of this kind and give to your friends
to solve.
Now, how do we compare 4875 and 3542?
This is also not very difficult.These two numbers have the
same number of digits. They are both in thousands. But the digit
at the thousands place in 4875 is greater than that in 3542.
Therefore, 4875 is greater than 3542.
Next tell which is greater, 4875 or
4542? Here too the numbers have the
same number of digits. Further, the digits
at the thousands place are same in both.
What do we do then? We move to the
next digit, that is to the digit at the
hundreds place. The digit at the hundreds
place is greater in 4875 than in 4542.
Therefore, 4875 is greater than 4542.
Find the greatest and the smallest
numbers.
(a) 4536, 4892, 4370, 4452.
(b) 15623, 15073, 15189, 15800.
(c) 25286, 25245, 25270, 25210.
(d) 6895, 23787, 24569, 24659.
Rationalised 2023-24
Page 3
Counting things is easy for us now. We can count objects in large numbers,
for example, the number of students in the school, and represent them
through numerals. We can also communicate large numbers using suitable
number names.
It is not as if we always knew how to convey large quantities in conversation
or through symbols. Many thousands years ago, people knew only small
numbers. Gradually, they learnt how to handle larger numbers. They also learnt
how to express large numbers in symbols. All this came through collective
efforts of human beings. Their path was not easy, they struggled all along the
way. In fact, the development of whole of Mathematics can be understood
this way. As human beings progressed, there was greater need for development
of Mathematics and as a result Mathematics grew further and faster.
We use numbers and know many things about them. Numbers help us
count concrete objects. They help us to say which collection of objects
is bigger and arrange them in order e.g., first, second, etc. Numbers are
used in many different contexts and in many ways. Think about various
situations where we use numbers. List five distinct situations in which
numbers are used.
W e enjoyed working with numbers in our previous classes. W e have added,
subtracted, multiplied and divided them. We also looked for patterns in number
sequences and done many other interesting things with numbers. In this chapter,
we shall move forward on such interesting things with a bit of review and
revision as well.
1.1 Introduction
Chapter 1 Chapter 1 Chapter 1 Chapter 1 Chapter 1
Knowing our Knowing our
Knowing our Knowing our Knowing our
Numbers Numbers
Numbers Numbers Numbers
Rationalised 2023-24
MATHEMATICS
2
1.2 Comparing Numbers
As we have done quite a lot of this earlier, let us see if we remember which is
the greatest among these :
(i) 92, 392, 4456, 89742
(ii) 1902, 1920, 9201, 9021, 9210
So, we know the answers.
Discuss with your friends, how you find the number that is the greatest.
Can you instantly find the greatest and the smallest numbers in each row?
1. 382, 4972, 18, 59785, 750. Ans. 59785 is the greatest and
18 is the smallest.
2. 1473, 89423, 100, 5000, 310. Ans. ____________________
3. 1834, 75284, 111, 2333, 450 . Ans. ____________________
4. 2853, 7691, 9999, 12002, 124. Ans. ____________________
Was that easy? Why was it easy?
We just looked at the number of digits and found the answer.
The greatest number has the most thousands and the smallest is
only in hundreds or in tens.
Make five more problems of this kind and give to your friends
to solve.
Now, how do we compare 4875 and 3542?
This is also not very difficult.These two numbers have the
same number of digits. They are both in thousands. But the digit
at the thousands place in 4875 is greater than that in 3542.
Therefore, 4875 is greater than 3542.
Next tell which is greater, 4875 or
4542? Here too the numbers have the
same number of digits. Further, the digits
at the thousands place are same in both.
What do we do then? We move to the
next digit, that is to the digit at the
hundreds place. The digit at the hundreds
place is greater in 4875 than in 4542.
Therefore, 4875 is greater than 4542.
Find the greatest and the smallest
numbers.
(a) 4536, 4892, 4370, 4452.
(b) 15623, 15073, 15189, 15800.
(c) 25286, 25245, 25270, 25210.
(d) 6895, 23787, 24569, 24659.
Rationalised 2023-24
KNOWING OUR NUMBERS
3
9 8 6 7
1 0 2 7
4
4
9
9
1
If the digits at hundreds place are also same in the two numbers, then what
do we do?
Compare 4875 and 4889 ; Also compare 4875 and 4879.
1.2.1 How many numbers can you make?
Suppose, we have four digits 7, 8, 3, 5. Using these digits we want to make
different 4-digit numbers in such a way that no digit is repeated in them. Thus,
7835 is allowed, but 7735 is not. Make as many 4-digit numbers as you can.
Which is the greatest number you can get? Which is the smallest number?
The greatest number is 8753 and the smallest is 3578.
Think about the arrangement of the digits in both. Can you say how the largest
number is formed? Write down your procedure.
1. Use the given digits without repetition and make the greatest and smallest 4-digit
numbers.
(a) 2, 8, 7, 4 (b) 9, 7, 4, 1 (c) 4, 7, 5, 0
(d) 1, 7, 6, 2 (e) 5, 4, 0, 3
(Hint : 0754 is a 3-digit number.)
2. Now make the greatest and the smallest 4-digit numbers by using any one
digit twice.
(a) 3, 8, 7 (b) 9, 0, 5 (c) 0, 4, 9 (d) 8, 5, 1
(Hint : Think in each case which digit will you use twice.)
3. Make the greatest and the smallest 4-digit numbers using any four different
digits with conditions as given.
(a) Digit 7 is always at Greatest
ones place
Smallest
(Note, the number cannot begin with the digit 0. Why?)
(b) Digit 4 is always Greatest
at tens place
Smallest
(c) Digit 9 is always at Greatest
hundreds place
Smallest
(d) Digit 1 is always at Greatest
thousands place
Smallest
1
Rationalised 2023-24
Page 4
Counting things is easy for us now. We can count objects in large numbers,
for example, the number of students in the school, and represent them
through numerals. We can also communicate large numbers using suitable
number names.
It is not as if we always knew how to convey large quantities in conversation
or through symbols. Many thousands years ago, people knew only small
numbers. Gradually, they learnt how to handle larger numbers. They also learnt
how to express large numbers in symbols. All this came through collective
efforts of human beings. Their path was not easy, they struggled all along the
way. In fact, the development of whole of Mathematics can be understood
this way. As human beings progressed, there was greater need for development
of Mathematics and as a result Mathematics grew further and faster.
We use numbers and know many things about them. Numbers help us
count concrete objects. They help us to say which collection of objects
is bigger and arrange them in order e.g., first, second, etc. Numbers are
used in many different contexts and in many ways. Think about various
situations where we use numbers. List five distinct situations in which
numbers are used.
W e enjoyed working with numbers in our previous classes. W e have added,
subtracted, multiplied and divided them. We also looked for patterns in number
sequences and done many other interesting things with numbers. In this chapter,
we shall move forward on such interesting things with a bit of review and
revision as well.
1.1 Introduction
Chapter 1 Chapter 1 Chapter 1 Chapter 1 Chapter 1
Knowing our Knowing our
Knowing our Knowing our Knowing our
Numbers Numbers
Numbers Numbers Numbers
Rationalised 2023-24
MATHEMATICS
2
1.2 Comparing Numbers
As we have done quite a lot of this earlier, let us see if we remember which is
the greatest among these :
(i) 92, 392, 4456, 89742
(ii) 1902, 1920, 9201, 9021, 9210
So, we know the answers.
Discuss with your friends, how you find the number that is the greatest.
Can you instantly find the greatest and the smallest numbers in each row?
1. 382, 4972, 18, 59785, 750. Ans. 59785 is the greatest and
18 is the smallest.
2. 1473, 89423, 100, 5000, 310. Ans. ____________________
3. 1834, 75284, 111, 2333, 450 . Ans. ____________________
4. 2853, 7691, 9999, 12002, 124. Ans. ____________________
Was that easy? Why was it easy?
We just looked at the number of digits and found the answer.
The greatest number has the most thousands and the smallest is
only in hundreds or in tens.
Make five more problems of this kind and give to your friends
to solve.
Now, how do we compare 4875 and 3542?
This is also not very difficult.These two numbers have the
same number of digits. They are both in thousands. But the digit
at the thousands place in 4875 is greater than that in 3542.
Therefore, 4875 is greater than 3542.
Next tell which is greater, 4875 or
4542? Here too the numbers have the
same number of digits. Further, the digits
at the thousands place are same in both.
What do we do then? We move to the
next digit, that is to the digit at the
hundreds place. The digit at the hundreds
place is greater in 4875 than in 4542.
Therefore, 4875 is greater than 4542.
Find the greatest and the smallest
numbers.
(a) 4536, 4892, 4370, 4452.
(b) 15623, 15073, 15189, 15800.
(c) 25286, 25245, 25270, 25210.
(d) 6895, 23787, 24569, 24659.
Rationalised 2023-24
KNOWING OUR NUMBERS
3
9 8 6 7
1 0 2 7
4
4
9
9
1
If the digits at hundreds place are also same in the two numbers, then what
do we do?
Compare 4875 and 4889 ; Also compare 4875 and 4879.
1.2.1 How many numbers can you make?
Suppose, we have four digits 7, 8, 3, 5. Using these digits we want to make
different 4-digit numbers in such a way that no digit is repeated in them. Thus,
7835 is allowed, but 7735 is not. Make as many 4-digit numbers as you can.
Which is the greatest number you can get? Which is the smallest number?
The greatest number is 8753 and the smallest is 3578.
Think about the arrangement of the digits in both. Can you say how the largest
number is formed? Write down your procedure.
1. Use the given digits without repetition and make the greatest and smallest 4-digit
numbers.
(a) 2, 8, 7, 4 (b) 9, 7, 4, 1 (c) 4, 7, 5, 0
(d) 1, 7, 6, 2 (e) 5, 4, 0, 3
(Hint : 0754 is a 3-digit number.)
2. Now make the greatest and the smallest 4-digit numbers by using any one
digit twice.
(a) 3, 8, 7 (b) 9, 0, 5 (c) 0, 4, 9 (d) 8, 5, 1
(Hint : Think in each case which digit will you use twice.)
3. Make the greatest and the smallest 4-digit numbers using any four different
digits with conditions as given.
(a) Digit 7 is always at Greatest
ones place
Smallest
(Note, the number cannot begin with the digit 0. Why?)
(b) Digit 4 is always Greatest
at tens place
Smallest
(c) Digit 9 is always at Greatest
hundreds place
Smallest
(d) Digit 1 is always at Greatest
thousands place
Smallest
1
Rationalised 2023-24
MATHEMATICS
4
Ramhari
(160 cm)
Dolly
(154 cm)
Mohan
(158 cm)
Shashi
(159 cm)
` 2635 ` 1897 ` 2854 ` 1788 ` 3975
4. Take two digits, say 2 and 3. Make 4-digit numbers using both the digits equal
number of times.
Which is the greatest number?
Which is the smallest number?
How many different numbers can you make in all?
Stand in proper order
1. Who is the tallest?
2. Who is the shortest?
(a) Can you arrange them in the increasing order of their heights?
(b) Can you arrange them in the decreasing order of their heights?
Which to buy?
Sohan and Rita went
to buy an almirah.
There were many
almirahs available
with their price tags.
(a) Can you arrange their prices in increasing
order?
(b) Can you arrange their prices in
decreasing order?
Ascending order Ascending order means arrangement from the smallest to the
greatest.
Descending order Descending order means arrangement from the greatest to
the smallest.
Think of five more situations
where you compare three or
more quantities.
Rationalised 2023-24
Page 5
Counting things is easy for us now. We can count objects in large numbers,
for example, the number of students in the school, and represent them
through numerals. We can also communicate large numbers using suitable
number names.
It is not as if we always knew how to convey large quantities in conversation
or through symbols. Many thousands years ago, people knew only small
numbers. Gradually, they learnt how to handle larger numbers. They also learnt
how to express large numbers in symbols. All this came through collective
efforts of human beings. Their path was not easy, they struggled all along the
way. In fact, the development of whole of Mathematics can be understood
this way. As human beings progressed, there was greater need for development
of Mathematics and as a result Mathematics grew further and faster.
We use numbers and know many things about them. Numbers help us
count concrete objects. They help us to say which collection of objects
is bigger and arrange them in order e.g., first, second, etc. Numbers are
used in many different contexts and in many ways. Think about various
situations where we use numbers. List five distinct situations in which
numbers are used.
W e enjoyed working with numbers in our previous classes. W e have added,
subtracted, multiplied and divided them. We also looked for patterns in number
sequences and done many other interesting things with numbers. In this chapter,
we shall move forward on such interesting things with a bit of review and
revision as well.
1.1 Introduction
Chapter 1 Chapter 1 Chapter 1 Chapter 1 Chapter 1
Knowing our Knowing our
Knowing our Knowing our Knowing our
Numbers Numbers
Numbers Numbers Numbers
Rationalised 2023-24
MATHEMATICS
2
1.2 Comparing Numbers
As we have done quite a lot of this earlier, let us see if we remember which is
the greatest among these :
(i) 92, 392, 4456, 89742
(ii) 1902, 1920, 9201, 9021, 9210
So, we know the answers.
Discuss with your friends, how you find the number that is the greatest.
Can you instantly find the greatest and the smallest numbers in each row?
1. 382, 4972, 18, 59785, 750. Ans. 59785 is the greatest and
18 is the smallest.
2. 1473, 89423, 100, 5000, 310. Ans. ____________________
3. 1834, 75284, 111, 2333, 450 . Ans. ____________________
4. 2853, 7691, 9999, 12002, 124. Ans. ____________________
Was that easy? Why was it easy?
We just looked at the number of digits and found the answer.
The greatest number has the most thousands and the smallest is
only in hundreds or in tens.
Make five more problems of this kind and give to your friends
to solve.
Now, how do we compare 4875 and 3542?
This is also not very difficult.These two numbers have the
same number of digits. They are both in thousands. But the digit
at the thousands place in 4875 is greater than that in 3542.
Therefore, 4875 is greater than 3542.
Next tell which is greater, 4875 or
4542? Here too the numbers have the
same number of digits. Further, the digits
at the thousands place are same in both.
What do we do then? We move to the
next digit, that is to the digit at the
hundreds place. The digit at the hundreds
place is greater in 4875 than in 4542.
Therefore, 4875 is greater than 4542.
Find the greatest and the smallest
numbers.
(a) 4536, 4892, 4370, 4452.
(b) 15623, 15073, 15189, 15800.
(c) 25286, 25245, 25270, 25210.
(d) 6895, 23787, 24569, 24659.
Rationalised 2023-24
KNOWING OUR NUMBERS
3
9 8 6 7
1 0 2 7
4
4
9
9
1
If the digits at hundreds place are also same in the two numbers, then what
do we do?
Compare 4875 and 4889 ; Also compare 4875 and 4879.
1.2.1 How many numbers can you make?
Suppose, we have four digits 7, 8, 3, 5. Using these digits we want to make
different 4-digit numbers in such a way that no digit is repeated in them. Thus,
7835 is allowed, but 7735 is not. Make as many 4-digit numbers as you can.
Which is the greatest number you can get? Which is the smallest number?
The greatest number is 8753 and the smallest is 3578.
Think about the arrangement of the digits in both. Can you say how the largest
number is formed? Write down your procedure.
1. Use the given digits without repetition and make the greatest and smallest 4-digit
numbers.
(a) 2, 8, 7, 4 (b) 9, 7, 4, 1 (c) 4, 7, 5, 0
(d) 1, 7, 6, 2 (e) 5, 4, 0, 3
(Hint : 0754 is a 3-digit number.)
2. Now make the greatest and the smallest 4-digit numbers by using any one
digit twice.
(a) 3, 8, 7 (b) 9, 0, 5 (c) 0, 4, 9 (d) 8, 5, 1
(Hint : Think in each case which digit will you use twice.)
3. Make the greatest and the smallest 4-digit numbers using any four different
digits with conditions as given.
(a) Digit 7 is always at Greatest
ones place
Smallest
(Note, the number cannot begin with the digit 0. Why?)
(b) Digit 4 is always Greatest
at tens place
Smallest
(c) Digit 9 is always at Greatest
hundreds place
Smallest
(d) Digit 1 is always at Greatest
thousands place
Smallest
1
Rationalised 2023-24
MATHEMATICS
4
Ramhari
(160 cm)
Dolly
(154 cm)
Mohan
(158 cm)
Shashi
(159 cm)
` 2635 ` 1897 ` 2854 ` 1788 ` 3975
4. Take two digits, say 2 and 3. Make 4-digit numbers using both the digits equal
number of times.
Which is the greatest number?
Which is the smallest number?
How many different numbers can you make in all?
Stand in proper order
1. Who is the tallest?
2. Who is the shortest?
(a) Can you arrange them in the increasing order of their heights?
(b) Can you arrange them in the decreasing order of their heights?
Which to buy?
Sohan and Rita went
to buy an almirah.
There were many
almirahs available
with their price tags.
(a) Can you arrange their prices in increasing
order?
(b) Can you arrange their prices in
decreasing order?
Ascending order Ascending order means arrangement from the smallest to the
greatest.
Descending order Descending order means arrangement from the greatest to
the smallest.
Think of five more situations
where you compare three or
more quantities.
Rationalised 2023-24
KNOWING OUR NUMBERS
5
1. Arrange the following numbers in ascending order :
(a) 847, 9754, 8320, 571 (b) 9801, 25751, 36501, 38802
2. Arrange the following numbers in descending order :
(a) 5000, 7500, 85400, 7861 (b) 1971, 45321, 88715, 92547
Make ten such examples of ascending/descending order and solve them.
1.2.2 Shifting digits
Have you thought what fun it would be if the digits in a number could shift
(move) from one place to the other?
Think about what would happen to 182. It could become as large as 821
and as small as 128. Try this with 391 as well.
Now think about this. Take any 3-digit number and exchange the digit at
the hundreds place with the digit at the ones place.
(a) Is the new number greater than the former one?
(b) Is the new number smaller than the former number?
Write the numbers formed in both ascending and descending order.
Before 7 9 5
Exchanging the 1st and the 3rd tiles.
After 5 9 7
If you exchange the 1st and the 3rd tiles (i.e. digits), in which case does the
number become greater? In which case does it become smaller?
Try this with a 4-digit number.
1.2.3 Introducing 10,000
We know that beyond 99 there is no 2-digit number. 99 is the greatest 2-digit
number. Similarly, the greatest 3-digit number is 999 and the greatest 4-digit
number is 9999. What shall we get if we add 1 to 9999?
Look at the pattern : 9 + 1 = 10 = 10 × 1
99 + 1 = 100 = 10 × 10
999 + 1 = 1000 = 10 × 100
We observe that
Greatest single digit number + 1 = smallest 2-digit number
Greatest 2-digit number + 1 = smallest 3-digit number
Greatest 3-digit number + 1 = smallest 4-digit number
Rationalised 2023-24
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