1
NUMBERS BEYOND 999
Let’s recall ...
Ten ones (10 ones)
Ten tens (10 tens)
=
=
One ten (1 ten)
One hundred (1 hundred)
1. Write the number names.
(a) 287
____________________________________________________________
(b) 199
____________________________________________________________
(c) 304
____________________________________________________________
(d) 888
____________________________________________________________
2. Write 26, 87, 19, 145, 52 in ascending order.
______________________________________________________________________
3. Write 43, 96, 132, 190, 12, 85 in descending order.
______________________________________________________________________
4. Sort out the following into even and odd numbers.
23, 45, 7, 9, 16, 82, 14, 98, 1, 3, 6, 20, 43, 80, 50
Even numbers ________________________________________________________
Odd numbers ________________________________________________________
5. Put the correct sign >, < or = in the box.
(a) 15
23
(b) 37
18
(c)
9
16
(d) 143
140
(e) 97
97
(f ) 75
216
1
6. Write in expanded form.
(a) 538 =
+
+
(b) 906 =
+
+
7. Write the number that comes before.
(a) _____ 399
(b) ______ 870
(c) ______ 473
8. Write the number that comes between.
(a) 210, ______, 212
(b) 589, ______, 591
(c) 388, ______, 390
Let‘s learn further ...
Ten hundreds (10 hundreds)
9 hundreds
900
+
=
One thousand (1 thousand)
9 tens
90
+
9 ones
9
= 999
999 is the greatest 3-digit number. Let’s see what happens when we add one more to it.
one more
2
9 hundreds (900)
+
10 tens (100) = 1 thousand (1000)
10 hundreds
So, 999 + 1 = 1000
=
1 thousand
Th
H
T
O
1
0
0
0
Remember
We get 1000 which is the smallest 4-digit number.
Observe the following pattern.
On adding 1 to the largest 1-digit number, we get the smallest 2-digit number.
9 + 1 = 10
On adding 1 to the largest 2-digit number, we get the smallest 3-digit number.
99 + 1 = 100
On adding 1 to the largest 3-digit number, we get the smallest 4-digit number.
999 + 1 = 1000
Counting by Thousands
1000
One thousand
3
2000
Two thousand
3000
Three thousand
4000
Four thousand
5000
Five thousand
6000
Six thousand
7000
Seven thousand
4
8000
Eight thousand
9000
Nine thousand
10000
Ten thousand
Numbers and Number Names
Let’s learn to form 4-digit numbers.
Example 1: Represent the given 4-digit numbers in pictorial graphs and write their
number names.
(a) 1532
(b) 2645
(c) 9783
Solution:
(a) 1532
+
(1 thousand)
1000
+
+
(5 hundreds)
500
+
(3 tens) (2 ones)
+ 30 + 2 = 1532
It is read as one thousand five hundred thirty-two.
5
(b) 2645
+
(2 thousands)
2000
+
+
(6 hundreds)
(4 tens) (5 ones)
+
600
+ 40
+
5
It is read as two thousand six hundred forty-five.
= 2645
(c) 9783
+
+
(9 thousands)
9000
+
(7 hundreds)
700
(8 tens) (3 ones)
+
+
80 +
3
= 9783
It is read as nine thousand seven hundred eighty-three.
We can also form 4-digit numbers using an abacus. Consider a
4-digit number 3285. We represent this on an abacus as shown.
Remember
Th
H
T
O
3 2 8 5
Three thousand two hundred
eighty-five
6
Example 2: Represent (a) 5064, (b) 7213 and (c) 9989 on the abacus.
Solution:
(a) 5064
Th
H
T
(b) 7213
O
Th
H
(c) 9989
T
O
Th
H
T
O
EXERCISE 1.1
1. Complete the following number grid.
1001
1011
1031
1002
1051
1081
1022
1023
1063
1014
1074
1045
1006
1075
1056
1027
1087
1018
1068
1039
1010
1030
1099
1060
1090
1100
2. Observe the pictorial blocks and write the number they represent.
(a)
+
+
+
= ________
7
(b)
+
+
+
= ________
+
+
+
= ________
(c)
3. Draw beads to represent the following numbers on the abacus.
(a) 1064
Th
(b) 2731
H
T
O
(d) 9890
Th
8
Th
(c)
H
T
O
(e) 7342
H
T
O
Th
Th
(f )
H
T
O
5608
H
T
O
H
T
O
4576
Th
4. Write the numbers represented on the abacus.
(a)
(b)
Th
H
T
O
(d)
(c)
Th
H
T
O
(e)
Th
H
T
O
Th
H
T
O
Th
H
T
O
(f )
Th
H
T
O
5. Write the number names.
(a) 3463
= _________________________________________________________
(b) 7018
= _________________________________________________________
(c) 9920
= _________________________________________________________
(d) 5409
= _________________________________________________________
(e) 6999
= _________________________________________________________
Place Value and Face Value
Mental Maths
What is the place
value and face
value of 7 in 4706
and in 7821?
We know that the place value of a digit depends on its place or
position in a number, while the face value of a digit is the value of
the digit itself.
Example 3: Write the place value and face value of digits in 8632.
Solution: 8632 = 8 thousands + 6 hundreds + 3 tens + 2 ones
The place value of 8 in 8632 is 8000 and its face value is 8.
The place value of 6 in 8632 is 600 and its face value is 6.
The place value of 3 in 8632 is 30 and its face value is 3.
The place value of 2 in 8632 is 2 and its face value is 2.
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Expanded Form
Expanded form of a
number is the sum of the
place values of its digits.
Example 4: Write 9516 in expanded form.
Solution:
9516 = 9000 + 500 + 10 + 6 = 9 Th + 5 H + 1 T + 6 O
Short
form
Expanded form
EXERCISE 1.2
1. Fill in the boxes.
(a) 3623 =
Th +
H +
T +
O
(b) 4780 =
Th +
H +
T +
O
(c) 6095 =
Th +
H +
T +
O
(d) 9909 =
Th +
H +
T +
O
2. Write the number names in your notebooks. Then write their numbers.
(a) 5 Th + 3 H + 7 T + 1 O = _________
(b) 6 Th + 8 H + 0 T + 2 O = _________
(c) 4 Th + 9 H + 2 T + 4 O = _________
(d) 8 Th + 6 H + 5 T + 9 O = _________
(e) 7 Th + 0 H + 1 T + 8 O = _________
(f ) 3 Th + 5 H + 0 T + 3 O = _________
3. Write in expanded form.
(a) 1827 =
+
+
+
(b) 9869 =
+
+
+
(c) 8053 =
+
+
+
(d) 5899 =
+
+
+
4. Write in short form.
10
(a) 4000 + 300 + 10 + 9 = ___________
(b) 5000 + 700 + 80 + 6 = ___________
(c) 8000 + 400 + 60 + 1 = ___________
(d) 6000 + 0 + 90 + 8 = ___________
5. Write the place value and face value of each circled digit of the given numbers in
the table.
Number
9 671
2 0 83
398 0
94 4 2
18 8 5
Place Value
Face Value
6. Complete the sequence.
(a) 2035,
,
,
, 2039,
(b) 3210,
,
,
,
(c) 5995,
,
, 5998,
(d) 9788,
,
,
, 3215
,
, 9792,
Comparison of Numbers
While comparing two numbers, we must remember the following points:
• The number which is ahead in counting is the bigger number.
• If two numbers have different number of digits, then the number with more digits is
always greater.
Example 5: Compare the numbers 2685 and 798.
Solution: The number of digits in 2685 = 4 and in 798 = 3. Since, 4 > 3, therefore,
2685 > 798.
• If two numbers have the same number of digits, then always start comparing from
the leftmost digit, i.e., the digit at the thousands place in both the numbers.
Example 6: Compare the numbers 2982 and 3105.
Solution: The digit at the thousands place in 2982 is 2 and in 3105 is 3. Since, 3 > 2,
therefore, 3105 > 2982.
• If the digits at the thousands place are same, then compare the digits at the hundreds
place.
Example 7: Compare the numbers 4861 and 4539.
Solution: The digit at the thousands place in both the numbers is 4. So we move
ahead. The digit at the hundreds place in 4861 is 8 and in 4539 is 5. Since
8 > 5, therefore, 4861 > 4539.
• If the digits at the thousands and hundreds place are same, then compare the digits
at the tens place.
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Example 8: Compare the numbers 4861 and 4875.
Solution:
In both the numbers, the digit at the thousands place is 4 and at the
hundreds place is 8. The digit at the tens place in 4861 is 6 and in 4875 is
7. Since 7 > 6, therefore, 4875 > 4861.
• If the digits at the thousands, hundreds and tens place are same, then compare the
digits at the ones place.
Example 9: Compare the numbers 4861 and 4865.
Solution:
In both the numbers, the digits at the thousands place is 4, the hundreds
place is 8 and the tens place is 6. The digit at the ones place in 4861 is 1
and in 4865 is 5. Since 5 > 1, therefore, 4865 > 4861.
If all the digits in both the
numbers are same then the
numbers are equal and we
use the sign ‘=’.
Mental Maths
Which of these is greater?
(a) 3291
286
(b) 5071
5312
(c) 6289
6298
(d) 7341
7340
Before, After and Between
The numbers which follow one after the
other are called consecutive numbers. For
example, 1316, 1317, 1318, 1319, 1320 are
consecutive numbers.
Consecutive numbers
can also be written
backwards. For example,
1320, 1319, 1318, 1317, 1316
A number one less than a given number comes just before it and
is called its predecessor.
A number one more than a given number comes just after it and
is called its successor.
Consider a 4-digit number 5863.
Its predecessor = 5863 – 1 = 5862 and its successor = 5863 + 1 = 5864.
12
5862
5863
5864
predecessor
is between 5862 and 5864
successor
Ordering of Numbers
Comparison of two or more numbers becomes easy if we arrange the numbers in a
sequence. This sequence can be from smaller to bigger or from bigger to smaller.
Writing numbers in order from smaller to bigger is
called ascending order and from bigger to smaller
is called descending order.
• 6089, 6190, 7191, 8792 are in ascending order.
• 9791, 8790, 7787, 4688 are in descending order.
Mental Maths
Is 4271, 4281, 4396, 4402 an ascending
or descending sequence?
EXERCISE 1.3
1. Put the correct sign <, > or =.
(a) 237
(d) 9781
1201
9871
(b) 3645
98
(c) 5421
5412
(e) 1212
1212
(f ) 8064
7065
2. Arrange the following in ascending order.
(a) 3285, 4061, 298, 3469
,
,
,
(b) 1892, 1982, 1289, 1189
,
,
,
(c) 9099, 9909, 9990, 999
,
,
,
(d) 6341, 6143, 6431, 6314
,
,
,
(a) 7649, 7496, 7549, 7459
,
,
,
(b) 8291, 8192, 8091, 8129
,
,
,
(c) 1123, 1312, 1213, 1321
,
,
,
(d) 4523, 5619, 4807, 5032
,
,
,
3. Arrange the following in descending order.
4. Write the number that comes between the given numbers.
(a) 698,
(c) 1287,
, 700
, 1289
(b) 4039,
, 4041
(d) 8500,
, 8502
13
5. Write the predecessor and successor of the given numbers.
Predecessor
Number
Successor
(a)
889
(b)
2341
(c)
7038
(d)
9000
6. Choose and write the largest number from the given numbers.
(a) 3124, 2689, 708, 4925, 4259
(b) 1987, 2000, 2999, 2001, 399
(c) 6023, 6203, 6302, 6320, 6032
(d) 9989, 9819, 9899, 9879, 9897
Forming 4-digit Numbers
We can form numbers using the given digits by arranging them in different order. For
example, using the digits 6, 3, 8 and 1, the greatest 4-digit number that can be formed
is 8631 and the smallest 4-digit number that can be formed is 1368.
1. To form the greatest 4-digit number, arrange
the given digits in descending order.
2. To form the smallest 4-digit number, arrange
the given digits in ascending order.
Example 10: Write the greatest and the smallest 4-digit number using the digits 2, 9, 0
and 5.
Solution:
The greatest 4-digit number is 9520.
(on arranging the digits in descending order)
The smallest 4-digit number is 2059.
(on arranging the digits in ascending order)
Note that the smallest 4-digit number is 2059 and not 0259 as 0 in the beginning
of a number has no value.
Skip Counting
You have already learnt skip counting in 2’s, 3’s,
5’s and 10’s in the previous class. Now let’s learn
skip counting in 100’s and 1000’s.
14
Remember
Skip count in 100’s means skipping 100 places (digits at the tens and ones places remain
the same).
For example, 7108, 7208, 7308, 7408, 7508
Skip count in 1000’s means skipping 1000 places (digits at the hundreds, tens and ones
places remain the same).
For example, 2845, 3845, 4845, 5845, 6845, 7845
More Than and Less Than
Consider the number 8135.
To find a number 2 more than 8135, we add 2 to 8135, i.e., 8135 + 2 = 8137.
To find a number 3 less than 8135, we subtract 3 from 8135, i.e., 8135 – 3 = 8132.
You need not add or subtract
every time. You can also
observe the pattern and find
the number.
Mental Maths
What is 10 more than 90?
What is 10 less than 50?
EXERCISE 1.4
1. Build the greatest and the smallest number with the given digits, using each digit
only once.
Digits
Greatest Number
Smallest Number
(a) 3, 8, 2, 1
(b) 5, 6, 0, 3
(c) 9, 5, 8, 7
(d) 0, 2, 4, 6
2. Skip count in 100’s and complete the pattern.
(a) 4531, 4631,
,
,
,
(b) 5287, 5387,
,
,
,
(c) 1872, 1972,
,
,
,
(d) 6594, 6694,
,
,
,
15
3. Skip count in 1000’s and complete the pattern.
(a) 1045, 2045,
,
,
,
(b) 3986, 4986,
,
,
,
(c) 2105, 3105,
,
,
,
(d) 4999, 5999,
,
,
,
4. Match the following.
Column A
(a)
(b)
(c)
(d)
(e)
(f )
(g)
(h)
Column B
4 more than 2096
10 more than 8285
1 less than 4000
10 less than 9989
100 more than 7685
100 less than 3175
1000 more than 5893
1000 less than 6940
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
3999
7785
2100
3075
8295
5940
6893
9979
Rounding Off Numbers
Hey friends, can you guess
the number of ice creams in
the cart?
Hmm ... about
50 or 60!
When we are not sure of the exact number, we use the word about. It gives a rough
estimation of the number. We can also say that the number has been rounded off. We
can round off a number to the nearest 10, 100 or 1000.
Rounding off to the nearest 10
To round off a number to the nearest ten, look at the digit in the ones place.
• If the digit in the ones place is 4 or less, then place a zero in the ones place and let
the digit in the tens place remain as it is.
• If the digit in the ones place is 5 or more, then place a zero in the ones place. Also
add 1 to the digit in the tens place.
16
Example 11: Round off (a) 43, (b) 87 and (c) 65 to the nearest 10.
Solution:
(a) 43 is rounded off to 40 since the digit in the ones place is 3 which is
less than 4.
(b) 87 is rounded off to 90 since the digit in
Mental Maths
the ones place is 7 which is more than 5. Round off to the nearest 10.
(c) 65 is rounded off to 70 since the digit in (a) 68 _____ (b) 82 _____
the ones place is 5.
(c) 94 _____ (d) 55 _____
Rounding off to the nearest 100
To round off a number to the nearest hundred, look at the digit in the tens place.
• If the digit in the tens place is 4 or less, then place zeroes in the tens and ones place.
The digit in the hundreds place remains the same.
• If the digit in the tens place is 5 or more, then place zeroes in the tens and ones place.
Add 1 to the digit in the hundreds place.
Example 12: Round off (a) 243 and (b) 1887 to the nearest 100.
Solution:
(a) 243 is rounded off to 200 because the
Mental Maths
digit at the tens place is 4.
(b) 1887 is rounded off to 1900 because the Round off to the nearest
digit at the tens place is 8.
(a) 497
(b) 8383
Rounding off to the nearest 1000
(c) 216
100.
(d) 3541
To round off a number to the nearest thousand, look at the digit in the hundreds place.
• If the digit in the hundreds place is 4 or less, then place zeroes in the digits at the
hundreds, tens and ones place. Keep the digit in the thousands place as it is.
• If the digit in the hundreds place is 5 or more, then place zeroes in the digits at the
hundreds, tens and ones place. Also, add 1 to the digit in the thousands place.
Example 13: Round off (a) 6253 and (b) 7923 to the nearest 1000.
Solution:
(a) 6253 is rounded off to 6000 as the digit
in the hundreds place is 2.
(b) 7923 is rounded off to 8000 as the digit
in the hundreds place is 9.
Mental Maths
Round off to the nearest 1000.
(a) 7249
(b) 1621
(c) 5913
(d) 8469
Even and Odd Numbers
You have already studied that numbers in which we can form pairs are called even
numbers and numbers in which we cannot form pairs are odd numbers.
For example, 238, 1746, 3280, 7632 are even numbers and 413, 685, 7981, 9377 are odd
numbers.
17
To decide whether a given number is even or odd, we look at the ones place. If the digit
in the ones place is 0, 2, 4, 6 or 8, then the number is an even number. If the digit in
the ones place is 1, 3, 5, 7 or 9, then the number is an odd number.
EXERCISE 1.5
1. Round off the following numbers to the nearest 10.
(b) 922
(a) 63
(c) 35
2. Round off the following numbers to the nearest 100.
(b) 354
(a) 586
(c) 1177
3. Round off the following numbers to the nearest 1000.
(b) 7999
(c) 2534
(a) 6119
4. Match the following.
Number
Rounded off to the nearest 10
(a) 94
(i) 50
(b) 11
(ii) 100
(c) 46
(iii) 70
(d) 68
(iv) 10
(e) 95
(v) 90
5. Separate and write the even and odd numbers into their respective boxes.
46
83
175
220
1643
2040
9891
687
1849
7514
6322
9295
5040
4783
Even numbers
Odd numbers
LET’S EVALUATE
1. Observe the pictorial blocks and write the numbers they represent.
(a)
+
18
+
+
= ___________
(b)
+
+
= ___________
2. Draw beads to represent the numbers given in the boxes.
(a)
(b)
Th
H
T
O
(c)
Th
3628
H
T
O
Th
5907
H
T
O
9021
3. Write the number names of the numbers represented on the abacus.
(b)
(a)
Th
H
T
O
Th
H
T
O
4. Fill in the boxes.
(a) 7982 =
Th +
H+
T+
O
(b) 2805 =
Th +
H+
T+
O
(c)
= 6 Th + 0 H + 1 T + 9 O
(d)
= 8 Th + 9 H + 2 T + 7 O
19
5. Write in expanded form.
(a) 4208 =
+
+
+
(b) 8976 =
+
+
+
(c) 1635 =
+
+
+
6. Write the place value of the circled digit in the given numbers.
(a) 4 3 2 7
(b) 8 5 0 1
_____________
_____________
7. Write five consecutive numbers for the given numbers.
(a) 3186, _________, _________, _________, _________, _________
(b) 9247, _________, _________, _________, _________, _________
8. Put the correct sign <, > or =.
(a) 2531
1235
(b) 1607
1507
(c) 9875
9872
(d) 2304
2430
(e) 6287
6293
(f ) 3195
3195
9. Arrange 5624, 5426, 4571, 6245, 6345, 6340 in ascending order.
,
,
,
,
,
10. Arrange 1843, 1934, 1624, 1857, 1846, 1924 in descending order.
,
,
,
,
,
11. Colour the largest number blue and the smallest number pink.
(a)
9003
9130
9821
9128
9009
9812
(b)
5613
5420
5375
5289
5280
5614
12. Write True or False.
(a) The predecessor of 2090 is 2091.
(b) 4896 is an even number.
(c) The successor of 7819 is 7820.
(d) 2437 lies in between 2435 and 2436.
(e) 62 rounded off to its nearest 10 is 70.
(f ) In words 9038 is written as nine thousand thirty-eight.
20
13. Write five numbers backward from the given numbers.
(a) 5643, _________, _________, _________, _________, _________
(b) 9289, _________, _________, _________, _________, _________
14. There are 2015 students in a school. Write the number of students in words.
15. A school X has 1986 students and another school Y has 1896 students. Which school
has more students?
16. There were 163 people in a party. What is the rough estimate of the number of
people in the party?
17. In a game, Rima picked up four digits from a bowl containing digits from 0 to 9.
The digits she picked up were 3, 5, 6 and 8. What is the greatest number that Rima
could make using these digits?
18. Choose the correct answer.
(a) The place value of 7 in 8375 is:
(i) 700
(ii) 7000
(iii) 70
(ii) 8502
(iii) 8508
(b) 8503 is greater than:
(i) 9846
(c) The greatest 4-digit number formed using 4, 5, 3, 0 is:
(i) 5430
(ii) 5304
(iii) 5403
(d) The smallest 4-digit number formed using 9, 7, 2, 0 is:
(i) 0972
(ii) 2079
(iii) 2097
(ii) 9446
(iii) 9436
(e) 6 less than 9442 is:
(i) 9346
SCRATCH YOUR BRAIN (HOTS)
1. What is the difference between the largest 3-digit number and the smallest 2-digit
number?
2. 4087 stands for RANK, 5128 stands for STUN and 9073 stands for CAKE.
What do the following numbers stand for?
(a) 5904
(b) 1248
(c) 1307
(d) 4381
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Colour and Learn
5369
36
1023
00
19
9443
9999
70
40
77
21
80
1000
2684
22
24
54
90
6319
9301
3825
5686
1120
2892
1. Colour the smallest 4-digit number green.
2. Colour the largest 4-digit number orange.
3. Colour the numbers which are the predecessors of the following numbers red.
(a) 5370
(b) 1121
4. Colour the numbers which are the successors of the following numbers yellow.
(a) 2891
(b) 9300
5. Colour the even numbers pink.
6. Colour the odd numbers purple.
MATHS LAB ACTIVITY
1. Cut a big cardboard in the shape of a circle.
2. Now cut 10 small circles of different coloured sheets
of paper and mark them as 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
3. Paste these small numbered circles on the cardboard
in a mixed order.
4. Hang the cardboard on the wall.
5. Each child should come one by one and hit the
cardboard with a small plastic ball four times.
6. Each time the child hits a digit he/she should note it down. Thus every child will
have 4 digits.
7. Using the 4 digits each child should form the following and write their number
names.
(a) the greatest 4-digit number
(b) the smallest 4-digit number
(c) as many 4-digit numbers as possible
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