Numbers and

esson 1 Numeration
Numbers are all around us.

Rabindra Setu Mount Everest River Ganga

(Howrah Bridge) Height- 8848 m Length- 2525 km
Length- 705 m
List 4 things in which you use numbers in your daily life.
1. ...clak 2. ..aendaa.
3. .m..phama..RAmaaa.. 4. .fe.unhass.
We have already learnt numbers up to 9999 in Class III. Let us revise them.

Activity-1
Do you remember .

1. Write in words :
(a) 3849 Thane.thasand.cigt huadtsad.oi.
(b) 5308 tiu.Basanl..uadal..sght.
(c) 8074
(d) 7777 .Bounthuand..Sauonhundad.auãaann.
MATHENMATICS in Real Life 4 5
 Writein numeral form: Ly320
-.
three hundred twenty
thousand
(a)Four nine 1424
hundred eighty
Seven thousand four
(b) |999
thousand nine hundred nine
(c) One
seven hundred sixty five 8765
(d) Eight thousand

. Write in expandedform:
(a) 6827
60000.1.800.+.20.:+.1..
3ooco.t.l00.t.10.t.9....
(b) 3179
&o0Q.t.J00.*.0ta....
(c) 8105
oo.t.I00..0.t:.0.
(d) 4180

4. Write in short form:

6 = 3456
(a) 3000 + 400 + 50 +

(b) 7000 + 90 + 8 1098

(c) 4000 + 200 + 20

=yago
6005
(d)6000 + 5
5. Fillin the blanks :
is J944
(a) The predecessor of 2000
(b)The successor of 3270
is 3a1!..
of 8in 1278 ..3.
is
(c) The place value
in 7125 is
(d) The place value of 7
2058 is
(e) The place value of0 in
the smallest and greatest 4digit numbers using the digits 4, 0, 2 ar
6. Form
each only once.
Smallest number o24 Greatest number 210
1CSIn Real Li
 7. Arrange in ascending order :
(a) 4217, 4315, 4035, 4479
yo35 4315
(b) 2893, 2983, 2398, 2978
348 |a843 a418 a93
8. Arrange in descending order:
(a) 1728, 7128, 8127, 2718 |129
(b) 9256, 9526, 9652, 9729 |4662 |4526 9256
9. Conpare the numbers using >,<or =:
(a) 1002 < 1020 (b) 3540 3450
(c) 8357 8357 (d) 6825 6827

Numbers Beyond 9999

5-Diqit Numbers
In our earlier classes, we have studied the numbers from 1 to 9999. You would
naturally like to ask the question, "What number comes after 9999?"
Now we shall try to answer this question.
10000 is the smallest
We know that the greatest 4-digit number is 9999. 5-digit number.
9999 = 9 Thousands + 9 Hundreds +9 Tens +9 Ones
Let us add 1to 9999.
9999 t 1 = 10000
TTh Th H T
1 0

It is read as 'ten thousand'.

TTh denotes the ten thousands place.
On the abacus, it is represented as
shown.

TTh Th H T

Remember : 99999 is the greatest 5-digit number.

 numbersontheabacus. 3
represent5-digit
Letus

T 0 TTh Th H
TTh Th H
TTh Th H (11231) 21034
82541 Eleven thousand two Twenty one thousand
five
Eighty two thousand hundred thirty one thirty four
hundred forty one

Activity-2
write the number and number name.
Read the abacus and
you.
The first one has been done for 3.

T Th Th H TO
TTh Th H
TTh Th H T0
(54141 10634
12324
Twelve thousand three. a.thnans. Tenthaand,.Sske.. ..e...

hundred twenty four.

6.

T0
T Th Th H TTh Th H T 0 TTh Th H

(90,326 12,613
.Ninay.thAAnd,thae .hundsad.thistolonnhndd.n
8
hund.aySuä. Life 4 MATHEMATICSIn Real
 Indian Place Value Chart

Crores Lakhs Thousands Ones

Ten Ten
Lakhs
Ten Crores 'Crores Lakhs |Thousands Thousahds Hundreds Tens Ones
100000000 10000000 1000000| 100000 10000 1000 100 10

Interinational Place ValueChart

Millions Thousands Ones

Hundred Ten Hundred Ten

Millions Millions
Millions
Thousands Thousands Thousands Hundreds Tens Ones

100000000 10000000| 1000000| 100000 10000 1000 100 10 1

Example: Let usread the number 3276972,

In Indian system, it is written as 32,76,972.
It is read as "Thirty two lakh seventy six thousand nine hundred seventy two.'
InInternational system,it is written as 3.276.972.
Itis read as Three million two hundrèd seventy six thousand nine hundred seventy

Activity-3
1. Arrange the following numbers in Indian place value chart. Rewrite them in
blank spaces with commas at the right places.
(a) 19285 ..a,A65... (b) 247158 ...4158..
(c) 725175 .126,16... (d) 928750 ..3.01.59.
2. Arrange the following numbers in International place value chart. Rewrite them
inblank spaces with commas at the right places.
(a) 48517 ..98,511... (b) 932429 93242.3..
(c) 5172359 ...1239.. (d) 3327458 221,4.5.2.
3. Write the number names(in Indian system)
(a) 53,125 sal,sa.nA..Aa
() 1.87,819 h..la.,.sagh.en.sad.ht. handoedinr
(c) 9,27,471 Qana.lakda,...A.SAAn. thouand.,onhaunsad.
(4) 37,17,215 hal4 SNAZA,da.a.,AManun.thnand...
MATHEMATICS In Roal Life-4 13
 4. Writethe number names (in Internationalsystem)
(al 412.351 Jaahundud aast.,.hsas. harcad.l TA.
(b) 167,897 .hundud..Snly.Sasen,.Sgh.hunsad.nsnalyAuen.
ic) 3.993.457 he. mllion,.linahundrad, ninag thas,.goun. hswrd.
(d) 8,123.4566Sght.mlana, ra.hsundad.tuaniy.thus. mdlsena.
5. Write the number putting commas at the right places: hundd y sa
(a) Eight lakh ninety nine thousand four hundred twelve 699,912.
(b) Seven lakh twenty five thousand nine hundred thirty one
(c) Two hundred thirty five thousand four hundred sixty nine
.As,43..
.3.35,4s9...
(d) One million four hundred two thousand seventy five
.y.saa, 215.
6. Write the smallest and greatest 7-digit numbers both in figures and in words.
(a) Indian number system :
Smallest ...PPAO.en lats.
Greatest 44,94419..Nneg,.in. a.italy.Quna.tand..
(b) International number system: hunds ninel ine
Smalest ..,Aagana..ra.nli.
t9Ni.mlia,.Nin.huns.Niny.ine.thsuand
Nin hundud Ninety ine
Face Value and Plae Value
Face Value of a Digit
The face value of a digit is the value of the digit
number. itself irrespective of its place in the
Example: In the number 234567,
face value of 2 = 2
face value of 3 =3
face value of 4 = 4
face value of 5 = 5
 Place value of 6 =6 x I =6 =6 0nes T Th Th H T
Place value of 5 = 5 X 10= 50 = 5 tens 3 2 7 4 5 6
Place value of 4 = 4 X 100 = 400 = 4 hundreds
Place value of 7 =7x 1000 = 7,000 = 7thousands
Place value of 2= 2x 10000 = 20,000 = 20 thousands
Place value of 3 = 3 x 100000 =3,00,000 = 3lakhs
Expanded Notation of a Number
Example 1: Write the expanded form of 8,27,459.
g 27 459 = 8 X 1,00,000 + 2x 10,000 +7X 1000 + 4x 100 + 5 ×
10 + 9
= 8,00,000 + 20,000 + 7,000 t 400 + 50 + 9
This is the expanded form of the number 8.27.459
Example 2: Write the expanded form of 9,65,307.
LT Th Th H T
9 65 3 0 7

9.65,307= 9 x 1,00,000 + 6 × 10,000 + 5 X 1000 + 3 X 100 + 7x

=9,00,000 + 60,000 + 5000 + 300 + 7

Activity-4
1. Find the face value and place value of the coloured digit in the given numbers
(a) 13,791 J00..1... (b) 24,352 .Sceo.,.9..
(c) 1,47,173 J900.,.I.. (d) 3,56,735 ..ooa,.a...
(e) 8,23,179 .pA,.. (f) 51,757 ..ODa.....
(g) 67,236
..o09.J... (h) 9,87,617 4p900..4.
2. Find the difference between the place value and face value of 6in 3526521.
..Co00..s...599.4.
3. Find the sum of the place values of two 5s in 235257.
5000.+.50.....5.05.
MATHEMATICS In Real Life 4
 numbers :
form of each of the following
4. Write the expanded
(a) 25.308
Aoo.+.So..t.3Ot:0.t.8.
...0000..5909.+.00t.10.t.3...
(b) 75,173
(c) 1,37,478 .O900+.3000o.+.10.0.+.40a..IO.t.8.
(d) 3,47,785 .309,00.+.99O,90:+.7.0OQt.190.t.&.t.S...

(e) 87,928
..Booa0t.1D00.1.9o.t0t.2..
(f) 90,494 ..90000.t9.t.40.A.40.+.4..
5. Writethe short form of each of the following numbers :
(a) 1,00,000 + 30,000 + 2,000 + 100 + 70 +6 .,2.2.4.1.6..
(b) 5,00,000 + 60,000 + 5,000 + 400 + 80 + 7 .6.,4.0....
(c) 9,00,000 +90,000 + 9,000 + 900 + 90 +9 .9,9.9.,2.1.1..
(d) 70,000 + 5,000 + 60
(e) 3,00,000+ 6,000+ 70 + 7
(f) 4.00,000 + 400 + 40 + 4
.,o6,.1.....

Successor and Predecessor of a Number

Successor of a number
The successor of a number is 1 more
than the number. So, we add 1to the
get its successor. number
Examples : Successor of 13235 is 13236.
Successor of 99999 is 100000. 13235 + 1= 13236
99999 +1= 100000
Predecessor of a number
The predecessor of a
number to get its number is 1 less than the number. So, we subtract 1from
predecessor.
Examples : Predecessor of 34569 is 34568.
Predecessor of 160750 is 34569 1 =34568
 75.13
c 137478
To0004So0o4 100+104 3
347.785
i00043000o t100o+400t70t2
e) 87928
f) 90.494 30DOo+40000+.IO004.7o0tS
Booco t.100.t.900.tt8
S

(b)
I.00,000 30,000 4000t0t.4following
Wre che short form of
00..90t.numbers
each of
the
2,.000+ 100 +
4. :

(c)
5,00,0O00 + 70 + 6
60,000+ 5,000 + 400 + 80 + 7
9,00,000
(d)
70,000+ 90,000+ 9,000 + 900 + 90 + 9
5,000+ 60 565,41
(e)
(f) 3,00,000++
4,00,000
6,000 + 70 t 7
400 + 40 + 4
..9,99293
 18
1.
3,9TI...(g) (e) 39,900(c) 13,598(a) Write
7,38,099
1,23,478 (b) Comparing(a) the
wenumber. left
Thus,Comparing
the se smallest
successor the that place,
4,23,456 and we
...352.2...... numbers5,23,456
.39,.40......
.a.. <
5,23,456 6,27, se
of: t1hat
5,17,236 in > 75
ascendin5,g17,236. and the 4,2is3,4.
Activity-5 5,23,456
<
5,17,236. greatest
order
are
<
78,349
(d) 25,009(b)
O,D0
9,99,999(h)
...,.200.
3,47,199() 6,27,175 5 4 6

1 2

3
7
.a,alQ...
13.35D..
EMATICS In 22 4

3 5
 2. Write the predecessor of:
(a) 39,498 .. 9,49.1. (b) 57,000 56,99.9.
(c) 92,450
93949..... (d) 1,73,970 ..13,94.1...
(e) 8,48,300
,48,819... () 1.00,000.4,44.9...
3. Write >,< or = in the boxes :
(a) 10,337 10,370 (b) 72,478 7) 72,378
(c) 9,999 - ] 9,999 (d) 1.22.115 1,23.115

(e) 5.28,179 > 4,28,179 (f) 4,38,790 4,48,790

4. Circle the largest number:
(a) 1,23,410 1,23,425 1,23,517 (1,23,620)
(b) 197,630 198,715 (199,215) 195,768 Puzzle
5. Arrange in ascending order: Using the digits 1 to
9 (each exactly
(a) 20,280 20,820 20,028 20,082 once),form three
a0,.088,.a9,.082 o,a&a.,..a,aA..3digit numbers so
that the second
(b) 89,728 87,128 84,571 89,185 number is 2 times
4,511..1128.,..e,18s,..a,128.the first and the
third number is 3
(c) 3,17,230 4,17,230 5,28,470 4,28,217
times the first.

6. Arrange in descending order:

(a) 92,173 93,234 90,148 92,345 91,172
Sl,REA,.4,245,.3,3,..., ..99,.148.
(b) 72,059 72,509 72,590 72,950 72,905
E,029.12,49.,.3,530...,s0.,..,
(c) 8,23.333 8,43,126 8.17.338
051.
8,17,238 8,34,126
SA5,ak..,3%R.à,88,32..2,rL330.,..1,238
MATHEMATICS In Real Life-4 1
 Activity-6
1. Write the smallest and greatest 4-digit numbers using each of the following digits
only once :
(a) 4, 2, 9, 7 Smallest .a4.1.9....eatest ..2.14.2....
(b) 1,3, 7,0 Smallest ..1.0.9.1l..Greatest .... 13!.0......
(c) 5, 9, 3, 1 Smallest ...354.,.....Greatest ......5.3.!..
2. Write the smallest and greatest 5-digit numbers using each of the following
digits, repeating 4 twico
(a) 1,4, 2, 5 Smallest .542).....e.atest
.......!.. ......H.5..
(b) 3, 4, 0, 8 Smallest ...3948.....atest .....4.39.
(c) 9. 3., 4. 5 Smallest ...3.4.5.4...Greatest ......5.9..
3. Form the smallest 6-digit number using the digits 1, 3, 0,
5. 7 and 6 each only once. ..Jo35.61
4. Form the greatest 6-digit number using the digits 7, 8, 9,
3and 5 repeating 8 twice. A.38.1S3.

5. Form the smallest 5-digit number using the digits 1, 3, 5

and 0 repeating 1twice. Jol3.5....

Rounding Numbers
The number of people
There are about whoattended the rally
2800 students in was about 9000.
my school.

exact answer
situations where we do not know the
nour daily life, we
come across
been rounded off to the nearest te
which has
Some quantities. We give an answer
may be.
mundreds or thousands as the case
THEMATICS Examples
Round 3. 2. 1. 3. 2.3787 1. 2.
12617() (a) Round
() (a) Round 110774 (f) 57 (a)Go 10597 10349 tens digits
If
the
3278 6253 446 : and digit
by0
13000
Real
In
off
Round
off off ’ ’ ’ ones
Life-4 3000 to6300 Y0 to to atand
The The The off digits the
the the the keep
(b)
45817(g) nearest (b)
(g) nearest 819(g) -40nearest
(b)93 hundreds
hundreds
hundreds tohundreds
the by other
6938-T000 8899 719
nearest and 0
10O
thousands 8oo hundreds 8a0 tens digit digit digit increaseplace digits
: same.
Activity-7
983(h) 291(c) is thousands.
3 7 is
73417(h) (c) (h) (c) 5, < > equal
71711000 :
15728 983
: so, 5, 5, the
13000 so, so, thousands to
toD 10597
a90 10349 3787 or
1576o(i) 8o more
is
99978() (d) (d) (i) 380375(d) is is
rounded rounded digit than
rounded
I00600 9569 18997 1185 1733
by
5,
1.
replace
t0,000(e) 4000lj) I130 off off
oo to off to
11000. to4000.
32871() (e) (i) 588(e) 10000. the
3300 10734 24364 1736 35876 hundreds,
540
(ICO0 Suoo 35880
23
 Mental MathsCorner
1. Tick (the correct answer.
(a) Which is the same as 60 tens?
(i) 6ones (ii) 60 ones (ii) 6 hundredsiv) 60 hundreds
in 401406 is
(b) The sum of the place values of two 4s
(i) 400400(i) 400000 ii) 440000 (iv) 80000
(c) Asix digit number begins with place.
() lakhs M(ii) ten lakhs(ii)thousands(iv) tenthousands
(d) The difference between thegreatest and smallest 4-digit numbers formed by
the digits 1, 2, 3, 4 is
() 2087 (ü) 3087 M (i) 3067 (iv) 3807
2. The successor of (a) 38,999 is .A,0 (b) 59,289 is .59,d90
(c) 1,23,539 is 2 O(d) 23,450 is 9.3)45!.
3. The predecessor of (a) 82,475 is 414.. (b) 9,53,180 is ..4,53,.]J
(c) 99,999 is . , o (d) 3,25,988 is .3.35,987
4. (a) The place value of 7in 17,268 is ....lOOo..
(b) The place value of 4in 4,28,186 is ..4O0.000.
5. (a) The expanded form of 38471 is 3omt.Booct4o0.+1.0t1....
(b) The expanded form of 4,90,999is .AS0.+4QAO.10t900.+90
Review Exercise
1. Write the number names of:
(a) 3.52,179 thas.ake,to.tugnd.,.Oe.hunced.&ua.
6) 6825,173 Sae.Jakhy,.sa..hundoad.ata..hundad
2. Write the number for:
(a) Seven lakh forty two thousand
eight
hundred thirty
(b) Thirty eightthousand seventy
(c) Six hundred two thousand five ..38,010..
3. Writethe place value of each of
hundred twenty eight ..0.2,5a8..
the underlined digits:
(a) 26,278 (b) 3,28,347 (c) 9,11,324 (d) 287,783
24 300
MATHEMATICS In Real Life 4
 4. Arrange in ascending order:
32,475 32,745 32.754 32,574
39315,..2514,..24,145....32154.
5. Arrange in descending order :
1,82,824 1,84,728 1,84,628 1,85,625
..35.625.,..$t28.,.,84,628....L84,JA8
uOTS Form the greatest and smallest 5-digit numbers using the digits 4, 2, 0and
Ouest1on 8 repeating 2twice. Also, find their difference.

Maths Lab Activity

Representing a number on the abacus.
Follow the instructions and draw circles below.
4 in the ones place 3 in the tens place
*2 in the hundreds place 5 in thethousands place
*7 in the ten thousands place 31 inthe lakhsplace

Lakhs Ten Thousands Hundreds Tens Ones

Thousands
4 X 1 = 4

3 tens =3 X 10

2 hundreds =2 X 100 oo...

5 thousands =5 X 1000 5c00. Number
7 ten thousands = 7 X 10000 =

1 lakh = | X 100000 =
MATHEMATICS In Real Life-4 25