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SI NO
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DATE
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LESSON
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REMARK'S
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TEACHER'S SIGN
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LESSON -1
Knowing our numbers
·
Natural numbers: The numbers used for counting are called natural numbers.
i.e. 1,2,3, …
·
Whole numbers: natural numbers and zero
together called
whole number
i.e. 0,1,2,3…
·
Integers: negative numbers and whole numbers together called integers
i.e. -3, -2,
-1,0,1,2,3…
·
Digits: 0,1,2,3,4,5,6,7,8, and 9 are called digits.
·
Numerals: a group of digits denoting a number is called numerals.
Ex: 23562, 345,
78902134, etc.
·
Numeration: Expressing a number in words is called numeration.
·
Types of numeration:
a. Indian system of Numeration.
b. International system of Numeration.
·
Indian system of numeration: The numbers split into groups or periods. Starting from right,
groups are called ones, thousands, lakhs, crores, Arabs, kharab etc.
Rule: Use commas for
separating the periods. First comma comes after three digits from right then
after every two digits.
Example: Write the
following numbers in Indian system of numeration.
1. 2345689702
Ans; 2,34,56,89,702
A,
C, L, Th, O
Two Arab thirty-four
crore fifty-six lakh eighty-nine thousand seven hundred two
2.
12,03,59,871
Ans :
|
1
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2
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0
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3
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5
|
9
|
8
|
7
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1
|
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TC
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C
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TL
|
L
|
TTh
|
Th
|
H
|
T
|
O
|
Twelve crore three lakh fifty-nine thousand eight
hundred and seventy-one
3.
76,54,21,39,070
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76
|
54
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21
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39
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070
|
|
A
|
C
|
L
|
Th
|
O
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Ans: Seventy-six Arab fifty-four
crore twenty-one lakh thirty-nine thousand and seventy
4. 20,00,00,45,678
|
20
|
00
|
00
|
45
|
678
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A
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C
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L
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Th
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O
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Twenty Arab forty-five thousand six hundred seventy-eight
5.
70,62,001
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70
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62
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001
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|
L
|
Th
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O
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Seventy lakh sixty two thousand and one
Write in numerals
1. six Arab fifty-three crore seventy-two
lakh thirty-nine thousand and eight.
2. Ninety-five thousand two hundred seventy-six.
3. Eight thousand fifty-six
Ans:
1.
6,53,72,39,008
2.
95,276
3.
8,056
·
INTERNATIONAL SYSTEM OF NUMERATION
Rule: Use commas for separating the periods. comma comes from
right after every three digits.
101 = 10,
102 =10 X 10 = 100,
103 = 10 X 10 X 10 = 1000
Example: Write each of
the following in words in the International system of numeration.
1.
645,007
Ans:
|
6
|
4
|
5
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0
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0
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7
|
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HTh
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TTh
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Th
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H
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T
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O
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Six hundred forty-five thousand seven
2.
2,754,629
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2
|
754
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629
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millions
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Th
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o
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Ans: Two million seven hundred fifty-four
thousand six hundred twenty-nine.
3.
32,604,509
Ans:
|
32
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604
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509
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|
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Periods
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millions
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Th
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o
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Thirty-two million six hundred four
thousand five hundred nine.
4.
6,
570,763,422
Ans :
|
6
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570
|
763
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422
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billion
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million
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Thousands
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Ones
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Six
billion five hundred seventy million seven hundred sixty three thousands four
hundred twenty two.
5. 920,000,005,236
|
920
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000
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005
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236
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billion
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million
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Thousands
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Ones
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Nine Hundred twenty billion five thousand two
hundred thirty-six.
1)
WRITE IN NUMERALS
SEVEN HUNDRED SIX MILLION THIRTEEN THOUSAND EIGHTY-SIX
ANS: - 706,013,086
2.Five billion thirty-six million thirty-two thousand
Ans.
5,036,032,000
3.Nine million eight hundred eight thousand seven
Ans. 9,808,007
4.Nine million eighty-two thousand five hundred
Ans. 9,082,500
I.
Insert commas in the correct positions and write the
following number in words in Indian and internationals system of numeration
1. 2345678
Indian
system: 23, 45,678
Twenty-three
lakh forty-five thousand six hundred seventy-eight
International
system:
2,345,678
Two million
three hundred forty-five thousand six hundred seventy eight.
1. 30000009
Indian system: 3, 00, 00,009
Three crore nine
International system: 30,000,009
Thirty
million nine
2. 2020560
Indian system: 20,20,560
Twenty lakh
twenty thousand five hundred sixty
International system:
2,020,560
Two million
twenty thousand five hundred sixty.
3. 1114232
Indian system: 11, 14,232
Eleven lakh
fourteen thousand two hundred thirty-two
1,114,232
One million
one hundred fourteen thousand two hundred thirty-two.
Place value: place value of a digit in a
number depends upon the place it occupies in the given number.
Example: Place value of the digit 7 in 67895 is 7x1000=7000
Face value: The face value of a digit in a
number is the digit itself regardless of their place.
Example: Face value of 7 in 67895 is 7
Place value and face value of the digit zero is always zero.
Face value 256783 place
value
6
II.
Find
the place value of 5 in each number
1. 3572896
Ans. 35,
72,896
5 is in lakhs
place.
Place value of 5=5x100000=5,
00,000
2. 79523
Ans. Place value of 5=5x100=500
3. 9765321
Ans. Place value of 5=5x1000=5000
4. 8051
Ans. Place value of 5=5x10=50
III.
Find
the product of the place values of two 3’s in 6435378
64,
35,378
Place value of 3 at ten thousand places=3x10,000 =30,000
Place value of 3 at hundreds place = 3x100=300
Their products =30,000 x300 = 9000000
vi. Find the
difference of the place value and face value of the digit 5 in 715432.
Place value of 5 at thousands place =5,000
Face value of 5=5
Their difference =5,000-5 =4,995
vii. Write in expanded form
1.42491
Ans:-40,000+2,000+400+90+1
2.602732
Ans:-6,00,000+0+2,000+700+30+2
3.12006
Ans:-10,000+2,000+0+0+6
Viii .Write in short form
1.
7,000
+ 500+30+9
Ans:-7,539
2.
60,000+3,000+600+7
Ans:-63,607
3.
90,00,000+6,000+300+50+4
90,06354
Write all possible 2-digit
numbers that can be formed by using the digits 3,7 and 9 if the repeatition of
digits is allowed.
Ans:-The
given digits are :-3,7 and 9
Using 3 and 7 =37,
73, 33, 77
Using 7 and 9 =79,
97, 77, 99
Using
3 and 9 = 39, 93, 33, 99
Possible
two digits no:s are :-37, 73, 33, 77, 79, 97, 99, 39, 93
Find
the difference between the number 349 and that obtained on reversing it’s
digits ?
Number
=349
Reversed
no:= 943
Their
difference = 943-349
= 594
ix. comparison of numbers
1.which is greater 572845 or 569784?
572845 >569784
1.
which is greater 57349 or 4024683?
Ans: -4024683>57349
|
Successor
Number + 1
2400
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Number
2399
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Predecessor
Number-1
2398
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Before After
|
Successor(after) =
number + 1
Predecessor(before)=number-1
|
x.
Write successor and predecessor
Successor
= 4257
Find
the successor of 4256
Successor-4257
2
. write three consecutive numbers succeeding
70259?
Ans: -70260,70261,70262
3
Write three consecutive numbers predeceasing
37201?
Ans: -37200,37199,37198
METRIC SYSTEM
The system of measurement is called Metric
system.
The standard unit of length is meter(m).
The standard unit of measuring weight is
kilogram(kg)
The standard unit of measuring capacity is liter
(
).
Exercise 1.3
1. A merchant has ₹ 80290 with him. He
placed an order for purchasing 50 ceiling fans at ₹ 200 each. How much money
will remain with him after the purchase?
Ans: -
The amount of money
with him= ₹ 80290
Cost of one fan = ₹
1200
Cost of 50 fans = ₹
1200 x 50 = ₹ 60,000
The amount of money
left with him = ₹ 80,290 - ₹ 60,000
= ₹ 20,290
2). The distance between the school
and Rahim’s house is 1 km 420 every day he walks both ways. find the total
distance covered by him in 5 days.?
Ans: -
Distance between the
school and Rahim’s house = 1 km 420 m
Distance covered by
Rahim on both way =1 km 420 m + 1km 420 m =2km 840 m
Distance covered by
Rahim in 5 days = 2km 840m x 5 = 14km 200 m
3). The number of sheets of paper
available for making notebooks is 75,000. Each sheet makes 8 pages of a note books.
Each notebook contains 200 pages. How many notebooks can we made from the paper
available?
Ans:-
No of sheets of paper
available for making notebooks = 75,000
No of pages from 1
sheet =8
Total no of pages =
6,00,000
No of pages in 1 book =200
No of notebooks can be
made from 6,00,00 pages
= 6,00,000
200 = 3000 notebooks
4). A bottle contains 900 ml of oil. What
is the total quantity of oil contained in 40 such bottles?
Ans:
Amount of oil in one
bottle=900 ml
Quantity of oil in 40 such
bottle
= 900 ml x 40 =36,000ml=36
5. If 45 kg
450 gm of sugar be equally distributed among 15 persons, how much shall each
get?
Ans:
- Total weight of sugar =45 kg 450 gm
Total no of persons = 15
=45 kg 450 gm
15
= 3030 gm
= 3 kg 30 gm
6. In an election, the
winning candidate got 7,26,249 votes. His nearest rival got 5,26,351 votes and
third candidate got 45460 votes.2285 votes were declared invalid. What was the
total number of votes polled in that constituency.?
Ans:
No: of votes got for 1st candidate
= 7,26,249
No: of
votes got for 2nd candidate = 5,26,351
No: of
votes got for 3rd candidate = 45,460
No: of
invalid votes =2285
Total no:
of votes
=7,26,249
+5,26,351+45,460+2285
=13,00,345
votes
7. A factory produces
8565 screws a day. How many screws will it produce in a year if the factory has
291 working days in the year?
No: of
screws produced in a day = 8565
No: of
working days in a year = 291
No of
screws produced 291 days = 8565 x 291 = 24,92,415 screws
8. Population of a town
in the year 2011 was 3, 25,243 .In the year 2012,it was found to have increased
by 51,927.What was the population in the year 2012?
Population
of town in 2011 =3,25,243
Total
population of town in 2012 =
3,25,243
+51,297
=3,77,170
9. A box of Medicine
tablet contains 2,50,000 tablets each weighing 20 mg.What is the weight of all
the tablets in the box in grams and in kilograms?
Ans :-No
of tablets in a box = 2,50,000
Weight of
each tablets = 20 mg
Total
weight of all tablets = 2,50,000 x20
=5,00,000
mg
Gram= 5,00,000
1000 (1000 mg = 1 gm,1000 gm =1 kg)
= 5,000 gm
Kilogram
= 5 ,000 gm
1000 = 5 kg
10. A student
multiplied 8245 by 35 instead of 32. By how much was his answer greater than the correct answer.?
8245 x 35 =
288575
8245 x 32 =263840
288572-263840 = 24735
11. 2m 20 cm of cloth
is needed for one shirt. What length of cloth will be required for 16 such
shirts?
Ans: -
Length of cloth needed for shirt
= 2m 20 cm
Length of cloth needed for 16
shirts
= 2m 20 cm x16
=(200 cm + 20 cm) x 16
=35320 cm (100 cm =1 m)
=35 m 20 cm
5. If 45 kg 450 gm of sugar be equally distributed among 15 persons,
how much shall each get?
Ans :-Total weight of sugar =45 kg 450 gm
Total no of persons = 15
=45 kg 450 gm
15
= 3030 gm
= 3 kg 30 gm
6. In an election, the winning
candidate got 7,26,249 votes. His nearest rival got 5,26,351 votes and third
candidate got 45460 votes.2285 votes were declared invalid. What was the total
number of votes polled in that constituency.?
Ans:
No: of votes got for 1st candidate
= 7,26,249
No: of votes got for 2nd
candidate = 5,26,351
No: of votes got for 3rd
candidate = 45,460
No: of invalid votes
=2285
Total no: of votes
=7,26,249
+5,26,351+45,460+2285
=13,00,345 votes
7.A factory produces 8565 screws a day
.How many screws will it produce in a year if the factory has 291 working days
in the year?
No: of screws produced in
a day = 8565
No: of working days in a
year = 291
No of screws produced 291
days = 8565 x 291 = 24,92,415 screws
8. Population of a town
in the year 2011 was 3, 25,243 .In the year 2012,it was found to have increased
by 51,927.What was the population in the year 2012?
Population of town in
2011 =3,25,243
Total population of town
in 2012 =
3,25,243 +51,297
=3,77,170
9. A box of Medicine tablet contains
2,50,000 tablets each weighing 20 mg. What is the weight of all the tablets in
the box in grams and in kilograms?
Ans: -No of tablets in a
box = 2,50,000
Weight of each tablets =
20 mg
Total weight of all
tablets = 2,50,000 x20
=5,00,000 mg
Gram= 5,00,000
1000 (1000 mg = 1 gm,1000 gm =1 kg)
= 5,000 gm
Kilogram
= 5 ,000 gm
1000 = 5 kg
10. A student multiplied 8245 by 35
instead of 32.By how much was his answer greater than the correct answer.?
8245 x 35 = 288575
8245 x 32 =263840
288572-263840 = 24735
11. 2m
20 cm of cloth is needed for one
shirt .What length of cloth will be
required for 16 such shirts?
Ans:
-
Length
of cloth needed for shirt = 2m 20 cm
Length
of cloth needed for 16 shirts
= 2m 20 cm x16
=(200
cm + 20 cm) x 16
=35320
cm (100 cm =1 m)
=35
m 20 cm
12.One copy of newspaper has 14 pages.
Everyday 12928 copies are printed .How many total pages are printed every day?
Ans:-
No of pages of 1 copy of
newspaper = 14
Total no: of copies
=12928
Total no: of pages in
12928 copies = 12928 x 14 =180992
13.In one state the number of TV sets
sold in the year 2009-2010 was 8,47,200.In the year 2010-11, the number of TV
sets sold was 9,10,345 .In which year more TV sets were sold and how many more ?
Ans:-No: of TV sets sold
in the year 2009-10 =8,47,200
No: of TV sets sold in the year
2010-11 =9,10,345
The year 2010-11 was more TV sold
= 9,10,345-8,47,200
=63,145
14.Mohit travels 8 km 425 m towards
north ,13 km 210 m towards south and 15 km 675 m towards west. Calculate the
distance travelled by him?
Distance travelled by
Mohit towards north =8km 425 m
Distance travelled by
Mohit towards south =13km 210 m
Distance travelled by
Mohit towards west =15km 6755 m
Total distance travelled
by him
=8km 425 m+13km 210 m
+15km 6755 m
=37,310 m
=37 km 310 m
15.An engine pumps out 850 l of water
in one minute. How many hours will it take to pump out 13,77,000 liters of
water?
Amount of water pumped in
1 minute = 850 ml
No: of minutes taken to
pump 13,77,000 liters of water
=13,77,000 liters
850=1620 minutes
No: of hours taken to
pump 13,77,000 liters of water
= 1620
60 = 27 hours
ESTIMATION
Rounding off numbers nearest tens
Step 1. Choose the number
Example: 567
Step 2. Select the number in tens place
541
Step 3. Look at the number right of it
(one’s place 1)
Step 4. If the number in one’s place
is 4 or less than 4 ignore it
Ans:
540
Step 5. If the number in ones place
is 5 or more then add 1 to it
549
Ans: 550 (4 + 1=5)
Rounding off to the numbers
nearest hundreds
Step 1. Choose the
number
Example: 8967
Step 2. Select the number
in hundreds place
8347
Step 3. Look at the number
right of it (in tens place 4)
Step 4. If the number in
tens place is 4 or less than 4 ignore it
Ans
: 8300
Step 5. If the number in
tens place is 5 or more then add 1 to hundreds place.
8569
Ans: 8600 (5 + 1=6)
Rounding off numbers
nearest thousands
Step 1. Choose the
number
Example: 67567
Step 2. Select the number
in thousands place
62367
Step 3. Look at the number
right of it (hundreds place 3)
Step 4. If the number in
hundreds place is 4 or less than 4 ignore it
Ans:
62000
Step 5. If the number in
hundred places is 5 or more then add 1 to thousands place.
8569
Ans: 9000 (8 + 1= 9)
Estimating sum,difference
and product
1.Estimate the sum by
rounding off the numbers to the nearest hundred
Ans:-692 +237
692=700
237=200
Estimated sum=700+200 =900
2. 207+ 391
207=200
391=400
Estimated sum = 200 + 400 =
600
2.Estimate the difference
by rounding off the numbers to the nearest hundreds
a.883-466
Ans:-883=900
466 =500
Estimated difference =
900-500 =400
b. 781 – 539
Ans:-781-539
781=800
539 = 500
Estimated difference = 800
– 500 =300
3.Estimate the following
products
a. 28 x 67
Estimated product = 30 x 70
= 2100
b. 79 x 192
Estimated product =80 x 200
= 16,000
4.Estimate the following by
rounding off each numbers to its greatest place
a. 877 x 725
Ans : Estimation = 900 x
700 = 6,30,000
b. 9 x 792
Ans : Estimation =10 x 800
=8,000
5.Estimate the following by
rounding off each to the nearest rupee
a. ₹ 5.26 + ₹ 2.85
Estimated rupee = 5.00 +3.00
= 8.00
b. ₹ 1.78 + 6.82
Estimated rupee = 2.00 +
7.00
=9.00
6.Estimate thefollowing
result
a.6398 + 17928
Estimated sum = 6000+18,000
= 24,000
b.6893 –v789
Estimated difference =
7,000 -800
= 6,200
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