Saturday, 25 April 2020

knowing our number notes grade 6


                                                    
INDEX
SI NO
DATE
LESSON
REMARK'S
TEACHER'S SIGN

































































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
2
0
3
5
9
8
7
1
TC
C
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

76
54
21
39
070
A
C
L
Th
O

 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
A
C
L
Th
O

     Twenty Arab forty-five thousand six hundred seventy-eight

5.  70,62,001

70
62
001
L
Th
O
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
0
0
7
HTh
TTh
Th
H
T
O

Six hundred forty-five thousand seven
2.              2,754,629
2
754
629
millions
Th
o

Ans: Two million seven hundred fifty-four thousand six hundred twenty-nine.
3.            32,604,509
        Ans:

32
604
509
Periods
millions
Th
o
        Thirty-two million six hundred four thousand five hundred nine.

4.              6, 570,763,422
Ans :

6
570
763
422
billion
million
Thousands
Ones
 Six billion five hundred seventy million seven hundred sixty three thousands four hundred twenty two.

5.  920,000,005,236

920
000
005
236
billion
million
Thousands
Ones
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.
 

                                                                     6000
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
SUCCESSOR AND PREDECESSOR
Number
2399
Predecessor
Number-1
2398
 

                                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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