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 1^st candidate = 7,26,249

No: of votes got for 2^nd candidate = 5,26,351

No: of votes got for 3^rd 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 1^st candidate = 7,26,249

No: of votes got for 2^nd candidate = 5,26,351

No: of votes got for 3^rd 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