Note - 0587 Is A 3 Digit Number
Place,Place Value,Face Value
Remember
* In A No.The
Place Of A Digit Is Decided By Its Position
*The
Face Value Of A Digit Is The Digit Itself
*The
Place Value Of A Digit Is The Product Of The Place And Its Face Value
Some Examples
1) What Is The Place,Place Value,Face Value Of 7 In 9786
Place-Hundred
Face Value=Digit Itself =7
Place Value=Place*Face Value
=Hundred*7 =700
Exercise 1.1
1) Write The No.Names Of The (1) Indian System (2) International System
A) 451730 B) 9340001
2) Write The Numerals
A) Seventy Three Crore Five Lakh Eight Five Thousand Three Hundred Five
B) Six Hundred Sixty Six Million Six Hundred Thousand Sixty Six
3) Write The Place Value Of The Underlined Digits
A) 123456789
4) Write The Nos. in Expanded Form
A) 7058109
5) Find The Sum Of The Face Value Of Digit 3 In 93278
6) Write The Greatest And Smallest No.Using These Digits
A) 1,6,0,9 B) 4,9,2,3
7) Fill In The Blanks
A) 1 Crore =______ Lakhs
B) 1 Crore =______ Ten Lakhs
C) ______ Lakhs = 1 Million
D) _______Millions = 1 Crore
E) 1 Lakh =_______Ten Thousands
F) ______Ten Millions = 1 Billion ( Important Question )
Answers For Exercise 1.1
1-A-Four Lakh Fifty One Thousand Seven Hundred Thirty
1-B-Ninety Three Lakh Forty Thousand One
2-A-730585305
2-B-666600066
3-A-1=100000000
3=3000000
5=50000
4-A-7000000+00000+50000+8000+100+00+9
5-3003
6-A-Greatest No=9610 , Smallest No=1069
6-B-Greatest No=9423 , Smallest No=2349
7-A-100
B-10
C-10
D-10
E-10
F-100
Comparison Of Numbers
Remember
< Is Used For Less Than
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> Is Used For Greater Than
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≤ Is Used Is Less Than Or Equal To
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≥ Is Used For Greater Than Or Equal To
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= Is Used When Both The Nos are Equal
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Did You Know ?
The Symbols < And > Were Introduced By The English Astronomer And Mathematician Thomas Harriot. He Was Born In 1560 And was Educated At Oxford. He Served As A Tutor To Sir Walter Raleigh And was Appointed By Him To The Office Of Surveyor With The Second Expedition Of Virginia.
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Produce To Compare Two Numbers
Rule 1 Count The No.Of Digits In The Numbers.
Rule 2 If The Number Of The Digits Is Same In Both The Numbers,Start Comparing The Digits From Left To Right
Example 1 Use The < Or > Signs To Compare
A) Compare 379827 And 64508
Solution 1 379827---6 Digits
64508---5 Digits ( Rule 1 )
So, 379827>64508
B) Compare 237752 And 237786
Solution 1 237752---6 Digits
237786---6 Digits
Start Using Rule 2 Digits In L,TTh,Th,H Are Equal See the Tens Place
In The First No Tens Place Is 5
In The Second No Tens Place Is 8
So, 8>5
So, We Say That 237752<237786
Now Some Questions For You
1) Compare 57864 And 70483
2) Compare 7912384 And 7916015
Ascending And Descending Order
Ascending Means- Small To Big
Descending Means-Big To Small
Example 1 Arrange The No In Ascending And Descending Order
A) 42130,42580,125631,2810837,56943
Solution A-Ascending Order-42130,42580,56943,125631,2810837
Descending Order-28010837,125631,56943,42580,42130
Now Some Question For You
1) Arrange In Ascending and Descending Order
A) 74678,2725821,2364,2748920
Exercise 1.2
1) Put The Appropriate The Symbol <,>,=
A) 7895__25430
B) 92378__54490
C) 543186__543186
2) Arrange The Following In Ascending And Descending Order
A) 17704,99999,100000,30506,9807
B) 9801076,9950166,801235,4689432,90681
C) 23704,822704,9999,6217,10216
Answers For Exercise 1.2
1-A-<
1-B->
1-C-=
2-A-Ascending-9807,17704,30506,99999,100000
Descending-100000,99999,30506,17704,9807
2-B-Ascending-90681,801235,4689432,9801076,9619232
Descending-9619232,9801076,4689432,801235,90681
2-C-Ascending-6217,9999,10216,23704,822704
Descending-822704,23704,10216,9999,6217
Word Problems On Number Operations
Example 1 On A Particular Day John Has Rs 2723716 In His Saving Bank Account. He Withdraw Rs 1208417 From His Account. Find The Balance In His Account After Withdrawal ?
Solution 1
Amount In His Account
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Rs 2723716
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Amount Withdrawn
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Rs - 1208417
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( Subtracting )
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Balance In His Account
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Rs = 1515299
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Example 2 Mohammad Ali Spent The Following Amounts In 2006 Under Various Heads
Electricity Bill - Rs 813142
Water Charges - Rs 4375
Cooking Gas - Rs 3540
Find The Total
Amount Spent By Him Under These Heads ?
Solution 2
Amount Spent On Electricity Bill
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Rs 813142
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Amount Spent On Water Charges
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Rs 4375
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Amount Spent On Cooking Gas
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Rs + 3540
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( Adding )
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Total Amount Spent
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Rs= 821057
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Example 3 A Cabinet Maker Needs 72m Long board For Making One Cabinet How Many Cabinets Can He Make By Using 17496m Long Board ? ( m Stands For Metre )
Solution 3
Total Length Of The Board
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= 17496 m
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/ Means Divide
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Length Of The Board Required For One Cabinet
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= 72 m
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Number Of Cabinets He Can Make
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= 17496 / 72 = 243
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( Dividing )
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Example 4 A Printer Printed 123865 Copies Of A Book Containing 69 Pages. Find The Total No. Pages Printed By The Printer ?
Solution 4
No. Of Books Printed
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= 123685
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* Means Multiply
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No. Of Pages In One Book
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= 69
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No. Of Pages In 123865 Books
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= 123865 * 69
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( Multiplication )
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Total No Of Pages Printed
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= 8546685
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Now Some Question For You
1) Population Of A Village In 2006 Was 732568.If The Number Of males In This Village Was 419439, Then Find The No. Of Females It Had ?
Conversion Of Units Of Length And Mass
1 Km ( Kilometre )
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= 10 Hm
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1 Hm ( Hectometre )
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= 10 Dam
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1 Dam ( Decametre )
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= 10 M
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1 M ( Metre )
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= 10 Dm
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1 Dm ( Decimetre )
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= 10 Cm
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1 Cm ( Centimetre )
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= 10 Mm
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Mm = Millimetre
Note - When We Go From Higher To Lower We Multiply And When We Go From Lower To Higher We Divide
For Converting A Measure In Terms Of Next Lower Unit, We Multiply The Given Quantity With 10. Similarly For Converting A Unit From Next To Next Lower Unit We Multiply With 100 And So On...As In Of Next Upper Unit We Divide By 10 Similarly For Converting A Unit From Next To Next Upper Unit We Divide With 100 And So On..
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Km
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Hm
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Dam
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M
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Dm
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Cm
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Mm
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10
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10
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10
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10
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10
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10
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A) 1 Km = 1000m ( Because 10*10*10=1000m )
B) 1 M = 100cm ( Because 10*10=100cm )
Similarly Units For Measuring Weight ( Mass ) Kilogram ( Kg ) Hectorgram ( Hg ) Decagram ( Dag ) Gram ( G ) Decigram ( Dg ) Centrigram ( Cg ) Milligram ( Mg )
1 Kg = 1000g
1 Gm = 1000mg
Units For Measuring Capacity Kl,Hl,Dal,L,Dl,Cl, And Ml
Litre ( L ) Is Used For Measuring Large Quantities
Example 1 Shilpa Bought 12m And 50cm Cloth Of One Kind And 17m And 25cm Cloth Of Another Kind. Find The Total Cloth ?
Solution 1
Length Of The First Kind Of Cloth
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12m 50cm
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Length Of The Second Kind Of Cloth
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+17m 25cm ( Adding )
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Total Cloth
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= 29m 75cm
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Example 2 A Shopkeeper Has 500 kg Of Sugar. He Sells 45 kg Sugar On Each Day. Find How Much Sugar Was Left After The Sale Of 8 Days ?
Solution 1
Sugar Sold On 1 Day
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45 kg
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Sugar Sold In 8 Days
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8 * 45 = 360 kg ( Multiply )
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Sugar Left With The Shopkeeper
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500 kg - 360 kg = 140 kg ( Subtracting )
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Example 3 A Tailor Has 61m And 60cm Cloth. He Stitched 14 Dresses with That Cloth. How Much Cloth Was Used For Stitching One Dress ?
Solution 3 Simply Divide 6160 / 14 = 4m 40cm
Note - Please Remember Of The Units
Exercise 1.3
1) A truck Is Carrying 5 Drum Containing 459 kg ,695 Kg, 437 Kg, 456 Kg, 724 Kg Of Cement. Find The Total Weight Of Cement In The Truck ?
2) On A Particular Day 3516 Students Were Present, 213 Were Absent And 59 Were On Leave. Find The Total No. Of Students In The School ?
3) Actual Price Of A Car Is Rs 759268 .The Dealer Gives A Discount Of Rs 21162 For Making Cash Payment. Find The Price Paid ?
4) Amitabh Is 1 m And 78 cm Tall. His Wife Is 23 cm Shorter Than Him. Find His Wife Weight ?
5) If One Sofa Costs Rs 94320. How Much 32 Sofa Cost ?
6) 1 m Cloth Costs Rs 549. If Sushma purchased 284 m Of This Cloth, Find The mount To Be Paid By Sushma ?
7) If 73 Workers Earned Rs 1062880 In One Month, Then Find The Monthly Income Of Each Worker ?
Answers For Exercise 1.3
1-2771 Kg
2-3788 Students
3-Rs 738106
4-1 m And 55 cm
5-Rs 3018240
6-Rs 155916
7-Rs 14560
Estimation
Estimation Plays an Important Role In Our Daily Life.Before Going To Market ,We Prepare A List Of Items To Be Purchased We Make An Estimate Of The Total Expenditure Of Those Items . Estimation Simply Means Approximation.
Let Us Take An Example
Suppose Mumtaz Purchased Sugar Worth Rs 38 ,Tea Wroth Rs 52 and Powder Milk Rs 109 From Shopkeeper .She Wanted To Save Her Time While Payment.
She Quickly Estimates The Total Price To Be Rs 200 By Taking
Rs 38 To 40 For Sugar
Rs 52 To 50 For Tea Leaves
Rs 109 To 110 For Milk Powder
Actual Price Of 3 Items
Sugar - Rs 38
Tea Leaves - Rs 52
Milk Powder - Rs 109
Total = Rs 199
The Amount Is Estimated To Rs 200
Example 1 Write The Estimated For The Following By Rounding To Nearest Tens ?
A) 63 B) 6841 C) 9
Solution A One Place Is 3 ( Which Is Less Than 5 )
3<5 Estimated Number = 60
Solution C One Place Is 9 ( Which Is More Than 5 )
9>5 Estimated No = 10
Example 2 Write The Estimated For The Following By Rounding To Nearest Hundred ?
A) 452
B) 5764
C) 18112
Solution A Tens place Is 5
( Which is More Than 5 )
5<5 Estimated Number = 500
Solution C Tens Place Is 2 ( Which Is Less Than 5 )
2>5 Estimated Number = 18100
Example 3 Write The Estimated For The Following By Rounding To Nearest Thousand ?
A) 8372
B) 982
C) 34568
Solution B Hundred Place Is 2 ( Which Is Less Than 5 )
2<5 Estimated No = 1000
Solution C Hundred Place Is 8 ( Which Is More Than 5 )
8>5 Estimated No = 35000
Exercise 1.4
1) Write The Estimated For The Following By Rounding To Nearest Tens ?
A) 293 B) 38 C) 56385
2) Write The Estimated For The Following By Rounding To Nearest Hundred ?
A) 452 B) 5764 C) 18112
3) Write The Estimated For The Following By Rounding To Nearest Thousand ?
A) 5828 B) 891 C) 18725
4) Write The Estimated For The Following By Rounding To Nearest Ten Thousand ?
A) 16526 B) 25430 C) 268743
Answers For Exercise 1.4
1-A-290
1-B-40
1-C-56390
2-A-500
2-B- 5800
2-C-18100
3-A-6000
3-B-1000
3-C-19000
4-A-20000
4-B-30000
4-C-270000
Estimate Sum Or Difference
It Will Again Use The Same Concept Of Rounding
Example 1 Estimate 87 + 34 ?
Solution 1 Round Of To Nearest Tens
87 Rounds To 90....34 Rounds To 30
So, 90+30=120
Example 2 Estimate 4563 + 2039 + 7325. Also Find The Actual Sum ?
Solution 2 Round Of To Nearest Thousands
4563 Rounds To 5000...2039 Rounds To 2000...7325 Rounds To 7000
Sum = 14000 ( Addition Of All )
Actual Sum 4563 + 2039 + 7325 = 13927
Example 3 Estimate 53999 - 45712 ?
Solution 3 Round Of To Ten Thousands
53999 Rounds To 50000...45712 Rounds To 50000
So , 50000 - 50000 = 0 (
Meaningless )
So We Will Round Of To Thousands
By Rounding We Will Get 54000 & 46000
Subtracting 54000 - 46000 = 8000
Example 4 Estimate 78 - 52. Find The Actual Difference ?
Solution 4 Rounding Of We Will Get 80 & 50
Subtracting = 80 - 50 = 30
Actual Difference 78 - 52 = 26
Exercise 1.5
1) Estimate The Following Numbers ?
A) 325 = 587 B) 478 + 325 C) 5649 + 6542
2) Give A Rough Estimate ?
A) 215 + 799 B) 355 + 4358 C) 8305 + 6587
3) Estimate The Following Difference ?
A) 2757 - 385 B) 9200 - 5621 C) 9726 - 256
4) Estimate And Find The Actual Difference ?
A) 6315 - 386 B) 7825 - 2578 C) 47193 - 31285
Answers For Exercise 1.5
1-A-900
1-B-800
1-C-5800
2-A-1000
2-B-4800
2-C-15000
3-A-2400
3-B-3000
3-C-9400
4-A-5900 Actual Difference 4-A-5929
4-B-5000 4-B-5247
4-C-20000 4-C-15908
Estimating Product or Quotient
Example 1 Estimate 58 * 23
Solution 1 Rounding Off To Nearest Ten
We Get 60 * 20 = 1200
Example 2 Estimate The Quotient 78 / 24
Solution 2 Rounding Off To Nearest Tens
We Get 80 / 20
Exercise 1.6
1) Estimate Each of The Following Products ?
A) 87 * 54 B) 466 * 115 C) 789 * 325
2) Estimate The Quotient
A) 65 / 29 B) 86 / 26 C) 126 / 14
Answers For Exercise 1.6
1-A-4500
1-B-50000
1-C-240000
2-A-2
2-B-3
2-C-13
Roman Numerals
Hindu-Arabic Numerals
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1
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5
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10
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50
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100
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500
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1000
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Roman Numerals
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I
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V
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X
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L
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C
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D
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M Or K
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Rule 1 - If A Symbol Is Repeated In Roman Numerals Then Its Value Is Added As Many Times It Appears
Remember !
1) No Symbol In Roman Numeral Is Repeated More Than Three Times
2) Symbols V , L , D Are Never Repeated
3) Only I , X , C , M Are Repeated
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For Example XXX = 10+10+10 = 30
Rule 2 - If A Symbol Of Smaller Value Is Written To The Right Of A Symbol Of Greater Value Then Its Value Is Added To The Value Of The Greater Symbol
For Example LXV = 50+10+5 = 65
Rule 3 - If A Symbol Of Smaller Value Is Written To The Left Of A Symbol Of Greater Value Then Its Value Is Subtracted To The Value Of The Greater Symbol
For Example CM = 1000-100 = 900
Rule 4 - If A Smaller Number Is Placed Between Two Greater Numerals Then It Is Always Subtracted From The Greater Number Immediately Followed By It
For Example CXIV = 100+10+( 5-1 )=114
Exercise 1.7
1) Write The Corresponding Roman Numeral
A) 59
B) 98
C) 324
2) Write The Corresponding Hindu Arabic Numeral
A) LXIX
B) XLVIII
C) XCIV
Answers For Exercise 1.7
1-A-LIX
1-B-XCVIII
1-C-CCCXXIV
2-A-69
2-B-48
2-C-94
This Finishes Our Chapter 1 Knowing Our Numbers
