Preetika Sawhney
Mathematics
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HOLY FAITH INTERNATIONAL (P) LTD.
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Preface
Preface.indd 1Preface.indd 1 6/11/2014 5:20:44 PM6/11/2014 5:20:44 PM
CONTENTS
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�CONTENTS
Numbers upto Ten Crores 1 – 22
Roman Numerals 23 – 28
Operations on Large Numbers 29
1.
2.
3. – 50
Simplification 51 – 54
Factors and Multiples 55 – 69
Fractions 70 – 90
Decimals 91 – 109
Average and Percentage 110 – 116
Ratio and Proportion 117 – 121
Measurement of Length,
Mass and Capacity 122 – 145
Time and Temperature 146 – 162
Money 163 – 172
Perimeter and Area 173 – 182
Lines and Angles 183 – 197
Volume 198 – 205
Triangles 206 – 213
Circle 214 – 220
Spatial Geometry 221 – 227
Patterns 228 – 236
Data Handling 237 – 243
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
ANSWERS 244 – 264
3
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NUMBERS UPTO TEN CRORES
Learning Objectives
➠ Eight-digit numbers ➠ Nine-digit numbers
➠ Indian place value chart ➠ Expanded form
➠ Writing the numeral ➠ Successor and predecessor
➠ Skip counting ➠ Comparison of numbers
➠ The largest and smallest numbers using given digits
➠ Rounding off numbers ➠ International system
➠ Comparison of International and Indian numeral systems
You have learnt in class IV that—
● The places ones, tens and hundreds together are called the ones period.
● The places thousands and ten thousands together are called the thousands period.
● The places lakhs and ten lakhs together are called lakhs period.
● The periods are separated by commas.
Greatest Number Smallest Number
T.L L T.Th Th H T O
(4-digits) 9999 + 1 1 0 0 0 0 (5-digits)
(5-digits) 99999 + 1 1 0 0 0 0 0 (6-digits)
(6-digits) 999999 + 1 1 0 0 0 0 0 0 (7-digits)
1. 192475 can be written as ____________________ .
2. The numeral for : 4 lakhs, 3 ten thousands, 4 thousands, 3 hundreds, 6 tens and 3 ones is____________________ .
3. 82469 can be written in expanded form as ____________________ .
4. The numeral for : 5000000 + 60000 + 4000 + 700 + 20 + 5 is ________________________ .
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5. The number name for 4507141 is ____________________ .
6. The numeral for seven lakh fifty-six thousand nine hundred thirty-four is
_______________________________ .
7. Place value of 9 in 2931458 is _________________________________ .
8. The number with 2 at ones place, 8 at tens place, 8 at hundreds place, 7 at thousands
place, 5 at ten thousands place and 9 at lakhs place is _____________ .
9. The successor of 186990 is ____________________________ .
10. The predecessor of 327400 is __________________________ .
11. Write the next three numbers that come just after 12389 : ______________ .
12. Write the three numbers that come just before 831002 : _______________ .
13. Two numbers which come in between 371999 and 372002 are _______________________ .
14. Encircle the greater number : 4592643, 452600
15. Encircle the smaller number : 658699, 656900
16. Arrange 196362, 363763, 143982 in increasing order
_______________________________________________ .
17. Arrange 462902, 464620, 465642 in decreasing order
_______________________________________________ .
18. Make the largest and the smallest numbers of 6 digits using each digit only once.
Digits Largest number Smallest number
4, 5, 7, 2 , 8, 6
19. Make the largest and the smallest numbers of 5-digits using the given digits. You may
repeat the digits.
Digits Largest number Smallest number
6 , 4, 3, 7, 1
20. 73427 rounded to the nearest tens is __________________ .
21. 386225 rounded to the nearest hundreds is ___________________ .
22. 432894 rounded to the nearest thousands is _____________________ .
23. 765746 rounded to the nearest ten thousands is _____________________ .
24. 8356821 rounded to the nearest lakh is _______________________ .
Chap-01.pmd 6/12/2014, 11:01 AM2
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NUMBERS UPTO TEN CRORES
EIGHT-DIGIT NUMBERS
Now let us learn numbers bigger than 7-digits.
We know that the largest 7-digit number is 9999999. Let us find its successor.
To do this we add 1 to 9999999.
T.L L T.Th Th H T O
9 9 9 9 9 9 9
+ 1
1 0 0 0 0 0 0 0
We get a new place value. We will call it the crores place. We write C for it.
10000000 is read as one crore. It is the smallest 8-digit number.
Thus,
7-digits : 9999999 + 1 = 10000000 (8-digits)
Thus, 8-digit number means we have one place further to
the left in the place value chart.
NINE-DIGIT NUMBERS
Now let us learn numbers bigger than 8-digits.
We know that the largest 8-digit number is 99999999. Let us find its successor.
To do this we add 1 to 99999999.
C T.L L T.Th Th H T O
9 9 9 9 9 9 9 9
+ 1
10 0 0 0 0 0 0 0
We get a new place value. We will call it the ten crores place.
We write TC for it. 100000000 is read as ten crore. It is the
smallest nine digit number. The largest nine digit number is
999999999.
Thus, 8-digit : 99999999 + 1 = 100000000 (9-digits)
Thus, 9-digit number means we have one place
further to the left in the place value chart.
Crores and ten-crores together are crores period.
8-digit number begins
in the crores place.
1 hundred lakhs is
also called one crore.
● 100 thousand make
one lakh
● 100 lakhs make one
crore
How many 7-digits numbersare there ?
[Hints–9999999—999999]
Chap-01.pmd 6/12/2014, 11:01 AM3
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INDIAN PLACE VALUE CHART
Indian System
Place Value Chart
Periods CRORES LAKHS THOUSANDS ONES
Places
2 6 6 7 8 2 4 9 4
Ones period has three places — Ones, tens, hundreds
Thousands period has two places — One thousands, ten thousands
Lakhs period has two places — One lakhs, ten lakhs
Crores period has two places — One crores, ten crores
Reading a numeral : All the digits in the same period are
read together and the name of the period (except ones) is
read along with them.
Thus, we read 26 67 82 494 as — Twenty-six crore sixty-
seven lakh eighty-two thousand four hundred ninety-four.
❑❑❑❑❑ Example 1 : Write the number name of the numeral 23 90 11 237
Solution : T.C C T.L L T.Th Th H T O
2 3 9 0 1 1 2 3 7
We read it as — Twenty-three crore ninety lakh eleven thousand two hundred thirty-seven.
We read 16 38 07 520 as — Sixteen crore thirty-eight lakh
seven thousand five hundred twenty.
Finding the place value of a digit in a numeral
Find the place value of the digit underlined in each
numeral.
(a) 3 68 45 372 — 8 is in the lakhs place. So its
place value is 8 lakhs or
8 00 000
Ten
Lak
hs
10 0
0 0
00
Ten
Cro
res
10 0
0 0
0 0
00
One
Cro
res
1 0
0 0
0 0
00
One
Lakh
s
1 0
0 0
00
Ten
Thousa
nds
10 0
00
One
Thousa
nds
1000
Hundre
ds
100
Ten
s
10
Ones
1
10 ten lakhs = ____ crore
To write the place value of a digit
in a number, write the digit and
write ‘0’ for all other digits to its
right.
Place value of 2 in 1234689 is
200000
Chap-01.pmd 12/23/2014, 5:54 PM4
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NUMBERS UPTO TEN CRORES
10 L
akhs
Cro
res
Lakh
s
10 T
housa
nds
Thousa
nds
Hundre
ds
Ten
s
Ones
(b) 14 25 86 305 — 4 crores or 4 00 00 000
(c) 34 53 01 649 — 3 ten crores or 30 crores or 300000000
(d) 485 98 364 — 3 hundreds or 300
❑❑❑❑❑ Example 2 : Write the numeral seventeen crores
eighty-two lakh six thousand nine
hundred three.
Solution : The number represents 1 ten crore 7 crores,
8 ten lakhs 2 lakhs, 6 thousands, 9 hundreds 3 ones.
Arrange these digits in the place value chart.
Place Value Chart (Indian System)
Periods CRORES LAKHS THOUSANDS ONES
Places
1 7 8 2 0 6 9 0 3
We find that places — ‘10 thousands’ and ‘tens’ are vacant. So, we put 0 to complete the
numeral.
Thus, the numeral is 178206903.
EXPANDED FORM
A number when expressed as a sum of the place values of its digits is said to be in expanded form.
T.C C T.L L T.Th Th H T O
6 4 3 2 4 2 1 7 8
Place value of 8 is 8
Place value of 7 is 70
Place value of 1 is 100
Place value of 2 is 2000
Place value of 4 is 40000
Place value of 2 is 200000
Place value of 3 is 3000000
Place value of 4 is 40000000
Place value of 6 is 600000000
REMEMBER
Lakhs has 2 places, thousands has
2 places and ones has 3 places.
Mark the periods using commas
(,) for convenience.
10 C
rore
s
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6MATHEMATICS-5
Expanded form of 643242178 = 600000000 + 40000000 + 3000000 + 200000 + 40000
+ 2000 + 100 + 70 + 8
T.C C T.L L T.Th Th H T O
4 9 3 5 6 7 1 2 8
Place value of 8 is 8
Place value of 2 is 20
Place value of 1 is 100
Place value of 7 is 7000
Place value of 6 is 60000
Place value of 5 is 500000
Place value of 3 is 3000000
Place value of 9 is 90000000
Place value of 4 is 400000000
Expanded form of 493567128 = 400000000 + 90000000 + 3000000 + 500000 + 60000
+ 7000 + 100 + 20 + 8.
❑❑❑❑❑ Example 3 : Write the following numbers in expanded form :
(a) 12598623 (b) 473416258
Solution : (a) 12598623 = 10000000 + 2000000 + 500000 + 90000 + 8000 + 600 +
20 + 3
(b) 473416258 = 400000000 + 70000000 + 3000000 + 400000 + 10000 +
6000 + 200 + 50 + 8
WRITING THE NUMERAL
To write the numeral for any number given in words, draw the place value chart and fill
in the numbers according to the periods and places. If there are any vacant places, fill them
with zeros.
❑❑❑❑❑ Example 4 : Write the numeral for six crore fifty-three thousand one.
Solution : Arrange the digits in the place value chart as :
C T.L L T.Th TH H T O
6 5 3 1
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NUMBERS UPTO TEN CRORES
Fill in the vacant places with zeros
C T.L L T.Th TH H T O
6 0 0 5 3 0 0 1
So, the numeral for the given number is 60053001.
❑❑❑❑❑ Example 5 : Write the numeral for the following :
(a) 700000 + 40000 + 5000 + 300 + 20 + 1
(b) 4000000 + 500000 + 60000 + 2000 + 400 + 30 + 5
Solution : (a) 700000 + 40000 + 5000 + 300 + 20 + 1 = 745321
(b) 4000000 + 500000 + 60000 + 2000 + 400 + 30 + 5 = 4562435
1. Write the place value of each digit of the following numbers :
(a) 24684135 (b) 23467802 (c) 478095386 (d) 8534656
2. Write the following numbers in the place value chart :
(a) 13525246 (b) 253408976 (c) 363975845 (d) 338532467
3. Write the number name for each of the following (in Indian system) :
(a) 32467504 (b) 534587126 (c) 95271843 (d) 382467500
4. Write the numeral for each of the following (in Indian system) :
(a) Six crore four lakh thirty-two thousand eight hundred sixty-nine.
(b) Seventy crore eight lakh seventy-nine thousand nine hundred seven.
(c) Six crore thirty-two lakh forty-nine thousand seven hundred fifteen.
(d) Seventy-two crore twenty-four lakh fifty- two thousand nine hundred twenty-nine.
5. Write the following in expanded form :
(a) 35425689 (b) 526078493 (c) 74590561 (d) 397254168
6. Write the numeral for each of these :
(a) 70000000 + 500000 + 80000 + 7000 + 100 + 90 + 1
(b) 900000000 + 600000 + 70000 + 8000 + 200 + 30 + 4
(c) 300000 + 70000 + 9000 + 300 + 8
(d) 3000000 + 400000 + 60000 + 8000 + 300 + 10 + 5
(e) 800000000 + 80000 + 80 + 8
7. Write the period, place and place value of the underlined digits :
(a) 634500432 (b) 798045632 (c) 72463921 (d) 463127983
(e) 12493459
LET US PRACTISE 1.1
Chap-01.pmd 6/12/2014, 11:01 AM7
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SUCCESSOR AND PREDECESSOR
The number that comes just after a given number is called its SUCCESSOR.
43123246 comes just after 43123245. So, 43123246 is the successor of 43123245.
154818321 is the next to 154818320. So, 154818321 is the successor of 154818320.
● We can obtain the successor of a number by adding 1 to it.
Successor of 1743245 is 1743245 + 1 = 1743246.
Successor of 314218320 is 314218320 + 1 = 314218321.
● We can add 1 to any number, so every number
has a successor.
● The number that comes just before a given
number is called its PREDECESSOR.
34234072 comes just before 34234073. So,
34234072 is the predecessor of 34234073.
154349099 is just before 154349100. So,
154349099 is the predecessor of 154349100.
● We can obtain the predecessor of a number
by subtracting 1 from it.
Predecessor of 1424073 is 1424073 – 1 =
1424072.
Predecessor of 232849100 is 232849100 – 1 = 232849099.
❑❑❑❑❑ Example 6 : (a) Write the successor of 36245195.
(b) Write the predecessor of 678134707.
(c) Write two numbers just after 45943499.
(d) Write two numbers just before 315768178.
Solution : (a) Successor of 36245195 = 36245195 + 1 = 36245196.
(b) Predecessor of 678134707 = 678134707 – 1 = 678134706.
(c) Successor of 45943499 = 45943499 + 1 = 45943500.
Successor of 45943500 = 45943500 + 1 = 45943501.
Required numbers are 45943500 and 45943501.
(d) Predecessor of 315768178 = 315768178 – 1 = 315768177.
Predecessor of 315768177 = 315768177 – 1 = 315768176.
Required numbers are 315768177 and 315768176.
The number ‘after’ another number
can be obtained by adding 1.
The number ‘before’ another
number can be obtained by
subtracting 1.
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NUMBERS UPTO TEN CRORES
SKIP COUNTING
In skip counting we start with a given number and write more numbers with a fixed gap
between the successive numbers.
Counting by twos : Gap of two between every two successive numbers.
Suppose we start with 14128581 .
Then counting by twos we get : 14128581, 14128583, 14128585, 14128587 and so on.
Counting by tens : Gap of ten between every two successive numbers.
Suppose we start with 45842105 .
Then counting by tens we get : 45842105, 45842115, 45842125, 45842135 and so on.
Counting by hundreds : Gap of hundred between every two successive numbers.
Suppose we start with 313352108 .
Then counting by hundreds we get : 313352108, 313352208, 313352308, 313352408
and so on.
❑❑❑❑❑ Example 7 : Counting by fours write four numerals from 362143285.
Solution : 362143285 + 4 = 362143289; 362143289 + 4 = 362143293;
362143293 + 4 = 362143297; 362143297 + 4 = 362143301
The numerals are: 362143289, 362143293, 362143297 and 362143301.
❑❑❑❑❑ Example 8 : Counting by two hundreds write four numerals from 54282147.
Solution : The numerals are : 54282347, 54282547, 54282747, 54282947.
❑❑❑❑❑ Example 9 : Counting by thousands write four numerals from 62872147.
Solution : The numerals are : 62873147, 62874147, 62875147 and 62876147.
❑❑❑❑❑ Example 10 : Counting by ten thousands write four numerals from 41522147.
Solution : The numerals are : 41532147, 41542147, 41552147 and 41562147.
❑❑❑❑❑ Example 11 : Counting by lakhs write four numerals from 18241256.
Solution : The numerals are : 18341256, 18441256, 18541256 and 18641256.
❑❑❑❑❑ Example 12 : Counting by ten lakhs write four numerals from 73214632.
Solution : The numerals are : 74214632, 75214632, 76214632 and 77214632.
1. Write the successor of each of the following :
(a) 25876134 (b) 75214663 (c) 414252103 (d) 734337142
2. Write the predecessor of each of the following :
(a) 82147643 (b) 932421217 (c) 976521811 (d) 876321449
LET US PRACTISE 1.2
Chap-01.pmd 6/12/2014, 11:01 AM9
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3. Write the next two numbers for each of the following :
(a) 74425131 (b) 86433146 (c) 2843647031 (d) 287364983
4. Write the two numbers that come just before each of the following :
(a) 73284632 (b) 207463415 (c) 73146283 (d) 930142561
5. Write the next three numbers for each of the following :
(a) 43286400 (b) 82146236 (c) 82464754 (d) 963258451
6. Write three numbers that come just before each of the following :
(a) 82147612 (b) 97643248 (c) 821473811 (d) 763214402
7. Write two numbers which come in between :
(a) 1284192 and 1284195 (b) 63422496 and 63422499
(c) 314214763 and 314214766 (d) 2147248 and 2147251
8. Write three numbers that come in between :
(a) 43525271 and 43525275 (b) 512474357 and 512474361
(c) 7418529 and 7418533 (d) 19769742 and 19769746
9. Find :
(a) Counting by threes write four numerals from 13938545.
(b) Counting by seven hundreds write four numerals from 39754203.
(c) Counting by five thousands write four numerals from 386847641.
(d) Counting by three lakhs write four numerals from 824125603.
(e) Counting by ten lakhs write four numerals from 321463245.
COMPARISON OF NUMBERS
The signs of comparison
The 'equal to' ( = ) sign shows that numbers on both sides have the same value.
232584 = 232584, 6364925 = 6364925 etc.
The 'greater than' ( > ) sign shows that the number on the left side has a greater value than
that of right.
823147 > 821874, 7436925 > 5272584 etc.
The 'less than' ( < ) sign shows that the number on the left side has a smaller value than
that of right.
153147 < 292874, 4426925 < 7772584 etc.
Chap-01.pmd 6/12/2014, 11:01 AM10
Humming Bird Mathematics-5
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ISBN : 9789351807254 Author : Preetika Sawhney
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