Mathematics - KopyKitab · smallest nine digit number. The largest nine digit number is 999999999....

Preetika Sawhney

Mathematics

��

��

��

��

�

HOLY FAITH INTERNATIONAL (P) LTD.

5

M.Sc., M.Ed.

1

PDF _ HF Mathematics-5.psD:\data\MGS-pm65\Holy Faith\Holy Faith Mathematics-5\Prelims Page\Prelims Page.cdrWednesday, June 11, 2014 5:24:14 PMColor profile: Disabled

Composite 150 lpi at 45 degrees

C M

Y K

C M

Y K

HOLY FAITH INTERNATIONAL

We are committed to serve students with best of our knowledge andresources. We have taken utmost care and paid much attention whileediting and printing this book but we would beg to state that authors andpublishers should not be held responsible for unintentional mistakes thatmight have crept in. However, errors brought to our notice shall begratefully acknowledged and attended to.

© All rights reserved. No part of this publication may be reproduced, storedin a retrieval system, or transmitted in any form or by any means,electronic, mechanical, photocopying, recording, or otherwise without theprior written permission of the publisher. Any breach will entail legal actionand prosecution without further notice.

Published by :

MANIK JUNEJA

HOLY FAITH INTERNATIONAL (P) LTD.

MBD House, Gulab Bhawan, 6, Bahadur Shah Zafar Marg,

New Delhi-110 002

Printed at :

23x36=8 (4 colour)

New Delhi:

Mumbai:

Chennai:

Chennai:

Kolkata:Jalandhar City:

Bengaluru:

Hyderabad:Ernakulam:

Pune:

Nagpur:

Ahmedabad:

Cuttack:Guwahati:

Lucknow:

Patna:Bhopal:

Jabalpur:Goa:

Jaipur:

Raipur:Karnal:

Shimla (H.P.):Jammu (J&K):

Ranchi (Jharkhand):

Sahibabad (U.P.):Dehradun (Uttarakhand):

Delhi (Shakarpur):Delhi (Daryaganj):Delhi (Patparganj):

MBD House, Gulab Bhawan, 6, Bahadur Shah Zafar Marg

A-683, T.T.C. Industrial Area, M.I.D.C. Off. Thane-Belapur Road, Navi Mumbai

No. 26 B/2 SIDCO Estate, North Phase, Pataravakkam AmbatturIndustrial Estate, Ambattur

Plot No. 3018, Old Y Block, 3rd Street, 12th Main Road, Anna Nagar West,

Satyam Building, 46-D, Rafi Ahmed Kidwai MargMBD House, Railway Road

124/31, 1st Main, Industrial Town (Near Chowdeshwari Kalyan Mantap), West ofChord Road, Rajajinagar

3-4-492, Varun Towers, BarkatpuraSurabhi Building, South Janatha Road, Palarivattom

Survey No. 44, Behind Matoshree Garden, Kondhwa - KhadiMachine - Pisoli Road, At. Post-Pisoli

Near N.I.T. Swimming Pool, North Ambazari Road, Ambazari Layout

Godown No.10, Vedant Prabha Estate, Opp. ONGC Pumping Station,Sarkhej Sanand Road, Sarkhej

Badam Bari, Link RoadChancellor Commercial, Hem Baruah Road, Paan Bazar

173/15, Dr. B. N. Verma Road, Old 30 Kutchery Road

Ist Floor, Annapurna Complex, Naya TolaPlot No. 137, 138, 139, Sector-I, Special Industrial Area,Govindpura

840, Palash Chamber, Malviya ChowkH. No. 932, Plot No. 66, Kranti Nagar (Behind Azad Bhawan),

Alto Porvorim, BardezC-66A, In front of Malpani Hospital, Road No.1, V.K. Industrial Area,

Sikar RoadBehind Kailash Provision Store, Ravi Nagar

Plot No. 203, Sector-3, HSIDC, Near Namaste Chowk,Opp. New WorldC-89, Sector-I, New Shimla-9

MBD Office, 48 Gujjar Colony, C/o Gurjar Desh Charitable Trust, N.H. ByePass Road

Shivani Complex, 2nd Floor, Jyoti Sangam Lane,Upper Bazar

B-9 & 10, Site IV, Industrial Area

GMS Road

MB 161, Street No. 4MBD House, 4587/15, Opp. Times of India

Plot No. 225, Industrial Area

Ph. 30912330, 30912301, 23318301

Ph. 32996410, 27780821, 8691053365

Ph. 2338107, 2347371

Ph. 2248104, 2248106, 2248649, 2245648

Ph. 2131476, 8822857385

Ph. 4010992, 4010993

Ph. 2581540, 2601535

DELHI LOCAL OFFICES:MBD PRINTOGRAPHICS (P) LTD.

Industrial Area Ram Nagar, Gagret. Tehsil Amb, Distt Una (H.P.)

C MY K

C MY K

YYYYY KKKKK

The Hummingbird series of Primary Books from I to V are based on National Curriculum Framework (NCF) 2005 and the new Syllabi for classes at the Elementary Level.

In the guidelines some of the objectives of teaching the different subjects at primary stage are:

• to train children to locate and comprehend relationships between the natural, social and cultural environment;

• to nurture the curiosity and creativity of the child particularly in relation to the natural environment;

• to develop an awareness about environmental issues;

• to engage the child in exploratory and hands-on activities.

The Hummingbird series focuses on themes that allow for a connected and interrelated understanding to develop and trigger the child’s thinking in new directions. They connect knowledge to the child’s life outside the classroom and also provide an overall development of children.

The series comprises of textbooks on:

MATHEMATICS Children need to develop a positive attitude towards and a liking for Mathematics at the primary stage, along with the cognitive skills and concepts that they acquire. The content includes Mathematical games, puzzles and stories that help in making connections between Mathematics and everyday thinking.

ENGLISH An integrated approach to the teaching of language is of particular relevance at the primary level. The books address different skills of language, namely listening, speaking, reading and writing, which focus on across the curriculum approach through a variety of genres – poems, stories, role-plays and drama to develop the language skills creatively.

SCIENCE Science education should develop competence and encourage inventiveness and creativity. The textbooks incorporate activities, observation, experimentation and encourage an active approach to science, connecting it to the world around the child, rather than information based learning.

SOCIAL SCIENCE The textbooks provide the social, cultural and analytical skills required to adjust to an increasingly interdependent world. The focus of the books is on a conceptual understanding rather than lining up facts to be memorized.

ENVIRONMENTAL STUDIES Environmental Studies is a subject dealing with Man’s relation to his whole environment, viz. his surroundings, his home, his neighbourhood, his city or town, extending ever outward. The books contextualize the relevance of the subject and bring it to life.

The textbooks present the subjects in a clear, concise, logical and chronological manner. It is expected that this new series will inspire the children to analyse, demonstrate and transform their world view.

Preface

Preface.indd 1Preface.indd 1 6/11/2014 5:20:44 PM6/11/2014 5:20:44 PM

CONTENTS

��

��

��

��

�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

PDF _ HF Mathematics-5.psD:\data\MGS-pm65\Holy Faith\Holy Faith Mathematics-5\Prelims Page\Prelims Page.cdrWednesday, June 11, 2014 5:24:16 PMColor profile: Disabled

Composite 150 lpi at 45 degrees

1

KY

C M

KY

C M

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 ________________________ .

Chap-01.pmd 6/16/2014, 4:07 PM1

KY

C M

KY

C M

2MATHEMATICS-5

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

3

KY

C M

KY

C M


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

KY

C M

KY

C M

4MATHEMATICS-5

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

5

KY

C M

KY

C M


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









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

Chap-01.pmd 12/23/2014, 5:54 PM5

KY

C M

KY

C M

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










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

Chap-01.pmd 6/12/2014, 11:01 AM6

7

KY

C M

KY

C M


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

KY

C M

KY

C M

8MATHEMATICS-5

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.

Chap-01.pmd 6/12/2014, 11:01 AM8

9

KY

C M

KY

C M


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.


Then counting by tens we get : 45842105, 45842115, 45842125, 45842135 and so on.

Counting by hundreds : Gap of hundred between every two successive numbers.


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.


❑❑❑❑❑ Example 11 : Counting by lakhs write four numerals from 18241256.


❑❑❑❑❑ Example 12 : Counting by ten lakhs write four numerals from 73214632.


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

KY

C M

KY

C M

10MATHEMATICS-5

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

Publisher : MBD GroupPublishers

ISBN : 9789351807254 Author : Preetika Sawhney

Type the URL : http://www.kopykitab.com/product/12315

Get this eBook

40%OFF

https://www.kopykitab.com/Humming-Bird-Mathematics-5-by-Preetika-Sawhney

Mathematics - KopyKitab · smallest nine digit number. The largest nine digit number is 999999999....

Documents

Transcript of Mathematics - KopyKitab · smallest nine digit number. The largest nine digit number is 999999999....