10. 11. 12. 13. 14. Contents Knowing Our Numbers 1-19 Whole Numbers 20-35 Playing with Numbers 36-60 Basic Geometrical Ideas 61-81 Understanding Elementary Shapes 82-107 Integers 108-124 Fractions 125-149 Decimals 150-170 Data Handling 171-193 Mensuration 194-216 Algebra 217-235 Ratio and Proportion 236-258 symmetry 259-271 Practical Geometry 272-292‘The method of expressing a number in words is called numeration, ‘While reading numbers, itis always easy to use words instead of reading individual digits, For example : Instead of reading 5632 as Five, Six, Three, Two, it is easy to read it as “Five thousand six hundred thirty wo" In this section, we shall discuss two commonly used methods of numeration, (i) Indian system of Numeration. i) International system of Numeration. Indian System of Numeration ‘The Indian system of numeration is used in India. as wellas in Bangladesh, Nepal and Pakistan, In this system, we use ones, tens, hundreds, thousands and then lakhs and crores. The first comma comes after hundreds place the second comma comes two digit later, the third comma comes afer another two digits as soon, ‘The following place value chart is used to write numbers, Periods > Crores Lakhs Thousands ‘Ones Places> | Ten | Crores | Ten | Lakhs] Ten | Thousand] Crores Lakhs Thousands |Hundreds}Tens | Ones 140000000} 10000000 | 1000000} 100000] 10000 | 1000 | 100 J 10 | 1 5 6 0 3 f2[es 4 1 3 7 2 s_j4ale ‘This place value chart is populary known as Indian Place Value Chart Reading Numbers In order to read number in the Indian system of numeration, we group place values into periods, ‘Ones’, “thousands' “lakhs, ‘crores’, “Arabs' are periods, ‘The digits in the same period are read together and the name of the period (except units) is read along with them. Thus, the number 5,43,87,539 is read as ‘five crore forty three lakh eighty seven thousand five hundred thirty nine’ Writing Numbers Consider the number ‘Seven lakh six hundred five’. This number represents a collection of 7 lakhs, no thousands, 6 hundreds, no tens and 5 units. So, it is expressed as 700605 ‘The expanded form of this number is 7 100000 +0 * 10000 +0» 1000+ 6 x 100+0 10+5%1EBD_7137 (2 tena International System of Numeration International system is followed by most of the countries of the world, In this system, we use ones, tens, hundreds, thousands, millions and billions. A number is also split into different groups called periods such as ones, thousands, millions and billions. Given below is the place value chart inthe International system, [NOTE : The digits in the same period are read together and name of the period (except ones) is read along with them, ‘Consider the number 456732001 Billions Millions ‘Thousands ‘Ones up | 18 | B| wm | ™ | mM [am] rm] mi] n{ tr lo 4 5 6 | 7 3 |2]o]o ]a (On inserting the commas after each period, we write the number 456732001 as 456,732,001 ‘Thus, this number is read as “four hundred fifty six million seven hundred thirty two thousand one”. ‘We may write this number in the expanded form as 456,732,001 = 4 * 100,000,000 + 5 * 10,000,000 + 6 « 1,000,000 + 7 » 100,000 + 3 = 10,000 + 2 1000 +1x1 of the digit in the number. COMPARISON OF NUMBERS] When the Number of Digits are Different (i) Check the number of digits in each number. ii) The number having more number of digits is the greater one than the number having less number of | digi. For example: 12456 > 2345 1534-< 12345 When the Number of Digits are the Same (Compare the left most digit ofeach number. i) Thenumber with the greater left most digit is greater For example: 4378 > 2378Knowing Or Number LT] (iii) Incase, the left most digit is same, compare the next digit ofboth numbers. The number with the greater digit is greater. For example: 5765 > 5467 ILLUSTRATION : 1 Which number is greater ? (64527 or 3482 SOLUTION : (As weknow that the number with more digits is greater. ‘Therefore, 64527 > 3482 Gi) Asweknow that ifthe number of digits in both numerals are equal, then we compare the digits at the extreme left ‘Therefore, 95806 > 85893, Eee We know that Greatest single digit number is 9 Greatest two digit number is 99 Greatest three digit number is 999 Greatest four digit number is 9999 If we add 1 to the above numbers, we get 9+ 1= 10 (smallest 2 digit number) 99 + 1 = 100 (smallest 3 digit number) 999+ 1 = 1000 (smallest 4 digit number) 9999+ 1 = 10000 (smallest 5 digit number) So, from above observation, itis clear that on adding one to the greatest number of any number of digits gives smallest number of next number of digits, TEE ae In our daily life, we have to use different units of measurements to measure different things. For liquid, we use litre o millilitre, for weight, gram or kilogram, for distance, metre or kilometre etc. You maybe familiar with £85893 o 95806 most of them, However, et us do.a quick revision, Units of mass Units of fengths Units of volume Tkg = 1,000 @ Tim= 1,000 m 1 g= 1,000, Im=100em 1L= 1000 my Ekg = 1,000,000 me, Tem= 101m 1 ky = 1,000,000 my Lay 1,000mm ILLUSTRATION : 2 How many cm makes a km? SOLUTION Weknow that, and So, 1000 « 100em 00,000 em. Thus 1,00,000 om makes a km, ILLUSTRATION : 3 How many mm makes 1m?EBD_7137 (2 temas RES ‘Thenumerals 0, 1,2,3,4, ..,9 are used in writing numbers, These numerals are originated in India and the Arabs picked them up and spread to Europe. Therefore, these are called Hindu-Arabie numerals system, ‘This is not the only system available. One of the early systems of numeration still in common use today was developed by Romans and is called the Roman numerals system, ‘Roman numerals were developed by the Ancient Romans. We can see them in the numbers on clock faces, ‘number of chapters, denoting ranks in the class, etc. Unlike the Hindu ~ Arabic numeral system, Roman numeral system uses 7 basic symbols to represent different ‘numbers, The symbols ate as follows Roman Numerals ify x L c D M Hindu-Arabie Numerals 1 3 10 30 | 100 | 300 1000) Using these symbols, we can write any number by following certain rules which are given below. Rules to form Roman Numbers Rule 1 Repetition ofa symbol in a Roman Numerals means addition, Nott i) Only I, X, C, M can be repeated. Gi) V, Land D can never be repeated Gii)_No symbol in Roman numerals can be repeated more than 3 times. For example (i) W=(+1)=2 (i) XX= (10+ 10)=20 iii) CCC = (100 + 100 + 100) = 300 (iv) MM = (1000 + 1000) = 2000 Rule 2 Ifa symbol with smaller value is written on the right ofa number with greater value, then smaller value is added to the greater value. For example : @ ViE=G+1) (i) XV= (10+ 5)= 15 iil) LX = (50 + 10) = 60 (iv) CL= (100+ 50)= 150 Rule3 Ifa symbol with smaller value is written on the left of a number with greater value, then smaller value is subtracted from the greater one. NOT! i) V, Land D are never subtracted. (ii)_ [can be subtracted from V and X only (iii) X can be subtracted from L and C only (iv) _Ccan be subtracted from D and M only. For example ow 10-1)=9 (50-10) =40 iy) CD = (500 - 100) =400 (v) CM= (1000 — 100)= 900 Rule 4 When a smaller numeral is placed between two larger numerals, it is always subiracted from the larger numeral, immediately following it. For example : (i) XIV i) CxIVKnowing Our Number LE] ‘SOLUTION : (9683 when rounded off — = 10000 4815 when rounded off +5000 Estimated sum = 15000 (ii) 3945 when rounded off 4000 1243 when rounded off 1000 Estimated difference 3000 (ii) 3042 when rounded off — = 3000 1101 when rounded off x 1000 Estimated product = 3000000 i) We can estimate the sum and difference of two or more numbers by rounding off the numbers. (Gi) We can estimate the product and quotient of two numbers by rounding off the numbers to the| greatest place. TEE Use of brackets help us to calculate in systematic and accurate way. It allows us to avoid confusion in the problems where we need to carry out more than one operations. While using brackets, first tum everything. inside the brackets ( ) intoa single number and then do the operation outside. ILLUSTRATION : 6 Is 35 x (8+2) is equal to35 x 8 +35 x2, SOLUTION : 35x (8+2)=35 x 843552 35x 10= 280+ 70 350= 350 ILLUSTRATION : 7 Solve the following with the help of bracket. NOTE: (a) 2523 (b) 25 * 98 (©) 25* 109 SOLUTION : @) 25%23=25%(20+3) [Expanding 23 a8 20+] 252025 *3 =500-+ 15575 (b) 25 x 98 = 25 x (100 — 2) [Expanding 98 as 100 ~ 2] 25 « 100-25 «2 {98 can also be expand es 90 +8) 3500 50= 2450 (9 25% 109=25«(100+9) [Expanding 109s 100-9] =25 x 100+25*9 ILLUSTRATION : 8 ‘Write the expressions for each of the following by using brackets - od by the difference of 35 and 5 le the difference of 620 and 80 by 12 (c) Eighty two divided by four times the sum of § & 2 SOLUTION : (@) 30*(35~5) (b) (620-80) +12 (©) 8254*(5+2)EBD_7137 (temas SOLUTION : ‘We know that, 1 m= 100 em 10mm 100 em 00 > 10 mm = 1000 mm, Thus 1,000 mm makes a metre, ILLUSTRATION : 4 A container has a capacity of $00 litres. Ifthe liquid presenti 2.1 500 mf, how many bottles can be filled? SOLUTION : We know that, LL = 1000 mi So, 2 L $00 m/=2500 mf oF 2.5 L ‘Therefore, number of bottles required to fill $00 litres would be- 200 So, 200 bottles are required Ha Rounding off a Number to the Nearest Ten (i) Ifthe one’s digit is less than 5, replace it by 0 For example: 23 is rounded off as 20 284 is rounded off as 280 (i) I the one’s digit is equal to or more than 5, increase the ten’s digit by 1 and replace one’s digit by 0. For example: 249 is rounded off as 250, Rounding off a Number to the Nearest Hundred (i) the ten’s digit is less than 5, replace the tens and ones digits by 0 only For example: 627 is rounded offas 600. 2434 is rounded off as 2400. (i) Whe ten’s digit is equal to or more than 5, inerease hundreds digit by | and replace each digit on its right bya. For example: 6587 is rounded off as 6600 6557 is rounded off as 6600 Rounding off a Number to the Nearest Thousand (i) I the hundreds digit is tess than 5, replace the hundreds, tens and ones digit by 0. For example: 1482 is rounded off as 1000 4341 is rounded off as 4000 (i) the hundreds digit is equal to or more than 5, increase thousands digit by 1 and replace each digit ‘on its right by 0. For example: 1877 is rounded off as 2000 5936 is rounded off as 6000 ILLUSTRATION : 5 Estimate each of the following by rounding off to nearest thousands. (9683 + 4815 ) 3945 — 1243 3042. 1101Knowing Or Number LT] CONCEPT MAP Comparing Number Tndian and Tnternational For comparing we System of Numeration numbers, the * Inthe Indian System of ‘number having numeration starting rom [To catimate or Found more disitsis| ight, mark periods as off'a number to the zgreaterthan a Units, Thousands, Laks rarest tens, ‘umber having less and Crores. The unit hundreds, thousands digit period has thee places. sete, we + For comparing two Remaining periods have “observe the digit at ‘number having ‘wo places each ‘ones, tens, hundreds, same number of + Inthe international te. resp. this digits, compare System of numeration, digits less than 5, digits at left most starting from right, mark then round off the positon. In case, periods as Units, ‘number down wards they re same, ‘Thousands and Millions. other wise upwards compare next di Each period has three and 0 on places Uses of Brackets + Brackets are used to avoid confusion in the problems having rmore than one operations. [ ] are known as rectangular brackets { } are known as euy brackets. () are known as round Otel ta Numbers Roman Numerals ~ There are seven basic symbols, brackets. ~ is ‘used in Roman known as line System for bracket ot vinculum. forming different + When more than one: ‘numbers. These set of brackets are used in an expressions, we simplify them in the order —,(), {},and (}.C2} $$ rent > eet —— SOLVED E )(AMPLES—— 1. Which s greater 96880734 0F967216832 gay yee pepe ee pee Lecusarrangethe given umbersinthepace- 8p) tt | | [ele value chart. “ ade ded? “ Tnexpandel form, wemay wit them asunder ¢ |t1/ & [eth mH | TO (i) 3,58,27,604 = (3 x 10000000) + (5 « vfetstsfolr[sta Toor) (8 100000) (2 10000) = (7 1000)=(6= 100)-(0=10)"(8 1) S]se{7j2jijejs}3 (ii) 97,34,68,256 = (9 * 100000000) + (7 « A the eres place bth have the sare digit, 10000000) + (3 ~ 1000000) + 4 = namly9. Ae elas place bth have the Toodro) = (6 » 10000)» (8 » 1000) + same digit namely 6 Bt, tthe lakhs place, (2 100) #3" 10) 461) thers numborhas$,whilethesecondhas 7,6 — Rewrite each ofthe fllowing numbers with Cleary, 7> 5 So, the second number lng proper commas, using Hence, 96721643 > 96580734. value chart: 2 Writethesmallest digit numberformed by @)_ 1286478 (iy a9earsee Also, write the number name of each in the ‘ernational system and Indian system, Sol. Let us arrange the given numerals in an international place-value chart. Then separating using the digits 0, 2 and 4 repe Sol, ‘The required number is 2024, 3. Write the greatest digit number using three 12.2 twice. different digits. the periods, we write them as shown below. Sol. The greatest three different digits are9, 8 and 7. The required number is possible only when we srations | tuowsanis | ones repeat the largest digit namely 9 four time. mw) m) wlanfrnd nl na Jol Hence, the required number is 999987. 4. Arrange the folowing : @ Papel e [a] sp racers 784,597, 2038, 175inascending order [co|_| + |» | | so] s | « [2] morse (ii) 1791, 21345, 15788, 47592 in descending bh Frode | fol order. Tn the Intemational system, we waite them in Sol. (i) Here, the greatest numbers 4897 and the words as smallest is 175 (i) One million two hundred eighty-six ascending orders: thousand four hundred seventy-five Thenseendng order © eee aes thousand five hundred eighty-two In the Indian system, these numbers ate (i) Twelve lakh eighty-six thousand four (ii) Here, the greatest number is 47592 and the smallest is 1791. ‘The descending orderis: 47592, 21345, hundred seventy-five 18788, 1791 ii) Four crore ninety-six lakh thirty-seven 5. Write the expanded form of each of the thousand five hundred eighty-two following numbers: 7. Population of Delhi was 1,29,35,297 in 1999, @ 35827604 (i)_-973468256 Itincreased by 45,34,214 in next two years, Sol, Putting the given numbers in the place-value but 13,29,417 migrated to Bombay and Bangalore. So, What was the population of chart, wehave Delhi in 20017 EBD_7137Knoxing 0 Number LT] Sol. Population of Delhi in 1999 = 1,29,35,297 Increase in population $45,34.214 Increased population 1.746951 Migrated population =13.29.417 Hence, final population in 2001 = 1,61,40,094 8 Abustravelsa distance of 356 km 500 m daily and for this travelling it consumes I /o per 15 km. Find (how much distance does the bus travel ina month of 30 days? (i)_-how much diesel does the bus consume ina month? sok @) Inidasthedntsels a distance of 356 km _ oO me in 30 days 36 500 (Cnt italy» 3 " 0000 aon titonce of 36 888 8 7 10695 000 Hence, the bus travelsa distance of 10695 km in a month. (ii) The bus consumes 1/ of diesel per 15 km. The quantity of diesel consumed by the bus for 10695 km (in 1 month) is given by 10695 = 15, 13 18) 10695 Lo: Hence, the bus consumes 713 / of diesel ina month. 9. Estimate the followin, (283+ 1732 i) 8435597 Sol. (i) Out of 283 and 1732, the smaller number is 283, Hence, we have to round off both the ‘numbers to the nearest hundred, 1732 > 1700 283 > +300 Estimated value of 1732+283 = 2000 (ii) Out of 8435 and 597, 597 is the smaller number. So, we round off these numbers tothenearest hundred, 8435 > 8400 507 > _600 Estimated value of 8435 - $97= 7800 Estimate the following 87313 Sol. Estimated product of 87 « 31 (ii) 795» 800 95 x10 Estimated product of 9 « 795 = (iil) For $46 = 7, we have to round off $46 to the multiple of 7. Let us say 490 or 560. Since $46 is closer to 560, s0 $46 should be rounded off to 560, Now, estimated value of 546=7 = 560=7=80 (iv) 1189 should be rounded off to 1200 and 56 should be rounded off to 60. Now, the estimated value of 1189 = S6= 1200 = 60=20 implify each of the following expression : 8x47) i) (7-2) x (12+ 8) ) 23+9% (6~3)-20 Sol. () 8X G+N=8% 10 Gi) (7-2) (128) (iit) 23-49 « 63) 2 =23+27-20= 50-2 0 20= 100 23+ (9x3)-20 0 12. Write the following in Hindu-Arabic ‘numerals: LXXXIX COXXVI DCXCVIL MMMCDVI Sol. Gil) CDXLVI= CD+XL + VI=400+40+ 6= 446 (iv) DEXCVI=DC+XC + VIE=600 + 90+ 7-607 () MCIX=MC +IX= 1100+ 9= 1109 IMM +CD + VI= 3000 3,406 (vi), MMMCDVI +400+6(]}_ $$ eta EXERCISE Mone DIRECTIONS : Complete the following statements with an appropriate worl /term tobe filled in the lank spaces). 1 Terore ‘llion 2, By reversing the order of digits of the greatest ‘number made by five different non-zero digits, the new number is the ‘number of five digits 3. By adding I to the greatest digit number, we get ten lakh, 4. Thenumber five crore twenty three lakh seventy eight thousand four hundred one can be written, using commas, in the Indian system of Numeration as 5. In Roman Numeration, the symbol X ean be subtracted from and C only. 6. The largest 4-digit number, using any one digit twice, from digits 5,9, 2 and 6 is. The 6-digit number +1 = F-digit smallest number. 8 Ifa symbol is ofsmaller valueis written on the of symbol larger value, then its value is added tothe larger numeral The difference of two place values of 2 in 3230452 is 10, 17819 rounded to nearest hundred is DIRECTIONS: Read the following statements and rite your answer as true or false. 1. Estimated sum of 7826 and 12469 rounded off tonearest hundredsis 20,300. 2, The largest six digittelephone number that can be formed by using digits 5,3, 4, 7, 0, 8 only once is 875403, 3. ‘Thenumber LIV is greater than LVI 4. The difference in the face value and the place value of Sin 85419 is 85414, In Roman numerals V, L and D are never subtracted. 6 The estimated value of 46,530 to the nearest hundreds 46500, 7.100 lakhs make a milion, 8 InRoman numeration, ifa symbol is repeated, its value is multipliedas many times at curs, 9. The number $1652318 will be read as eighty one crore six lakh fifty two thousand three hundred eighteen. DE DIRECTIONS : Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in column-I have to be ‘matched with statements (p,q. ) in column-I 1. Mateh the following. Column-1 Column. (A) Twohundred thousand (p) Two erore (B) Two billion () Twenty lakh (©) Twentymillion ———@) Twohundred (0) Twonillion (9) Twolakh (Oe DIRECTIONS : Give answer in one word or one sentence. 1. Write the place value of 9 in (390345 ii) 42379502 2. Arrange the following numbers in ascending order : 243795, $1395, 3795, 5343, 3. Express the following as Roman numeral : 4s i) 51 ai) 79 (iv) 92 4. Write the following numbers in words: () 33,06,759 Gil) 6,03,56,034 5. Write each of the following in Hindu-Arabie aumeral (@ CLXVI (ii), CCXXVI Gi) COCXL (iy) CDXLVT EBD_7137Knowing Our Number fi] 6. Write the folowing numbers in expanded form: (i) 81,85, 204 (ii) 7,24, 05, 620 7. Write the following numbersin figures: (i) Eight-lakh twenty thousand eighty-seven. (i) Thirty-nine lakh forty thousand thisty- eight (iii) Five crore five lakh thirty-six thousand 8 Howmany mm are therein Im? 9. How many em makes a km? 10, place the commas in each of the following, ‘numbers in both Indian and International system ‘of numeration : (iy 73325 ii) 234637 (iii) 8089627 Ee ee sentences. 1. Givethenumber name of the following in both the systems of numeration (2856721 i) 7008562 2 Is45* (10+ 3) is equal to45 x 10+ 45 ~ 3, 3. Write each of the following in Hindu-Arabie ‘numeral: () XXxxIx i), XCVIT Gi) LXXXVI iy) LXIV. Estimate the following: (. 2962+4173 Gil) $658 ~ 2846 Gi) 1242«87 iv) 4758-=26 Express each of the following numbers as a Roman numeral: @ 479 Gil) 556 (ii) 625 iv) 769) Estimate the sum (274 + 143) to the nearest hundred Estimate the difference (673 ~ 258) to the nearest hundred. A.vessel contains 51625 ml of milk is distributed among some children. Ifeach child gets 125 ml cofmilk, then find the number of children, 2m 10 emf cloth is required to stich a shirt How much cloth will be needed to stich 45 shirts? How many- (thousands make I lakh? (ii) lakhsmake 1 million? (ii) crores make 10 million? Solve the following with the help of brackets: (27 «105 (i) 2798 Gi) 27 « 109 EXERCIS co 1, Population of Sundarnagar was 2,35,471 inthe year 1991. In the year 2001 it was found to be increased by 72,958, What was the population of the city in 20017 Shekhar is a famous cricket player. He has so far scored 6,980 runs in test matches. He wishes tocomplete 10,000 runs. How many more runs ddoos he need? In one state, the number of bicycles sold in the year 2002-2003 was 7,43,000. In the year 2003- 2004, the number of bicycles sold was 8,00, 100, Inwhich year were more bicycles sold? and how many more? ‘A merchant had ® 78,592 with her. She placed an order for purchasing 40 radio sets at ® 1,200 cach, How much money will remain with her after the purchase? ‘The town newspaper is published every day. One copy has 12 pages. Everyday 11,980 copies are printed. How many total pages are printed everyday?(8) tena 6. 10. ML 2. ‘A student multiplied 7236 by 65 instead of multiplying by 56. How much was his answer greater than the correct answer? ‘The number of sheets of paper available for making notebooks is 75,000, Each sheet makes 8 pages ofa notebook. Each notebook contains 200 pages. How many notebooks can be made from the paper available? ‘Medicine is packed in boxes, each weighing 4 kg 500 g. How many such boxes can be loaded in a van which can not eatry beyond 800 kg? ‘The distance between the school and the house ofa student is km 875 m, Everyday she walks both ways, Find the total distance covered by her in six days. A vessel has 4 litres and $00 ml of curd. In how many glasses, each of 25 mil capacity, can it be filled? Give a rough estimate (by rounding off to nearest hundreds) and also closer estimate (by rounding olf to nearest tens): (439433444317 Gi). 1,08,734—47, $99 Estimate the following products using general rule: (1291 392 (i) 925029 Cn L ‘The diameter of Jupiter is 142800000 metres. Insert commas suitably and write the diameter according to International System of Numeration, Radius ofthe Earth is 6400 km and that of Mars is 4300000 m, Whose radius is bigger and by how much? In 2001, the poplulations of Tripura and Meghalaya were 3,199,203 and 2,318,822, respectively. Weite the populations of these two states in words, Chinmay had & 610000. He gave ® 87500 to Jyoti, € 126380 to Javed and & 350000 to John. How much money was let with him? ‘A mobile number consists of ten digits. First four digits are 9,9,7 and 9. Make the smallest mobile number by using only one digit twice from 8,3,5,6.0 6 Find the sum of the greatest and the least six digit mumbers formed by the digits ,0,4,7.65 using each digit only once. 7. The population of a town was 78787 in the year 1991 and 95833 in the year 2001. Estimate the increase in population by rounding off each population to nearest hundreds, 8 A-vessel has 13 litres 200 ml of fruit juice, In how many glasses each of capacity 60 ml can it be filled? 9. ‘The population of a town is 450772, Ina survey, twas reported that one out of every 14 persons is illiterate. In all how many illiterate persons are there in the town? 10, How many lakhs make five billions? 11, A loading tempo can carry 482 boxes of biscuits weighing 15 kg each, whereas a van can carry 518 boxes each of the same weight, Find the total weight that can be carried by both the vehicles, 12. Aboxcontains 5 strips, each having 12 capsules ‘of $00 mg medicine in each capsule, Find the total weight in grams of medicine in 32 such boxes. Go 1. Using 6 and 9 equal number of times, form all possible 4-digit numbers, Find the greatest and. the smallest number. 2 Ramesh buys 548 chairs and 123 tables for his showroom. Ifa chair costs €2470 and a table costs € 5664, find the total money spent byhim, 3. Thediflerence between the greatest and smallest ‘numbers which when rounded offto the nearest hundred $6700, is 4. The difference between the greatest and the smallest numbers which when rounded off to the nearest thousand as 9000, is 'S. The difference between the largest three digit ‘number and the largest three digit number with, distinet digits is 6 Write the number 235879403 1629 in words. EBD_7137Knowing ur Number Li] EXERCISE BI DIRECTIONS : This section contains multiple choice questions. Each question has 4 choices (a). (8), (0) and (d) out of which ONLY ONE is correct. 1. Which digit in the number 568731 has a place value of thousands? (8 (b) 7 ©) 6 (@) 5 2 Sum of the greatest 8 digit number and the smallest 9 digit number is (a) 199999 —(b)_ 199999999 (©) 999999999 (@)_ 10000999 3. In Indian system of numeration, the number 58695376 is written as, (a) 58,69,53,76 —(b)_ 58,695,376 (©) 5,8695,376 —(d)_586,95,376 4. Compare 67389145 and 673891450 using (>, @ < (be) > ©) = (@) None 5S. Numeral for five hundred three million eight thousand seven hundred two is (a) 500380702 (b) 503800702 (©) 503008702 (d)_ 503080702 6, 1512 when rounded offto the nearest hundred (a) 1600 (b) 1500 (©) 1510 (6) None of these ‘The smallest 4-digit number having three different digits is (@) 1102 (b) 1012 (©) 1020 (@) 1002 & 3 10000+7 «1000 +9 x 100+0« 10+4 is the same as (a) 3794 (b) 37940 (©) 37904 (@) 379409 9. The smallest 4-digit number formed by using the digits 5, 0 3, Lonly once contains (2) Gin unit's place () Sinten’s place (©) 3 inten’s place (©) Vin unit’s place (EeiEnnrre kent DIRECTIONS : This section contains multiple choice questions. Each question has 4 choices (a), (®), (c) and (A) out of which ONE or MORE may be correct. 1. Which of the following Roman symbol ean be repeated? @ 1 @ Xx 2. 24% 105 is same as (@) (20+4) = 105 (b) 24 (100-+5) (©) 24 (100-5) (d) None 3. The value of 9307 «937 ~ 9307 » 837 is (a) 93700 (b) 930700 (©) 930070 (a) 9307 « 100 4. The fivedigit number formed with the 7,5, 3 and 2 using 7 twice isare (bo) Vv @c (@) 78523 (b) 77523, (77532 (@) 77253 5. Which of the folloiwng Roman numerals is incorrect? (@) XC (b) XD (©) DM @) VL 6. Which ofthe following is meaningful? (@) VX (b) XV (© _Xxv (@) XXxv. 7. Which ofthe following is meaningful? @ cl (b) Cll ©) Ic @ xe 8. Which ofthe following is meaningful? (XIV (b) XV (©) XI (@) XxI(3)} temas rnc DIRECTIONS : Each of these questions contains «an Assertion followed by Reason. Read them carefully ‘and answer the question on the basis of following “options. You have to select the one that best describes the two statements (@)_Ifboth Assertion and Reason are correct and reason is the correct explanation of assertion. (b) Ifboth Assertion and Reason are correct but reason isnot the corret explanation of assertion, (©) IfAssertion is correct but Reason is incorrect (@)__IfAssertion is incorrect but Reason is correct, 1. Assertion: After placing commas in the number 56943821 according o international system ofnumeration, the number is written jo write a numeral in the Indian system, commas are first put after three digits from the right and then after every two digits DIRECTIONS : Study the given passage(s) and answer the following questions. PASSAGE -1 Priya read 38 pages of her storybook on Monday. She read 27 pages more on Tuesday than on Monday. She found that there were still another 220 pages le. 1, How many pages did Priya read on Tuesday? (@) 56 (&) 65 © 35 (a) 66 2. How many pages were there in the storybook? (@ 319 (by 332 (©) 323 (@) 285 PASSAGE - I ‘On Monday, the temperature of Delhi at 10 a.m. was 13°C bat by the mid-night, it fell down t0 6°C. The temperature of Chennai at 10 a.m. was 18°C but fell down to 10°C by the mid-night. 3. Which fallis greater? (a) Chennai (b) Delhi (©) Both (8) None of these 4. On Wednesday the temperature of Delhi at 12 noon was 20°C, decrease by 2°C after ev- cry two hours then what will be the tempera ture of Dethi at 8 p.m on Wednesday, (10°C (b) 20°C (© Ic (@) 18°C OT DIRECTIONS: Answer te following questions. The cansiver fo each ofthe question isa single digit integer ranging from 0 109. 1. ‘The number of zeroes that comes after | for 10 millionsis 2. Thediflerence between the greatest and smallest numbers which when rounded offa number to the nearest tens as 540, is 3. The difference of the smallest three digit ‘number and the largest two digit numbers is 4. The difference between smallest three digit ‘number having three distinct digits and smallest 3-digit numbers is 5. Thenumber of 3 digit numbers formed by using digits 3,59, taking each digit exactly once, is. EBD_7137Knowing Our Number Li] Diane 1. 10million 2. smallest 2 6 4. 5,23, 78, 401 SL 6. 9965 7. greatest Bright 9. 1,99,998 10, 17800 Dyas LT. FOR F 4 6 T. FR PF LAB). ).0)-@ oa Ey (The place value of 9 in 390345 is 90,000. (ii) The place value of 9 in 42379502 is 9,000. 2. Number having mote numberof digits is greater Clearly, 3795 < $343 < 51395 < 243795 3. Wewirte () 45.as40+5=XL+V =XLV, (i) Stass0+1=L+I=LL (ii) 79.as50+20+9=L+XX+IX=LXXIX. (iv) 92.5 90+2=XC +I1= XCIL 4. Gi) 33,06,759 =Thirty-three lakh six thousand seven hundred fifty-nine (ii) 6,03,56,034 = Six crore three lakh fifty six thousand thirty-four 5. Wehave: () CLXVI= 100+ 50+ 10+(S+ 1)= 166 i) CCXXVI= 200 +20+ (5 + 1) = 226 (ili) CCCXL = 300+ (50 ~ 10) = 340 liv) CDXLVI= (500 ~ 100) + (S010) + (+1)=446 6 (i) 81,85,204=80,00,000+ 100,000 + 80,000 +$,000+ 200+4 (ii). 7.24.05, 620=7,00,00,000+ 20,00,000-+ 4,00,000 + 5,000 + 600 +20 WYOLUTIONS Eieaet ects of Selected Questions 7. (i) Bight lakh twenty thousand eighty-seven = 8,20,087 (ii) Thirty-nine lakh forty thousand thirty-eight 39,40,038 (iil) Five crore five lakh thirty-six thousand seven. = 5,05,36,007, 8. Weknow that 1 m= 100 emand I em= 10mm So, 1 m= 100 em = 100 * 10 mm= 1,000 mm 9. Weknow that 1 km= 1000 mand 1 m= 100em So, 1 km= 1000 m= 1000 * 100 em = 100000 em= 1, 00, 000 em ‘Thus 1,00,000.em makes a km, 10. (i) 73,325 = Indian system 73,325 — International system Gi) 2,34,637 Indian system 234,637 International system, (iii) $0, 89, 627 — Indian system 8,089,627 — International system Daa rd 1. (i) Indian System of Numeration 28,56,721 ~ Twenty eight lakh, fly six thousand seven hundred twenty one, International System of Numeration 2,856,721 ~ Two million, eight hundred fifty six thousand and seven hundred twenty one, (i) Indian System of Numeration 70,08,562 ~ Seventy lakh, eight thousand and five hundred sixty two. International System of Numeration 7,008,562, - Seven million, eight thousand and five hundred sixty two. 2 45x (10 +3)=45 «13 = 585 And 45 « 10+ 45 3 = 450+ 135 = 585 Thus, 45 «(10+ 3)~ 45 10 +45 %3 3 (i) XXXIX=10+10+10+(10~1)=39. Gi), XCVIM= (100-10) + 5+ 1+ 1 +1 =90+5+3=98,(58)] temas liv) LXIV=50+10+(5 4. fi) Rounding off 2962 to thenearest thousand, we get 3000 rounding off 4173 to the nearest thousand, we get 4000 (ii) Rounding off 5658 to nearest thousand, we get 6000 Rounding off 2846 to nearest thousand, we get 3000 Estimated difference= 6000 ~ 3000 = 3000, (ii) Rounding off 1242 to nearest hundred we get 1200 Rounding off 87 to ten, we get 90 Estimated product = 1200 90 = 10800. (iv) Rounding off 4758 to nearest hundred, we wet 4800. Rounding off 26 to nearest 10, we get 30 Estimated quotient 160 30) 4800 /=30_ 180 180 00 00 0 i.e, 4800 + 30= 160 100 + 70 +9 = CDLXXIX (ii) $86= 500 +50+6=DLVI (iil) 625 = 500 + 100+ 20+ 5 = DCXXV (iv) 769 = 500 + 200 + 60 +9 = DCCLXIX 6, 274estimated to the nearest hundred = 300, 143 estimated to the nearest hundred = 100, Hence, the required estimation = (300 + 100) = 400. 7. 673 estimated to the nearest hundred = 700. 258 estimated to the nearest hundred = 300. Hence, the required estimation = (700 - 300) 400. 8 Total milk in the vessel = 51+ 625 ml (5 * 1000) ml + 625 ml 000 mi + 625 ml 625 ml Milk given to each child = 125 ml ‘Number of children = 5625 + 125=45 ‘Thus, 45 children ean be given the milk. 8. Length ofeloth equted for stiching I shirt <2 10cm (2 * 100 cm) + 10 cm. 2o0em-+ em =210em Number ofshints=45 “otal leh equed for 4 shirts a35-<210em =9450em _ 9880 = 8 94m 506m 10. Gt akh= 100 thousands {iL million = 100,000 Tah 1,00,000 1,900,000 60,000 = 10 So TOlaks make | million, (iii) 10 million = 10,000,000 1 erore= 1.000.000 000000 » 10000000 — 1 {ero will make I million AL. (i) 27 * 105 =27 * (100 + 5) cere 100827» 8 2700+ 135-2855 (ii) 27 «98 =27% 100-272 (iii) 27 * 109 = 27 * (100 + 9) Paps 00227 92700 +243 =2943 Bian: a ee) 1. Population ofthe city in 2001 = Population ofthe city in 1991 + Increase in population 2,35,471 + 72,958, Now, 238471 +1958 308429 Population ofthe city in 2001 was 3,08,429. 2. Runs that he wishes to score = 10,000 Runs scored = 6,980, Runs needed = 10000 ~ 6980 ~ 3,020 3. Cleatly, 8,00,100 is more than 7,43,000. So, in that state, more bieyeles were sold in the year 2003-2004 than in 2002-2003. EBD_7137Knowing ur Number Li] ETT ets 1 2 3. ) © @ ns: Pages read on Tuesday = 38-+27= 65, Total pages = 38 + 65 +220 = 323 Fallin Dethi’s temperature =13°C-6°C=7°C Fall in Chennai’s temperature = 18° C-10°C=8°C Clearly, 8° >7C Hence, fall in temperature of Chennai is greater. 4, (©) From 12 noon to 8 p.m. =8 hours ‘Temperature at 8 p.m. = 20°C -8°C ‘Temperature on Wednesday = 12°C, Dr @) (8) 544-535=9 @) 100-9 @) 102-100=2 ©EBD_7137 (58)} temas 8 10, nL. 2. Por L 13 200 m/= 13000 + 200 = 13200 mi number of glasses can be filled ~ 13200 = 60 20 No ofilliterate person = 450772 = 14 32198, 5 billions = 5000000000 = $0000 100000 = 50000 lakhs ‘Weight of I box = 15 ke ‘Weight of 482 boxes ‘Weight of 518 boxes Total weight, both vehicles can carry = 7230 + 7770 = 15000 kg ‘Weight of medicine in 1 capsule = 500mg ‘Weight of medicine in 12 capsules=12 «500mg = 6000 mg~6 grams ‘Weight of medicine in Istrips= 6 Weight of medicine in 5 strip ‘Weight of medicine in 1 bor ‘Weight ofmedicine in 32 boxes=32* 30=960 g 5 « 482 = 7,230 kg, ns: The possible numbers are 6699, 6969, 9696, 9966, 6996, 9669. ‘Smallest number = 6699 Greatest number = 9966 Cost of one chair ~€ 2470 Cost of $48 chairs = 2470 x $48 = 1353560 Cost of one table = ¥ 5664 Cost of 123 tables = € 5664 « 123 = 8 696672 Total money Ramesh spends = 1353560 + € 696672 2050232, ‘The greatest number which when rounded off to the nearest hundred as 6700, is 6749 ‘The smallest number which when rounded off to the nearest hundred as 6700 is 6650 ‘The required difference = 6749 ~ 665099 ‘The greatest number which when rounded off to the nearest thousand as 9000 is 9499 ‘The smallest number which when rounded off to the nearest thousand as 9000 is 8500 ‘The required difference = 9499 - 8500 =999 S.Thelargest three digit number = 999 ‘The largest three digit number with distinet digits = 987 “The required difference = 999 - 987 = 12 ‘The number contains 13 digits. Starting from the right put commas after every group of 3 digits. Thus, we have 2,358, 794,031,629, Stated in words, the number istwo trillion three hundred fifty eight billion seven hhundsed ninety four million thirty one thousand six hundred twenty nine, E Eas Pens 1. (a) Place value of 8 is $000 2. (0) Greatest -8 digit no, = 99999999 Smallest -9 digit no, = 100000000 ‘Their sum = 199999999 2 © 4. (@)_ 67389145 < 673891450 (comparing the numbers) 5. (©) 503,008,702 6 0) 7 @ & © % © 1035 DECADE kre 1 Ged) 2 (ab) 3. (id) 4. (ye) 5 (bcd) 6 (byesd) 7. (abd) 8 cd) Cini 1. (b) 56943821 is written as $6,943,821 according tolnternational place value system, Assertion: True; Reason : True and is not the correct explanation of the Assertion, 2 (@)_As 7004 rounds off to 7000 and 469 Rounds off to 500, their estimated sum = 7000 + $00 = 7500 Assertion: True; Reason: True and is the correct explanation of AssertionKnowing ur Number Li] 800100 =743000 — 057100 57,100 more biey 2003-2004. 4, Total moneyshehad = ¥ 78,592 Cost of I radioset. — =8 1,200 Cost of 40 radio sets =¥ 1,200 x 40 £48,000 78,592 ~ 48,000 = £30592 5. Each copyhhas 12 pages. 11,980 copies will have 12 * 11,980 pages. 11980 x12 23960 4119800 143760 Now, les were sold in the year Money left with her Everyilay 1, 43, 760 pages are printed, 6. Student multiplied = 7236 » 65 He was suppposed to multiply = 7236 * $6 Difference in answer = 7236 65 7236 % 56 = 7236 « (65 ~ 56) = 7236 «9 = 65,124 7. Bach sheet makes 8 pages. 75,000 sheets make 8 75, 000 pages. ‘Thus, 6,00,000 pages are available for making notebooks. Now, 200 pages make 1 notebook. Hence, 6,00,000 pages make 6,00,000 ~ 200 notebooks. Thus, 3,000 notebooks can be made. 8. Weight of | box =4 kg 500 gm or 4500 gms. ‘Maximum weighta van ean carry = 800 kg oF 800000 gms ‘Number of boxes which can be loaded = 800000 = 4500 17 "300000 4500 35000 31500 35000 31500 3500 4500 ‘Thus, the maximum no. of boxes can be loaded =17 9. The distance between school and house = 1 km 875 m (1000 +875) m = 1875 m Distance covered by her every day = 2 1875 m=3750m Distance covered by her in six days = 6 = 3750 m= 22500 m = 22 km 500 m, 10. Curd in vessel ~ 41500 ml = 4000 ml +500 .m Number of glasses that ean be. 4500 25 Rough estimate 439+ 334+ 4317 = 400 * 300 + 4, 300 = $000 (b) Closer estimate 43943644317 = 440 + 330-+ 4,320= 5,090. Rough estimate 108,734 ~47,599 1,08,700 47,600 = 61,100 (b) Closer estimate 1,08,734 ~47,599 ='1,08,730 ~ 47,600 = 61,130, m= 180 glasses 0 @ (i) @ (1291 «592 Estimated product = 1300 = 600 80,000 iy 9250 « 29 Estimated product =9000 x 30 =2,70,000 Exner 1. 142,800,000 Earth, 2100000 m 3. Tripura-three milllion one hundred ninety- nine thousand, two hundred three Meghalaya-Two million three hundred eighteen thousand eight hundred twenty two, 4. 610000 ~ (87500 + 126380 + 350000) = 46120 5. 9979003568 6. 765420 + 204567 = 969987 7. Population in 1991 = 78787 rounded to 78800 Population in 2001 = 95833 rounded to 95800 Estimated increase = 95800 ~ 78800 in poputation = 17000