Unlock the Passwords Look at the picture. Honey, the butterfly has forgotten the password needed to unlock the gates. The password to unlock each of the gates is a 2-digit number. Obtain the passwords by solving the questions. The passwords are the first two digits of your answer from the left. Find the passwords and help Honey reach the end. Unlo ‘Sum of the place value of 6 in 36,459 and the face 7 value of 3 in 42,345 Oo s = - Numeral for forty-five ‘thousand six hundred \e : ' ee i Standard form of Round off 34,893 to 10,000 + 3,000 + 500+9 the nearest hundredsameer was playing his oie video game. Once the game was over, he looked at his score. He was surprised to see that his score was 1000000. He wos finding it difficult to read such a large number. Let us help him. There are two ways in which we can read large numbers. 1. Indian Place Value Chart 2. International Place Value Chart We know that, the greatest 6-digit number is 999999. When we add | to it, we get the smallest 7-digit number i.e., 1000000. Again, the largest 7-digit number is 9999999. If we add | to the greatest 7-digit number, we get the smallest 8-digit number, ie., 10000000. Similarly, the greatest 8-digit number is 99999999. Can you find the greatest and the smallest 9-digit numbers? Let us now observe the Indian place value chart. The place value chart for our Indian number system is as shown below. Thousands | Ones Crores | Lakhs : Ten Crores | Crores | ten Lokhs| Lakhs |__Ten Thousands 10,00,00,000 00,000} 10,00,000 1,00,000 (dais) | (@.cigis) | 17 digits) (6 digits) Thousands] Hundreds | Tens | Ones | 10,000 {S digits) 1,000 100 10 1 (4 digits) | (3 digits) | (2 digits) |(1 diait)In the place value chart, the place value of a digit is ten times the place vaiue of the next digit on the right. Thus, J ten = 10 ones | hundred = 10 tens ] thousand = 10 hundreds 1 ten thousand = 10 thousands lakh = 10 ten thousands 1 ten lakh = 10 lakhs ] crore = 10 ten lakhs ten crore = 10 crores Use of Commas We use commas to separate the periods which helps us to recognise the number names easily. For example, consider the number 6543215. It can be written as 65,43,215. Here, the digits are separated by commas. The digits in the same period are read together and the name of the period is read alongside. Indian Place Value Chart Number Lakhs Thousands Ones 65,43,215 é 5 4 3 2 1 ) It is read as sixty-five lakh forty-three thousand two hundred fifteen. Similarly, consider the number 85623612. We can represent it using the Indian system of numeration as follows: Indian Place Value Chart 8,56,23,612 It is read as eight crore fifty-six lakh twenty-three thousand six hundred twelve.Exercise {4 n the place value chart. 1. Write the given numbers 0! a aon e | esl Number | TC Deal é 5 | 152165238 | | 5 a | 1527398 ~ 53567695 34610276 e. | 198761432 alo|o\e o the Indian system of numeration. 68,98,002 2. Insert commas according tt a. 6898002 . 862420028 . 53086198 |. 830609760 . 75639125 351721346 9 ang 3. Write the numerals for the following number names. a. Fifty-seven lakh thirty 57,00,030 'b. Six crore eight lakh thirty thousand twelve ra ¢. Four crore thirty-three lakh forty-five thousand three hundred six pes. d. Sixteen crore four lakh sik thousand ni hundred sixty-eight ea any. ©. Thirty-six crore forty-seven lakh ‘i se thousand seven hundred two lee eee Twenty crore two }. Forty-six crore eight lakh five thousand seven4. Write the following numerals in words using the Indian system of numeration. Number Number Names a 1,47.32516 | One crore forty-seven lakh thirty-two thousand five hundred sixteen By 67,89,021 Ce 6,00,56,715 Gli 3,25,17,920 e. 81,09,81,012 f 56,82,15,382 g. 9,00,70,000 Place Value and Face Value The place value of a digit depends on the position of the digit in the place value chart, whereas the face value of a digit is the digit itself. For example, consider the number 3,58,64,321 and write the place value and face value of 5 and 4. Let us first write the given number on the place value chart. c TL L TTh Th H T °o = 3 5 8 6 4 3 2 1 : Now, using the place value chart, we have Number Place Value | Face Value 3,58,64,321 50,00,000 5 | . 3,58,64,321 4,000 4 Help the students understand that the place value of O lalse, zero always has the same place value and face fExample: Find the sum of the place value of 9 and the face value of _ a the number 13,96,05,432. Solution: Here, the place value of 9 is 90,00,000 and the face value of . iso, 9000009 i 5 "a 2000005 Ra Thus, 90,00,000 + 5 = 90,00,005. Expanded Form and Standard Form The expanded form of a number is a way of expressing it as the sum of the place value of all its digits. For example, the expanded form of 9,53,24,123 is 9,00,00,000 + 50,00,000 + 3,00,000 + 20,000 + 4,000 + 100 + 20 + 3. Similarly, the expanded form of 2,13,72,565 is 2,00,00,000 + 10,00,000 + 3,00,000 + 70,000 + 2,000 + 500 + 60 + 5. When a number is written in figures, it is known as the standard form. It is also called short form. For example, the standard form of 3,00,00,000 + 40,00,000 + 3,00,000 + 20,000 + 1,000 + 500 + 20 + 3 is 3,43,21,523, Similarly, the standard form of 10,00,000 + 200,000 + 50,000 + 9,000 + 300 + 60 + 7 is 12,59,367. 1. Write the period, place value and face value of the encircled digits. Number Period Place Value Face Value a. 76,28,007 b. Q5,36,259 cc. @1,28,09,712 d. 3,66,29,100 EPC Lan 32,67,890.7 pare the digits starting ee i we com rule 2. If the number of digits are the same, ight. from the left to the righ er For example, consider the numbers 43,47,230 a reer hcich Here, the number of digits are the same so we sia! / Thus, we get es Thus, 43,47,230 < 43,57,651. Ascending and Descending Orders When the numbers are aranged from the smallest to the largest, they are said to be in ascending order. For example, 35,64,321; 72,69,000; 1,23,45,631; 2,24,00,000 When the numbers are arranged from the largest to the smallest, they are said to be in descending order. For example, 9,87,65,321; 5,43,21,500; 74,65,469; 32,23,650 1. Insert >,< or = sign in the space provided. a. 91,56,281 29,51,207 b. 81,50,501 | 81,50,501 Cc. 6,66,67,777 | 6,66,67,888 — d. 23,00,123 | 24,67,123 €. 66,77,44,881 56,297,123 f. 25,67,963 25,68,988 2. Arrange the following numbers in ascending order. Q. 26,47,212; 34,39,107; 12,12,112: 68,39,393 b. 3,85,47,986; 38,54,79,860; 38,54,798; 38,54,79,850 C. 1,86,53,496; 33,85,34,896; 43,85,34,896; 9,99,99,999 d. 6,34,398; 66,64,398: 6,66,64,398; 4,39,86,666 3. Arrange the following numbers in descending order. Q. 51,52,63,786; 50,20,101; 91,21,216; 70,009 b. 33,29,567; 34,26,799: 34,15,999; 30,25,859 C. 12,34,56,789; 23,45,67,891: 34,56,78,912; 34,56,78,901 d. 57,83,421; 5,78,34,210; 57,83,42,100; 47,83,42,100To form the largest number using the given digits, we arrange the digits in the descending order whereas to form the smallest number, we arrange the digits in the ascending order. Example 1. Form the largest and the smallest 8-digit number using the given digits, without repetition. COECCeCEe Solution: We know that, 0<2<3<5<6<7<8<9 Largest 8-digit number - 9,87,65,320 Smallest 8-digit number - 2,03,56,789 Example 2. Form the largest and the smallest 7-digit number using the given digits, with repetition. CoUew Solution: The largest 7-digit number formed is 99,97,650 and the smallest 7-digit number formed is 50,00,679. The number that comes just after the given number is called the successor ‘of that number. This can be obtained by adding | to the given number. For example, consider the number 3,56,23,129. The successor of 3,56,23,129 is 3,56,23,129 + 1 = 3,56,23,130. The number that comes just before the given number is called the predecessor of that number. This can be obtained by subtracting 1 from the given number. For example. consider the number 12,34,78,699.. The predecessor of 12,34,78,699 is 12,34,78,699 — 1 = 12,34,78,698.st and the smallest number using all the given digits, . Form the large: without repetition. b. 642 Write the predecessor of the following: Q. 23,42,105 b. 3,54,69,231 Cc. 2,69,54,320 d. 15,89,69,015 ©. 56,24,35,961 f. 1,29,79,562 . Write the successor of the following: a. 16,75,333 b. 38,25,511 c. 1,20,35,685 G. 24,72,13,659 ©. 1,75,36,922 f. 20,41,9234, Form the number by repeating the given digits. a. Smallest 8-digit number i, 3,4,0,5,6 i, 9.1,5,6,2 ii, 1.5623 b. Largest 9-digit number i. 7,8,0,5,6 i, 3,1.5,.8,0 ii, 9.6512 Millions Thousands Ones Hundred | Ten | a Hundred | Ten 7 Mitions | itions | MMPS |mousanas|thousands| "ousenes|Hunareds) Tens | ones 100,000,000 | 10,000,000] 1,000,000} 100,000 | 10,000 | 1,000 100 10 1 (9 digits) | (8 digits) | (7 digits) | (6 digits) | (5 digits) | (4 digits) | (3 digits) | (2 digits) | (1 digit) In the above table, there are 3 periods — the ones period, the thousands period and the millions period. In the Intemational system of numbers, we separate the periods using commas by placing it after every 3-digits. For example, 361257901 is written as sea Ue ae 361,257,901. in a million. In the Intemational system of numbers, we use | 1 hundred thousands and millions instead of ‘fo lakhs and crores. Consider the number 56923520. Let us place commas and write its number name using both Indian and International system of numeration. Indian System 5,69,23,520 — Five crore sixty-nine lakh twenty-three thousand five hundred twentyfem Intemational Sys1 and five hundreg 56,923,520 — Fifty-six mill twenly Thus, on comparing, We get : et International System ion nine hundred twenty-three thous Indian System One Hundred Thousands 1,00,000 = One Lakh 100,000 - 10,00,000 — Ten Lakhs 1,000,000 - One Million - One Crore 10,000,000 — 1,00,00,000 Ten Millions = One Hundred Millions 10,00,00,000 - Ten Crores 100,000,000 MATH LAB IDEAS ioreeet a eee on an abacus, take an abacus and place jumber of beads on each spil nae spike as represented by the face value For example, for represent esi presenting the number 1,25,67,830 on an abacus, Now, write the numbe: name usit . system of numeration. me vsing both Indian and international Repeat this activity and represent other numbers.\ i Exerd 15 Write the numbers on the place value chart. Number HM|™ | M | HTh ia [a 1 a, [261271351 2 | 6 | 1 |-2 ieee lee — + + b. | 27682035 | hina Baas - a c. [560760890 | | | ape + T T 7 d. [101876815 | | fede [4573921 to aleldee le fi Bue lil isles Rewrite the following numbers, using the periods of the International place value chart. a. 80,80,80,808 b. 17,06,542 c. 7,22,60,318 d. 6,00,80,308 Write in words using the International number system. Numeral | Number Names Six hundred thirty-five million two hundred one a. | 635,201,385 thousand three hundred eighty-five b. | 9,300,007 c. | 307,101,202 bee i 82,525,111 | 123,456,789 100,000,1114. Write in numerals. a. Four hundred thirty-eight milli sixty-five thousand seven hun b. Ninety-eight crore twelve lakh forty-eight ion six hundred dred forty-eight pee thousand four hundred two ea c. Fighteen crore twenty-six lakh two thousand nine hundred six —— d. Eight hundred million six hundred eighty-one thousand four hundred one 5. Write the number names of the following numerals. a. 166,000,784 b. 14,40,72,706 c. 23,602,414 d. 6,75,13,006 €. 1,18,43,006 6. Insert commas according fo the Indian and International systems. Number Indian System International System a. | 23012351! 2,30,12,351 23,012,351 b. | 235060081 c. | 981002526 d. | 70951210 a e. | 46812127 ifs 505125621 7. Mrs Singh has a bungalow worth & 1532 f b 16215. Place commas and write the number name using both Indian and intemaicndl systems.Sonia and Chinmayee are studying the concepts of rounding off. They revisit the concepts already learnt in their previous class by observing the table given below. Round off to the nearest | Numbers Tens Hundreds Thousands 1,935 1,940 1,900 2,000 82,613 82,610 82,600 83,000. 35,946 35,950 35,900 36,000 4,61,575 4,61,580 4,61,600 4,62,000 After revising the concepts they study the rules of rounding Off to the nearest ten thousands. In this case, they studied that if the digit at the thousands place is less than 5, round off the number to the earlier lower multiple of 10,000 and if the thousands digit is 5 or more than 5, round off the number to the next higher multiple of 10,000. Example: Round off the following numbers to the nearest ten thousands. a. 6,13,575 b. 3,15,696 Cc. 7,51,98,465 Solution: a. 6,13,575 is rounded off to 6,10,000 as the thousands digit is 3 and 3 < 5. b. 3,15,696 is rounded off to 3,20,000 as the thousands digit is 5 and 5 = 5. 7,51,98,465 is rounded off to 7,52,00,000 as the thousands digit is 8 and Gy 17,91 98: 8>5. qg1s Complete the given table. ) the | Round off to the | Round off to the | Round off to | Rump nearest 10 nearest 100 nearest 1000 36,754 29,64,372 3,91,24,983 4,26,390 3,46,579 3,43,21,053 2,21,96,576 7,56,34,215 Round off the following numbers to the nearest ten thousands. a. 46,257 b. 3,17,963 iG 21,726 d. 14,957 e. 1,20,500 f. 31,256 g. 2,16,532 h. 1,96,757 i. 8,13,421 Anil purchased a car costing €15,42,795. Round off the cost of the car to the nearest tens, hundreds, thousands and ten thousands. The principal of XYZ school wants to construct Q separate building for primary classes. The expenditure for the cost of construction is %3,15,62,196. Round off the cost to the nearest ten thousands. Arrange the digits 3, 6, 5, 7 in such a way that it forms a number that becomes 6,000 when rounded off to the nearest thousands. How many such numbers can be formed from the given digits?Take 8 paper cups and a packet of beads. Now, using a sketch pen name them as shown. Ask a student to put the beads from the packet in the cups. The student cannot put more than 9 beads in a cup and can also skip putting the beads in a cup. However, the student must put beads in the cup labelled C. Now, ask the other student to count and speak aloud how many beads are there in each cup. Rest of the students will write down the number of beads in each cup. Now, ask each student to write the number name using the Intemational system of numeration, and also form the smallest and the greatest 8-digit number. The student who completes the task first will call out DONE and show it to his/her teacher. Link to if. The class teacher divides the class into groups of four and cs provides each group with an abacus to represent the ¢ number 42,65,30,238 correctly. Also, write its number name using both Indian and Intemational system of numeration. While working, by mistake the abacus of Rahul's group fell down and broke. The group without losing hope, worked as a team and joined the pieces of the abacus. The group also managed to represent the number and answer the questions correctly. 1. Represent the number on the abacus and also write its number name which Rahul's feam answered. 2. Discuss why it is important to be positive even in the worst situation. 3. Discuss why it is important to work together. Also, talk about the last time you worked together as a team.There are 7 symbols in the Roman numeral system to write numbers. itv [xe Le | 2 | ™ | Roman Numerais 1 [5 | 10 | 0 | 100 | 500 | 1000 | Hindu-Arabic Vaiues Rule 1. The 7 symbols are used in different combinations involving addition or subtraction to form numbers. Examples: lil=1+1 = 2 XX =10+10=20 IX=10-1=9 V=S—1) =4 Rule 2. Symbols |, X, C, M can be repeated 3 times at any given time, Symbols V, L, D cannot be repeated. XXX = 10+ 10+ 10=30 000 + 1,000 + 1,000 = 3,000 Rule 3. Symbol | can be added to or subtracted from symbols V and X only. Examples: MW=14+1+1=3 CCC = 100 + 100 + 100 = 300 MMM Examples: Vi=5+1=6 WH=S-1=4 xXl=10+1=11 IX=10-1=9 Rule 4. Symbol X can be added to or subtracted from L and C only. Examples: LX =50+10=60 XL = 50-10= 40 CX= 100 + 10=110 XC = 100-10=90 Rule 5. Symbol C can be added to or subtracted from D and M only. Examples: DC = 500+ 100 = 600 CD = 500 - 100 = 400 MC = 1,000 + 100 = 1,100 CM = 1,000 - 100 = 900 Reading large Roman numbers can be confusing sometimes. This can be made simpler by splitting the given Roman number into different symbols and then considering them one at a time. Example: Which number does MCML denote? Solution: Let us find MCML using the following steps. Step 1: M = 1,000 = 1,000 Step 2; CM Step3: L 1,000-100 = 900 " 8 ih 8Addition and Subtraction of Roman Numerals Example 1. Add CDXC and CML. Solution: Here, CDXC = (500 - 100) + (100 - 10) = 400 + 90 = 490 CML = (1,000 — 100) + 50 = 900 + 50 = 950 Hence, 490 + 950 = 1440 = MCDXL, Example 2. Subtract DCLIV from MDLXXXVII. Solution: Here, DCLIV = 500 + 100 + 50+ (5-1) = 500 + 100 + 50 + 4 = 654 MDLXXXVII = 1,000 + 500 + 50 + 10 + 10 + 10 + 7 = 1,587 Hence, 1,587 — 654 = 933 = CMXxXxXill. 1. Write the Roman numerals for the following: a. 1,100 = b. 900 = ce, 2,000 = d. 1,650 = e. 600 = f. 1,020 = 973125 >= h. 1,347 = i 1,525 = [731 = kK. 1.765 = 1.2130 = 2. Write the Hindu-Arabic numerals for the following: a. LX = b. XL = CEX = d. CDXX = e. MDCCCLX = f. MCMXL = g. MCDXCVI = h. MMCCCX = i, CLXXXIX = j. DCCLXX = |. MDCXxI k. CCXCIV3. Cross out (x) the numerals which do not represent Roman numerals, a. Ix be Vi ey e. UL VV e. MMD f, VIV 4. Simplify and express your answer as a Hindu-Arabie numeral. a. MDC + MMMDCL b. CCCXX - XVI c. XVI + XXXIll d. MMMDCL — MCMXCVIII e. MCCLVI + MDIX f. MMCCCVI — MDXLIX Q. LXXX + LXX -— LX h. XCVI + LIX + LXIV 5. Subtract DXLIIl from the sum of MMMDXxI and DCCL. 6. Form the smallest 4-digit numbers using the given digits and represent them using Roman numerals. 19,706 b. 3,9,0,4 c. 1,0,5,3 2,5) 16 40 hel 5A OT ga ee 1. What should 2. Form a number with the following: a. 5 tens, 3 crores, 7 lakhs, 0 thousands b. 3 ten thousands, 7 ten lakhs, 8 Crores, 9 ones ¢. 5 thousands, 6 lakhs, 7 crores, 9 tens | d. 8 ten thousands, 2 tens, 3 crores, 5 hundreds, 6 onesThe ancient Egyptians had devised a writing system almost 5000 years ago, It is based on hieroglyphs which are small pictures representing words. The Eqyptians used seven different symbols as follows: is j nl Ill For example, 10,035 = & [) I Use the above information and tick () the correct option. The number nome for Mt Mii EIll:, a. Two million thirty-one hundred one fe) '. Two million thirty-one thousand three | c. Two lakh thirty-one thousand three LJ . The place value of 3 in the number Sy CCC Nis a. 300 LJ b. 3000 LI c. 30 ie% When we round off a» whiz Il to the nearest ten thousands, we get a. 140000 [J] b. 130000 [] c. 120000 [_] |. We can write we ewIN using the Indian place value chart as a. three lakh two thousand ten [uel b. thirty lakh twenty thousand ten ry c. thirty lakh two thousand one ) . The Roman numeral representing LIecellll is a.mcccv [_] b.MMcCCIV [-] c.mmciV [J . The sum of ANNI |1and @N lis a xuv (J buv [] c. CxuV [JREVISION CAPSULE Fill in the blanks with Roman numerals. L You were born in the year____- b. You joined school in the year ; Your father was born in the year d. Your mother was born in the year e. Youare studying in class V in the year 2. State true or false. One million five hundred six is written as 10,000,506. b. The place value of 6 in the number 78,63,42,101 is 60 lakhs. ¢. 59,43,07,136 = 50,00,00,000 + 9,00,00,000 + 40,00,000 + 00,000 + 7,000 + 100 + 30+6 ta d. 45,000 when rounded off to the nearest ten thousands is 40,000. — | e. MDCLXV in Hindu-Arabic numerals is 1655. f. The sum of the face values of all the digits in the number 56293475 is 41 3. Match the following: @ 1 lakh is equal to i 8 b. Lerore is equal to ii, 0 c. Face value of 8 in 7,82,65,002 is ili, 534,000 Place value of O in 5,80,36,524 js iv. 100 lakhs &. 5,34,205 rounded of f + 1 nearest thousands is a iapaee ousands Form the smallest and igi aa the greatest 8-digit number using the following