(1~) Decimals /!J!7 TEXTBOOK QUESTIONS SOLVED. Learn and Remember EXERCISE 8.1. (b)

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$DECIMALS 93 Decimals /!J!7 Learn and Remember. The Dot represent the decimal. 2. A fraction with denominator 0 can be written in decimal notation and vice-versa. 3.$

1 DECIMALS 93 Decimals /!J!7 Learn and Remember. The Dot represent the decimal. 2. A fraction with denominator 0 can be written in decimal notation and vice-versa. 3. One block divided into 00 equal parts means each part is ~ of a unit. It can be written as 0.0 in decimal notation. Hundreds Tens Hundreds I Tens Ones (00) I (0) () Tenths Tenths (~) 4. Every fraction with denominator 00 can be written in decimal notation and vice-versa.. All decimals can be represented on number line. 6. Every decimal can be written as a fraction. 7. Any two decimal numbers can be compared among themselves. The comparison can start with the whole part. If the whole part is equal then the tenth part can be compared and so on. TEXTBOOK QUESTIONS SOLVED SoL Hundreds Tens Ones Tenths I Number a I 0 b 3 o 2 I Q2. Write the following decimals in the place value table: 9,4 (6) j i i SoL Hundreds Tens Ones Tenths EXERCISE 8. Ql. Write the following as numbers in the given table: Hundreds Tens Ones Tenths Tens Ones Tenth~ Hundreds Tens Ones Tenths Hundreds Tens Ones Tenths 2 0 9

2 94 MATHEMATlCS-VI DECIMALS 9 Q3. Write each of the following as decimals: (0) seven-tenths Two tens and nine-tenths Fourteen point six One Hundred and two-ones Six hundred point eight 7 7 tenths = 0 = tens and 9-tenths = 2 x = = 20.9 Fourteen point six = 4.6 One hundred and 2-ones = x = 02.0 Six hundred point eight = Q4. Write each of the following as decimals: (f) (g) - (h) - (i) (j) 3- (k) 4" = = = = 8ft + ~ 2 2 (f) 4- =4+ - =42 0 0ft =8+ - =88 0. (g) ~ = 3x = '= x x 2 _ -±- = 0.4 (h) " = x 2-0 x (k) 4- =4+ - =4+ -- =4+ - = x 0. Q. Write the following decimals as fraction. Reduce the fractions to lowest form: (f) 2.2 (g) 6.4 fi 3 0.6= ;0' =" o +.0 = + - = = = = 0 4 (g) 6.4 = = = = ~ =% = = ~ 9 =;0'= 2 (f) 2.2 = ~ ;0' =-+-=-= Q6. Express the following as cm using decimals: 2 mm 30 mm 6 mm 4 cm 2 mm 62 mm (f) 83 mm 0 rom = em 0 mm = em mm = 0 em rom = 0 em 0 =-+-=+-= (i) 2 = 2x2 = 24 x ft ft 0 4 = = x2 (j) 3 - = = x2 6 = = = rom = - x2em 0 30 mm = ( 0 X30) em 2 = - em=0.2em 0 = 3 em or 3.0 em 0 mm = em 4 em 2 mm rom = 0 em =4cm+2mm 2 6 mm = 0 x 6 =4cm+ 0 em

96 MATHEMATICS-VI DECIMALS 97 6 0+6 = 0 em= --w em =4.2em 6 = + 0 em =.6 em 0 mm = em Lmm e - em 0 62 mm «0 x 62 62 60+2 =- em=--- 0 0 2 = 6 + - = 6 2 em 0.

3 96 MATHEMATICS-VI DECIMALS = 0 em= --w em =4.2em 6 = + 0 em =.6 em 0 mm = em Lmm e - em 0 62 mm «0 x =- em= = = 6 2 em 0. (j) 83 mm 0mm= lem Lrnm e - em 0 =83mm= - x = 0 em= 0 em 3 = = 8.3 em. Q7. Between which two whole numbers on the number line are the given numbers lie? Which of these whole numbers is nearer the number? (j) 4.9 ( I I I I I I I I I I I I I ) o from 0 to, 0.8 is nearest to. from to 6,. is nearest to. from 2 to 3, 2.6 is nearest to 3. from 6 to 7, 6.4 is nearest to 6. from 9 to 0, 9. is nearest to 9. (j) from 4 to, 4.9 is nearest to o Q8. Show the following numbers on the number line: ~"""t""",tl""t""""""" ) o 2 3 Q9. Write the decimal number represented by the points A, B, C, D on the given number line. 8 A = = B = + - = C = = D = =2.9 0 '''' o A B 2 C D3 Q.0. ThelengthofRamesh'snotebookis9cmmm. What will be its length in cm? The length of a young gram plant is 6 mm. Express its length in em, 9 em mm = 9 em + mm =gem+ - em=9.em ff 6 mm = - em = -- = em 0 0 Iff 0 EXERCISE 8.2 = em = 6. em. 0 Q. Complete the table with the help of these boxes and use decimals to write the number: ~,!II,~,,, 'ii.(i -ilil., +""'""'"""'"',.,. > : r.t ~J. ~ :. : :; ~ III ~ fiil'i' " \I f;.,. ::::::' "',.,.,.,",,', 'i '!I III eo -. e

98 MATHEMATIcs-VI ~I Tenths I Hundredths INumbers Ones Tenths Hundredths Numbers 0 2 6 0.26 3 8.38 2 8.28 Q2.

4 98 MATHEMATIcs-VI ~I Tenths I Hundredths INumbers Ones Tenths Hundredths Numbers Q2. Write the numbers given in the following place value table in decimal form: Hundreds Tens Ones Tenths Hundreds Thousandths x x 0 + x x x x 0 2 = = xl + 0 x 0 + x x x x = = x x 3 + x x x x 2 = = x x + x + 0 x x x 2 DECIMALS = = x x + x x x x 2 4 = = Q3. Write the following decimals in the place value table: i Numbers Hundreds Tens Ones Tenths Hundredths Thousandths Q4. Write each of the following as decimals: _ = 2 x x + 4 x 0 + x 00 = = x x x + 0 x = 37.0

00 7 6 4 0 + 00 + 000 =7x - +6x - +4x-- 0 00 000 = 0.764 MATHEMATICS-VI DECIMALS 0 0.8 (g) 0.066 fo(f _ ~ 0.60 = ;eo - 0.2 (f) 0.2 t 0.

5 =7x - +6x - +4x = MATHEMATICS-VI DECIMALS (g) fo(f _ ~ 0.60 = ;eo (f) 0.2 t 0.0 = ;eo = = 2 x x + 2 x x x 000 = ;J _, =~ 0.7 = ;eo - J;O 4 ~ t _.! 0.2 = ;eo = J;O - 4 fo6 ~ (g) = ).006 = 00. ;S = ;eo = 0 ;2 ~ _L=.!. (f> 0.2 = ).006 = JOO - ft6 8. = 7 x x 0 + x + 0 x x 00 = Q. Write each of the following decimals in words: (f).008 Zero point zero three. (f> One point two zero. One hundred and eight point five six. Ten point zero seven. Zero point zero three two. Five point zero zero eight. Q6. Between which two numbers in tenths place on the number line does each ofthe given number lie? All the numbers lies between 0 to 0.06 is nearer to is nearer to is nearer to 0.9 Q7. Write as fractions in lowest terms: (f) is nearer to is nearer to 0.7 (f> 0.7 is nearer to EXERCISE 8.3 Q. Which is greater? 0.3 or or 0.0 (g). or.0 (j).64 or = - '0.4=-. 0' or or.2 (h).43 or rO.S (f) or 0.9 (i) 3.3 or The tenth part of.0.4 is greater than 0.3. Therefore 0.3 < = 00 ; 0.02 = 00 The hundredth part of 0.07 is greater than that of Therefore 0.07 > = 3 x + 0 x = 0 x + 8 x 0 The ones part of 3 is greater than that of 0.8. Therefore 3 > = x x = 0 x 0 + x 00 The tenth term of 0. is greater thanthat 0.> 0.0. of 0.0. Therefore

02 MAHEMATlCS-VI - -.23 = x + 2 x 0 + 3 x 00.2 = x + 2 x - + 0 x - 0 00 The hundredth term of.23 is greater than that of.2. Therefore.23 >.2. (f) 0.099 = 0 x - + 9 x - + 9 x -- 0 00 000 0.

6 02 MAHEMATlCS-VI = x + 2 x x 00.2 = x + 2 x x The hundredth term of.23 is greater than that of.2. Therefore.23 >.2. (f) = 0 x x x = x x The tenth term of 0.9 is greater than that of Therefore 0.9 > (g). = x + x 0.0 = x + x x 00 Therefore. =.0. (h).43 = x + 4 x x 00 + x = x + 4 x x x 000 The hundredth term of.490 is greater than that of.43. Therefore.490 >.43. DECIMALS 03 (i).82 is greater than.8 (ii).09 is greater than.0009 (iii) 00. is greater than 0.0 (iv).00 is greater than.000 (u) is greater than EXERCISE 8.4 Q. Express as rupees using decimals: paise 7 paise 0 rupees 90 paise 00 paise = f. ' paisa = -, 00. paise = - x 00 = - Re=0.0f 00 Therefore paise = f paise = f. paisa = - f paise = 00 x paise 72 paise 00 paise = f. paisa = - f paise = 00 x 7 f 7 = - f = 0.7 f 00 Therefore 7 paise = f rupees 90 paise = f paise Now 00 paise = f (i) 3.3 = 3 x + 3 x l~ = 3 x + 3 x x x 000 Therefore 3.3 = (j).64 = x + 6 x :0 + 4 x ~0.603 = x + 6 x x x 000 The hundredth term of.64 is greater than that of.603. Therefore.64 >.603. Q2. Make five more examples and find the greater (i).8 or.82 (ii).0009 or.09 (iii) 0.0 or 00. (iv).00 or =-=02f 00. Therefore 20 paise = f paise = f paisa = 00 f paise = 00 f = 00 f. paisa = - f paise = 00 f =.9 f Therefore f paise = 0 f f = f 0.9 (v) or 042.3

04 MATHEMATICS-VI DECIMALS 0 2 = 7 + - ~ = 7.2 ~ 00 Therefore 72 paise = ~ 7.2. Q2. Express as metres using decimals: em 6 em 9 m 7 em 49 em 00 em = m em= - m 00 em= - x 00 = - m=0.

7 04 MATHEMATICS-VI DECIMALS 0 2 = ~ = 7.2 ~ 00 Therefore 72 paise = ~ 7.2. Q2. Express as metres using decimals: em 6 em 9 m 7 em 49 em 00 em = m em= - m 00 em= - x 00 = - m=0.m 00 Therefore em = 0. m. 2 m 4 em = 2 m + 4 em Now 00 em = m em= - m em= - m=04m 00. Therefore 2 m + 4 em = 2 m m = 2.4 m Therefore 2 m 4 em = 2.4 m. 00 em = m em= - m em = - x49= - m = 00 m = = = 4.9 m Therefore 49 em = 4.9 em. Q3. Express as em using decimals: mm 60 mm 9 em 8 mm 93 mm 00 em = m 2 m 4 em em= - m 00 6em= - x = - m=0.06m 00 Therefore 6 em = 0.06 m. 9 m 7 em = 9 m + 7 em Now 00 em = m -- m em = em = - m = 0 07 m 00. Therefore 9 m + 7 em = = 9.07m Thus 9 m 7 em = 9.07 m 64 nun 0 mm = em mm= - em 0 mm = - x = - em 0 0 Therefore mm = 0. em = 0. em 0 mm = em Lmm e - em 0 64 mm = 0 x = - 0 em = 6.4 em Therefore 64 mm = 6.4 em 0 mm = em Lrnm e - em 0 93mm= - x em = 9.3 em Therefore 93 mm = 9.3 em. Q4. Express as km using decimals: 8m 8888 m 000 m = km m= -- km m= -- km 000 = km Therefore 8 m = km 000 m = km m= -- km m = 8888 km mm = em Lrnm e - em 0 60 mm = - x 60 em = 6 em 0 Therefore 60 mm = 6 em.] 9 em 8 mm = 9 em + 8 mm Now 0 mm = em Lmm e - em 0 8 8mm= - em=08em 0. Therefore 9 em 8 mm = 9.8 em 88 m 70km m 000 m = km m= -- km m= -- km 000 = km Therefore 88 m = km 70 km m Lm e -- = 70km +m km 000

06 MATHEMATICS-VI DECIMALS 07 = 8.888 km m= -- km 000 H T 0 Tenth Hund. Thou. Therefore 8888 m = 8.888 km = 0.00 km 0 0 0 0 Therefore 70 km m 6 3 2 = 70.00 km. + 3 8 Q.

8 06 MATHEMATICS-VI DECIMALS 07 = km m= -- km 000 H T 0 Tenth Hund. Thou. Therefore 8888 m = km = 0.00 km Therefore 70 km m = km Q. Express as kg using decimals: 2g 00 g 370 g = kg8g 26kg0g 000 g = kg 000 s= kg H T 0 Tenth Hund. Thou. 9= 000 kg g= 000 kg g = 000 kg = kg 00 g= 000 kg = 0. kg Therefore 2 g = kg Therefore 00 g = 0. kg 000 g = kg kg 8 g = kg + 8 g EXERCISE = = - kg 9= - kg H T 0 Tenth Hund. Thou g = -- kg = 3.70 kg 8g= - = kg Therefore 370 g = 3.70 kg. Therefore kg 8 g =.008 kg kg 0 g = 26 kg + 0 g = = - kg H T 0 Tenth Hund. Thou. 0g= - kg=0.0kg Therefore 26 kg 0 g = 26.0 kg Q. Find the sum in each of the following: I 3 7 = (j) H T 0 Tenth Hund. Thou (f) H T 0 Tenth Hund. Thou = II = Q2. Rashid spent ~ 3.7 for Maths book and ~ for Science book. Find the total amount spent by Rashid.

DECIMALS 09 08 MATHEMATICS-VI Money spent for Maths book = (3.7 Money spent for Science book = ( 32.60 Total money spent = 3.7 + 32.60 Therefore total money 3.7 + 32.60 68.

9 DECIMALS MATHEMATICS-VI Money spent for Maths book = (3.7 Money spent for Science book = ( Total money spent = Therefore total money Therefore total money spent by Rashid is ( Q3. Radhika's mother gave her ( 0.0 and her father gave her f.80. Find the total amount given to Radhika by the parents. Money given by mother = ( 0.0 Money given by father = (.80 Total money received by Radhika = Therefore total money received by Radhika is ( Q4. Nasreen bought 3 m 20 cm cloth for her shirt and 2 m em cloth for her trouser. Find the total length of cloth bought by her. Cloth bought for shirt = 3 m 20 em = 3.20 m Cloth bought for trouser = 2 m cm = 2.0 m Therefore 3.20 m m.2 m Therefore total length of cloth is.2 m. Q. Naresh walked 2 km 3 m in the morning and km 7 m in the evening. How much distance did he walk in all? Distance travelled in morning = 2 km 3 m = 2.03 km Distance travelled in evening = km 7 m =.007 km Total distance travelled = km Therefore total distance travelled by Naresh is km. Q6. Sunita travelled km 268 m by bus, 7 km 7 m by car and 00 m by foot in order to reach her school. How far is her school from her residence? Distance travelled by bus = km 268 m =.268 km Distance travelled by car = 7 km 7 m = km Distance travelled on foot = 00 m = 0.00 km Total distance travelled =.268 km km km km Therefore total distance travelled is ( km. 7. Ravi purchased kg 400 grice, 2 kg 20 g sugar and 0 kg 80 g flour. Find the total weight of his purchases. Weight of Rice = kg 400 g =.400 kg Weight of Sugar = 2 kg 20 g = kg Weight of Flour = 0 kg 80 g = 0.80 kg Total weight =.400 kg kg kg.400 kg kg kg kg Therefore total weight of Ravi's purchases = kg. EXERCISE 8.6 Q. Subtract. Rs. 8.2 from f 20.7 Rs..36 from f kg from 2.07 kg = ( = ( m from 20 m 2.0 km from.206 km = m.206 km -2.0 km 3. km = 3. km

0 MAHEMATlCS-VI DECIMALS 2.07 kg - 0.34 kg.793 kg =.793 kg Q2. Find the value of: 9.76-6.28 8. - 6.79 9.76-6.28 3.476 8.0-6.79 = 3.476.7 =.7 2.0 -.27.6-9.847 2.0 -.27 0.78 =.78.600-9.847.73 =.73 Q3.

10 0 MAHEMATlCS-VI DECIMALS 2.07 kg kg.793 kg =.793 kg Q2. Find the value of: = = = =.73 Q3. Raju bought a book for t 3.6. He gave t 0 to the shopkeeper. How much money did he get back from the shopkeeper? Total amount given to shopkeeper = t 0 Cost of book = 3.6 Remaining amount = Therefore Raju got back t 4.3 from the shopkeeper. Q4. Rani had t 8.0. She bought one ice-cream for t.7. How much money does she have now? 'lbtal money = ~ 8.0 Cost ofice-cream = t.7 Remaining amount = Remaining money = t 6.7. Q. Tina had 20 m cm long cloth. She cuts 4 m 0 cm length of cloth from this for making a curtain. How much cloth is left with her? 'lbtallength of cloth = 20 m cm = 20.0 m Length of cloth used = 4 m 0 cm = 4.0 m Remaining cloth = 20.0 m m m Length ofremaining cloth is. m. Q6. Namita travels 20 km 0 m every day. Out of this she travels 0 km 200 m by bus and the rest by auto. How much distance does she travel by auto? Total distance travel = 20 km 0 m = m Distance travel by bus = 0 km 200 m = m Distance travel by auto = ( ) m Therefore distance travel by 9.80 km. Q7. Aakash bought vegetables weighing 0 kg. Out of this 3 kg 00 g is onions, 2 kg 7 g is tomatoes and the rest in potatoes. What is the weight of the potatoes? Weight of onions = 3 kg 00 g = 3.00 kg Weight of tomatoes = 2 kg 7 g = 2.07 kg Total weight of onions and tomatoes = kg kg.7 kg 'lbtal weight of vegetables = 0 kg Therefore weight of potatoes = 0 kg -.7 kg kg Therefore weight of potatoes is 4.42 kg. DO

The fractions in which the denominators are 10,100, 1000, etc..., are known as decimal fractions.

$The fractions in which the denominators are 10,100, 1000, etc..., are known as decimal fractions.$ Decimals CHAPTER 8 Introduction A part of a whole can be expressed in decimal or decimals are another way of representing fractions. In earlier classes, we learnt that dot represents a decimal point. Now,