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Exercise-1, 1. (a) Seven and six-tenths, (b) Twenty-one and forty-five-hundredths, (c) Seven and three hundred fifty-eight-thousandths, 2., Decimal fraction, , 17, 100, , 471, 1000, , 47, 10, , 825, 100, , 59, 100, , 3578, 1000, , Decimal number, , 0.17, , 0.471, , 4.7, , 8.25, , 0.59, , 3.578, , 7, 2, 3. (a) 5.72 = 5 ++, 10, 100, , (b) 491.987 = 400 + 90 + 1 +, , 9, 8, 7, ++, 10, 100, 1000, , 8, 1, +, 10, 100, 1, 3, 5, ++, 4. (a) 400 + 7 +, 10, 100, 1000, = 400 + 7 + 0.1 + 0.03 + 0.005 = 407.135, , (c) 28.81 = 20 + 8 +, , (b) 9000 + 800 + 70 + 6 + 0.5 + 0.04 + 0.003, = 9876.543, 5. (a) Place value of 6 = 6 × 10 = 60,, Place value of 3 = 3 × 1 = 3,, 1, 4, =, ,, 10, 10, 1, 7, Place value of 7 = 7 ×, =, ., 100 100, (b) Place value of 2 = 2 × 10 = 20,, , Place value of 4 = 4 ×, , Place value of 8 = 8 × 1 = 8,, 1, 3, =, Place value of 3 = 3 ´, ,, 10 10, , Teacher's Resource Pack Mathematics-5, , 57

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1, 4, =, ,, 100, 100, 1, 9, Place value of 9 = 9 ×, =, ., 1000, 1000, (c) Place value of 1 = 1 × 100 = 100,, , Place value of 4 = 4 ×, , Place value of 7 = 7 × 10 = 70,, Place value of 2 = 2 × 1 = 2,, 1, 9, Place value of 9 = 9 ×, =, ,, 10 10, Place value of 8 = 8 ×, , 1, 8, =, ,, 100 100, , Place value of 7 = 7 ×, , 1, 7, =, ., 1000 1000, , 6. (a) The whole number part is smaller in 35.7 than 53.9., \, 35.7 < 53.9, (b) As the whole number parts are same, we compare the decimal, parts., Since, 5 hundredths > 2 hundredths, \, 289.75 > 289.72, (c) As the whole number parts are same, we compare the decimal, parts., Since, 9 tenths > 0 tenths, \, 9.999 > 9.009, (d) As the whole number parts are same, we compare the decimal, parts., Since, 5 tenths > 4 tenths, \, 67.54 > 67.44, 7. (a) Arranging the given decimals in place value chart, we have, Decimal Hundreds Tens Ones Point tenths hundredths thousandths, number, 186.2, 1, 8, 6, ., 2, 0, 0, , 58, , 168.24, , 1, , 6, , 8, , ., , 2, , 4, , 0, , 186.45, , 1, , 8, , 6, , ., , 4, , 5, , 0, , 168.042, , 1, , 6, , 8, , ., , 0, , 4, , 2, , Teacher's Resource Pack Mathematics-5

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Comparing according to the place value, we have decimal, numbers in ascending order as 168.042 < 168.24 < 186.2 < 186.45, (b) Arranging the given decimals in place value chart, we have, Decimal, number, 9.999, , Ones, , Point tenths hundredths thousandths, , 9, , ., , 9, , 9, , 9, , 9.99, , 9, , ., , 9, , 9, , 0, , 9.09, , 9, , ., , 0, , 9, , 0, , 9.009, , 9, , ., , 0, , 0, , 9, , Comparing according to the place value, we have decimal, numbers in ascending order as, 9.009 < 9.09 < 9.99 < 9.999, 8. (a) Arranging the given decimals in the place value chart, we have, Decimal Tens Ones Point tenths hundredths, number, 75.4, 7, 5, ., 4, 0, 74.82, , 7, , 4, , ., , 8, , 2, , 74.7, , 7, , 4, , ., , 7, , 0, , 75.09, , 7, , 5, , ., , 0, , 9, , Comparing according to place value, we have decimal, numbers in descending order as : 75.4 > 75.09 > 74.82 > 74.7, (b) Similarly, 52.47 > 42.83 > 28.72 > 28.34, , Exercise-2, 1. (a) 0.35 has 2 decimal places., 35, 7, So, 0.35 =, =, 100, 20, (b) 2.04 has 2 decimal places., 1, 204 51, So, 2.04 =, =, = 2, 25, 100 25, (c) 0.836 has 3 decimal places., So, 0.836 =, , 836, 209, =, 1000, 250, , (d) 5.625 has 3 decimal places., 5625, 1125 225 45, 5, So, 5.625 =, =, =, =, = 5, 1000, 200, 40, 8, 8, Teacher's Resource Pack Mathematics-5, , 59

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(e) 0.375 has 3 decimal places., 375, 75 15, 3, So, 0.375 =, =, =, =, 1000, 200 40, 8, (f) 0.444 has 3 decimal places., 444, 111, So, 0.444 =, =, 1000, 250, 7, 7´, 5, 35, 2. (a), =, =, = 0.35, 20, 20 ´, 5 100, 9, 9´, 8, 72, (b), =, =, = 0.072, 125 125 ´, 8 1000, 3, 19, (c) 4 =, 4, 4, 4.75, 4 19.00, –1 6, 30, –2 8, 20, –20, 0, 3, \, 4 = 4.75, 4, (d) 8007 = 8.007, 1000, (e) 15 1 = 76, 5, 5, 5, , 15.2, 76.0, –5, 26, –25, 10, –10, 0, , (f), , 29 = 9.666, 3, 9.666, 3 29.000, –2 7, 20, –18, 20, –18, 20, –18, 2, , 1, \, 15 = 15.2, 5, , 60, , Teacher's Resource Pack Mathematics-5

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Exercise-3, 1. (a) 48.25 + 7.38 = 55.63, 1, , 1 ., , 399.123, + 112.475, 511.598, , (c) 288.17 + 132.48 = 420.65, , (d) 164.7 + 372.38 + 89.287, = 626.367, , 1 ., 2 1 1, , 288.17, + 132.48, 420.65, , 1, , ., , 164.700, 372.380, +89.287, 626.367, , (e) 972.15 + 343.343 = 1315.493, , (f) 758.837 + 102.139 + 128.343, = 989.319, , ., , 1 1, , ., , 1 1, , 48.25, + 7.38, 55.63, , 1 1, , (b) 399.123 + 112.475 = 511.598, , 1 1 1 1 ., , 972.150, + 343.343, 1315.493, , 758.837, 102.139, +128.343, 989.319, , 2. (a) 99.9 – 9.999 = 89.901, , (b) 78.09 – 29.13 = 48.96, , 8 18 18 9 10, , 6 17 10 ., , 9 9.9 0 0, – 9.9 9 9, 8 9.9 0 1, , 7 8.0 9, – 2 9.1 3, 4 8.9 6, , (c) 310.369 – 172.649 = 137.720, 2 10 9 13, , (d) 928.3 – 864.352 = 63.948, , ., , 8 12 7 12 9 10, , 3 1 0.3 6 9, – 1 7 2.6 4 9, 1 3 7.7 2 0, , 9 2 8.3 0 0, – 8 6 4.3 5 2, 6 3.9 4 8, , (e) 119.434 – 73.89 = 45.544, 0 11 8, , 13 13 ., , 1 1 9 . 4 3 4, – 7 3 . 8 9 0, 4 5 . 5 4 4, Teacher's Resource Pack Mathematics-5, , (f) 100 – 72.45 = 27.55, 0 9 9, , 9 10, , 1 0 0 . 0 0, – 7 2 . 4 5, 2 7 . 5 5, 61

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3. (a) 3.9 – 3.6 + 2.4 + 1.7 = 3.9 + 2.4 + 1.7 – 3.6 = 8.0 – 3.6 = 4.4, ., , 2, , 3, 2, + 1, 8, , ., ., ., ., , 9, 4, 7, 0, , 7, , 10, , 8 . 0, – 3 . 6, 4 . 4, , (b) 33.3 – 3.33 – 3.303 = 29.97 – 3.303 = 26.667, 2 12 12 10, , 6 10, , 3 3 . 3 0, – 3 . 3 3, 2 9 . 9 7, , 2 9 . 9 7 0, – 3 . 3 0 3, 2 6 . 6 6 7, , (c) 76 + 13.75 – 67.954 = 89.75 –67.954 = 21.796, 8, , 7 6 . 0 0, + 1 3 . 7 5, 8 9 . 7 5, , 16 14 10, , 8 9 . 7 5 0, – 6 7 . 9 5 4, 2 1 . 7 9 6, , (d) 8.28 – 1.45 – 3.285 – 0.5 = 6.83 – 3.285 – 0.5 = 3.545 – 0.5 = 3.045, 12 ., , 7 12 10, , 8 . 2 8, – 1 . 4 5, 6 . 8 3, , 6 . 8 3 0, – 3 . 2 8 5, 3 . 5 4 5, , 7, , 4., , 5 9 9, , 9 10, , 6 0 0 . 0 0, – 4 2 8 . 5 6, 1 7 1 . 4 4, 5., , 3 . 5 4 5, – 0 . 5 0 0, 3 . 0 4 5, , Thus, 171.44 should be subtracted from 600 to, get 428.56., , Quantity of wheat sold = 37.45 kg + 43.75 kg + 58.75 kg, = 139.95 kg, 1 1, , 1 1 1, , 3, 4, + 5, 1 3, , 7, 3, 8, 9, , ., ., ., ., , 4, 7, 7, 9, , 5, 5, 5, 5, , Quantity of wheat left = (150 – 139.95) kg = 10.05 kg, 62, , Teacher's Resource Pack Mathematics-5

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4 9, , 9 10, , 1 5 0 . 0 0, – 1 3 9 . 9 5, 1 0 . 0 5, So, 10.05 kg of wheat is still left with Murari Lal., 6., , 1, , 9 9, , 9 10, , 2 0 0 . 0 0, – 1 9 2 . 5 8, 7 . 4 2, Thus, 7.42 should be added to 192.58 to get 200., , Exercise-4, 1. (a) 6.25 × 10 =, , 625, 625, ´, 10 =, = 62.5, 100, 10, , (b) 3.835 × 100 =, , 3835, 3835, = 383.5, ´, 100 =, 1000, 10, , (c) 28.625 × 1000 =, (d) 0.2345 × 100 =, (e) 0.05 × 1000 =, (f) 19.09 × 10 =, , 28625, ´, 1000 = 28625, 1000, , 2345, 2345, ´, 100 =, = 23.45, 10000, 100, , 5, ´, 1000 = 50, 100, , 1909, 1909, ´, 10 =, = 190.9, 100, 10, , (g) 1.098 × 1000 =, , 1098, ´, 1000 = 1098, 1000, , (h) 0.0003 × 100 =, , 3, 3, ´, 100 =, = 0.03, 10000, 100, , (i) 0.12 × 10000 =, , 12, ´, 10000 = 1200, 100, , 2. (a) 36.5 × 5 = 182.5, 365, Arranging numbers as whole numbers, ×5, and multiplying., 1825, (Since the given decimal number has only 1 decimal place, so,, put the decimal point 1 place from the right.), Teacher's Resource Pack Mathematics-5, , 63

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(b) 5.2125 × 19 = 99.0375, (Since the given decimal number has only 4 decimal places, so,, put the decimal point 4 places from the right in the product.), 52125, × 19, 469125, + 521250, 990375, (c) 11.11 × 92 = 1022.12, 1111, × 92, 2222, + 99990, 102212, 86, ×14, 344, +860, 1204, , (d) 8.6 × 1.4 = 12.04, (Since the given decimal numbers have 2, decimal places in total, so, put the decimal, point 2 places from the right in the product.), , 75, ×29, 675, +1500, 2175, , (e) 0.75 × 0.29 = 0.2175, (Since the given decimal numbers have 4, decimal places in total, so, put the decimal, point 4 places from the right in the product.), (f) 0.478 × 17.6 = 8.4128, , (g) 0.93 × 0.84 = 0.7812, 93, ×84, 372, +7440, 7812, , 478, ×176, 2868, 33460, +47800, 84128, (h) 11.11 × 1.1 × 0.1 = 12.221 × 0.1, = 1.2221, , 64, , 1111, ×11, 1111, +11110, 12221, , Teacher's Resource Pack Mathematics-5

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(i) 1.11 × 2.2 × 0.9 = 2.442 × 0.9, = 2.1978, , 2442, ×9, 21978, , 111, ×22, 222, +2220, 2442, , 2550, × 45, 12750, + 102000, 114750, , 3. The cost of 45 pens = 45 × R 25.50, = R 1147.50, , 4. The distance covered by car in 18 hours = 18 × 40.5 km, = 729 km., , 5. The cost of 4 kg rice, , = 4 × R 75.50, = R 302.00, , 405, ×18, 3240, +4050, 7290, , 7550, ×4, 30200, , Exercise-5, 25.75 2575, =, = 2.575, 10, 1000, , 1. (a) 25.75 ÷ 10 =, (b) 67.8 ÷ 10 =, , 67.8, 10, , =, , 678, = 6.78, 100, , (c) 5047 ÷ 1000 =, , 5047, = 5.047, 1000, , (d) 80.75 ÷ 100 =, , 80.75, 8075, =, = 0.8075, 100, 10000, , (e) 215.4 ÷ 1000 =, (f) 0.9 ÷ 10 =, , 215.4 2154, =, = 0.2154, 1000 10000, , 0.9, 9, =, = 0.09, 10 100, , Teacher's Resource Pack Mathematics-5, , 65

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(g) 30.6 ÷ 100 =, , 30.6 306, =, = 0.306, 100 1000, , (h) 216.9 ÷ 1000 =, , 216.9, 2169, =, = 0.2169, 1000 10000, , (i) 71.571 ÷ 100 =, , 71.571, 71571, =, = 0.71571, 100, 100000, , 2. (a) 2.74 ÷ 20 =, , 2.74, 2.74, 2.74 1, 1, = =´, =, 0.274 ´, =, 0.137, 20, 10 ´, 2, 10, 2, 2, , (b) 42.8 ÷ 400 =, , 42.8, 42.8, 42.8 1, 1, = =´, =, 0.428 ´, =, 0.107, 400, 4´, 100, 100 4, 4, , (c) 27.3 ÷ 2000 =, , 27.3, 27.3, 27.3 1, 1, =, =´, =, 0.0273 ´, =, 0.01365, 2000 1000 ´, 2, 1000 2, 2, , (d) 819.63 ÷ 8000 =, , 819.63, 819.63, 819.63 1, 1, =, = ´, =, 0.81963 ´, 8000, 1000 ´, 8, 1000, 8, 8, , = 0.10245, (e) 68.4 ÷ 30 =, (f) 56.5 ÷ 600 =, , 68.4, 68.4, 68.4 1, 1, = =´, =, 6.84 ´, =, 2.28, 30, 10 ´, 3, 10, 3, 3, 56.5, 56.5, 1, = =, 0.565 ´, =, 0.094, 600 100 ´, 6, 6, , 3. (a) 20.4 ÷ 6 = 3.4, 6, , 66, , 3.4, 20.4, – 18, 24, –24, 0, , (b) 792.72 ÷ 16 = 49.545, 16, , 49.545, 792.720, – 64, 152, – 144, 87, – 80, 72, – 64, 80, – 80, 0, , Teacher's Resource Pack Mathematics-5

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(c) 3.528 ÷ 25 = 0.141, 0.141, 25 3.528, – 25, 102, – 100, 28, – 25, 3, (e) 243.18 ÷ 6.3 =, , (d) 29.24 ÷ 43 = 0.68, 0.68, 43 29.24, – 258, 344, – 344, 0, , 10, 243.18 243.18 ´, =, 6.3, 6.3 ´, 10, , 63, , 2431.8, = =, 38.6, 63, , (f) 72.696 ÷ 3.12 =, , 100, 72.696 72.696 ´, =, 3.12, 3.12 ´, 100, , 312, , 7269.6, = =, 23.3, 312, , (g) 0.108 ÷ 0.09 =, , 100, 0.108 0.108 ´, =, 0.09, 0.09 ´, 100, , 10.8, ==, 1.2, 9, , (h) 3262.5 ÷ 1.45 =, , 100, 3262.5 3262.5 ´, =, 1.45, 1.45 ´, 100, , 326250, = =, 2250, 145, , Teacher's Resource Pack Mathematics-5, , 9, , 38.6, 2431.8, – 189, 541, – 504, 378, – 378, 0, 23.3, 7269.6, –624, 1029, –936, 936, – 936, 0, , 1.2, 10.8, –9, 18, – 18, 0, 145, , 2250, 326250, – 290, 362, – 290, 725, – 725, 00, – 00, 00, 67

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(i) 0.0102 ÷ 17, 17, , = 0.0006, , 0.0006, 0.0102, – 102, 0, , 4. The other decimal number = 663.3 ÷ 40.2, 663.3, =, 40.2, 663.3 ´, 10, =, 40.2 ´, 10, 6633, ==, 16.5, 402, , 16.5, 402 6633.0, – 402, 2613, – 2412, 2010, – 2010, 0, , 5. The weight of one bag of wheat = (121.5 ÷ 15) kg, = 8.1 kg, , 15, , 8.1, 121.5, –120, 15, –15, 0, , 6. Other number = 378.255 ÷ 45.3, 378.255, =, 45.3, , 453, , 378.255 ´, 10, =, 45.3 ´, 10, 3782.55, =, 453, , 8.35, 3782.55, – 3624, 1585, – 1359, 2265, – 2265, 0, , =, 8.35, , 68, , Teacher's Resource Pack Mathematics-5

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7. The length of each piece = Total length ÷ number of equal pieces, = (30 ÷ 8) m, = 3.75 m, , 8, , 3.75, 30.00, –24, 60, – 56, 40, – 40, 0, , 8. The weight of each coin = (62.5 ÷ 5) g, 62.5, =g, 5, , = 12.5 g, , 5, , 12.50, 62.50, –5, 12, – 10, 25, –25, 00, –00, 0, , HOTS, 5.45 × 100 + 2.5 – 74.5 ÷ 100, = 5.45 × 100 + 2.5 – 0.745, = 545 + 2.5 – 0.745, = 547.5 – 0.745, = 546.755, , Teacher's Resource Pack Mathematics-5, , 69