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Module 1 Book 2 Place Value and Decimal Fractions Name _________________________ Class Code __________ 1 Numbers in Words 1 – one 2 – two 3 – three 4 – four 5 – five 6 – six 7 – seven 8 – eight 9 – nine 10 – ten 11 – eleven 12 – twelve 13 – thirteen 14 – fourteen 15 – fifteen 16 – sixteen 17 – seventeen 18 – eighteen 19 – nineteen 20 – twenty 30 – thirty 40 – forty 50 – fifty 60 – sixty 70 – seventy 80 – eighty 90 – ninety 100 – hundred 1,000 – thousand 1,000,000 – million .1 – tenth .01 – hundredth .001 – thousandth .0001 – ten thousandth $ - Dollars ¢ - Cents 2 Vocabulary Sum – The answer to an addition problem. Difference – The answer to a subtraction problem. Factors – The numbers you multiply together in a multiplication sentence. 5 x 6 = 30 Factor Factor Product – The answer to a multiplication problem. 5 x 6 = 30 Product Divisor – The amount that another amount is divided by. 30 ÷ 5 = 6 Divisor Dividend – The amount being split up in a division problem. 30 ÷ 5 = 6 Dividend Quotient – The answer to a division problem 30 ÷ 5 = 6 Quotient Remainder – The amount left over in whole number division 3 NOTES 4 If you line up the decimal points it helps you to line up the place values. Remember to put a zero in the empty spaces to help you add and subtract. 5 Adding Decimals Lesson 9 Application Problem Ten baseballs weigh 1,417.4 grams. About how much does 1 baseball weigh? Round your answer to the nearest tenth of a gram. Round your answer to the nearest gram. 6 7 Write the numbers in standard form 2 tenths + 6 tenths Now add vertically lining the numbers up by their place value. Write the numbers in standard form 2 ones 3 thousandths + 6 ones 1 thousandth Now add vertically lining the numbers up by their place value. Add using the same procedure 2 tenths 5 thousandths + 6 hundredths Write the answer in standard form 1.8 + 13 tenths 8 Write in standard form and then add. Make sure you line up your decimals in order to line up your place values a) 1 hundred 8 hundredths + 2 ones 4 hundredths b) 148 thousandths + 7 ones 13 thousandths c) 0.74 + 0.59 d) 7.048 + 5.196 e) 7.44 + 0.774 9 Lesson 9 Problem Set 1. Solve by writing the numbers in standard form first and then write your sum in standard form. a. 1 tenth + 2 tenths = ___________ b. 14 tenths + 9 tenths = ___________ c. 1 hundredth + 2 hundredths = ___________ d. 27 hundredths + 5 hundredths = ___________ e. 1 thousandth + 2 thousandths = ___________ f. 35 thousandths + 8 thousandths = __________ g. 6 tenths + 3 thousandths = _________ h. 7 ones 2 tenths + 4 tenths = _________ i. 2 thousandths + 9 ones 5 thousandths = __________ 10 2. Solve using the standard algorithm. a. 0.3+ 0.82 = ____________ b. 1.03 + 0.08 = ___________ c. 7.3 + 2.8 = ____________ d. 57.03 + 2.08 = __________ e. 62.573 + 4.328 = f. 85.703 + 12.197 = ____________ ____________ 11 3. Van Cortlandt Park’s walking trail is 1.02 km longer than Marine Park. Central Park’s walking trail is 0.242 km longer than Van Cortlandt’s. a. Fill in the missing information in the chart below. New York City Walking Trails Central Park ________ km Marine Park 1.28 km Van Cortlandt Park ________ km b. If a tourist walked all 3 trails in a day, how many km would they have walked? 4. Meyer has 0.64 GB of space remaining on his iPod. He wants to download a pedometer app (0.24 GB) a photo app (0.403 GB) and a math app (0.3 GB). Which combinations of apps can he download? Explain your thinking. 12 Lesson 9 Homework 1. Solve by writing the numbers in standard form first and then write your sum in standard form. a. 3 tenths + 4 tenths = ____________ b. 12 tenths + 9 tenths = ____________ c. 3 hundredths + 4 hundredths = ____________ d. 27 hundredths + 7 hundredths = ____________ e. 4 thousandth + 3 thousandths = ____________ f. 39 thousandths + 5 thousandths = _____________ g. 5 tenths + 7 thousandths = ____________ h. 4 ones 4 tenths + 4 tenths = ____________ i. 8 thousandths + 6 ones 8 thousandths = ____________ 13 2. Solve using the standard algorithm. a. 0.4 + 0.7 = ____________ b. 2.04 + 0.07 = ____________ c. 6.4 + 3.7 = ____________ d. 56.04 + 3.07 = ____________ e. 72.564 + 5.137 = __________ f. 75.604 + 22.296 = _________ 14 3. The walkway over the Hudson, a bridge that crosses the Hudson River in Poughkeepsie, is 2.063 kilometers. Anping Bridge, which was built in China 850 years ago, is 2.07 kilometers long. a. Which bridge is longer? How much longer? Show your thinking. b. Leah likes to walk her dog on the walkway over the Hudson. If she walks across and back, how far do she and her dog walk? 4. For his parents’ anniversary, Danny spends $5.87 on a photo. He also buys 3 balloons for $2.49 each and a box of strawberries for $4.50. How much money does he spend all together? 15 Lesson 10 – Subtracting Decimals Application Problem Lesson 10 At the 2012 London Olympics, Michael Phelps won the gold medal in the men’s 100 meter butterfly. He swam the first 50 meters in 26.96 seconds. The second 50 meters took him 25.39 seconds. What was his total time? 16 1. Subtract the following using the same method you used to add decimals. Write your final answer in standard form a) 5 tenths – 3 tenths b) 7 ones 5 thousandths – 2 ones 3 thousandths c) 9 hundreds 5 hundredths – 3 hundredths When you subtract decimals what must you make sure you do? 17 2) Write the numbers in standard form and then subtract a) 83 tenths – 6.4 b) 9.2 – 6 ones 4 tenths c) 0.831 – 0.292 d) 4.003 – 1.29 e) 6 – 4.08 18 Lesson 10 Problem Set 1. Subtract, writing the difference in standard form. a. 5 tenths – 2 tenths = _______ b. 5 ones 9 thousandths – 2 ones = _________ c. 7 hundreds 8 hundredths – 4 hundredths = _________ d. 37 thousandths – 16 thousandths = _________ 19 2. Solve using the standard algorithm. a. 1.4 – 0.7 = ______ b. 91.49 – 0.7 = ___ c. 191.49 – 10.72 = _ d. 7.148 – 0.07 = ___ e. 60.91 – 2.856 = _ f. 361.31 – 2.841 = _ 20 3. Mrs. Fan wrote 5 tenths minus 3 hundredths on the board. Michael said the answer is 2 tenths because 5 minus 3 is 2. Is he correct? Explain. 4. A pen costs $2.09. It costs $0.45 less than a marker. Ken paid for one pen and one marker with a five dollar bill. Use a tape diagram with calculations to determine his change. 21 Lesson 10 Homework 1. Subtract, writing the difference in standard form. a. 9 tenths – 3 tenths = ___________ b. 9 ones 2 thousandths – 3 ones = ___________ c. 4 hundreds 6 hundredths – 3 hundredths = ________ d. 56 thousandths – 23 thousandths = ________ 22 2. Solve using the standard algorithm. a. 1.8 – 0.9 = _____ b. 41.84 – 0.9 = ___ c. 341.84 – 21.92 = _ d. 5.182 – 0.09 = __ e. 50.416 – 4.25 = _ f. 741. – 3.91 = ____ 23 3. Mr. House wrote 8 tenths minus 5 hundredths on the board. Maggie said the answer is 3 hundredths because 8 minus 5 is 3. Is she correct? Explain. 4. A clipboard costs $2.23. It costs $0.58 more than a notebook. Lisa buys two clipboards and one notebook, and paid with a ten dollar bill. Use a tape diagram with calculations to show her change 24 Adding and Subtracting Decimals Practice – Topic D Review 1) 87 – 17.28 2) 32.58 + 5.635 38.215 3) 17. 3 – 5.09 4) 88.0 + 35.60 123.6 5) 65.04 - 50.414 6) 32. + 1.1 7) 47. - 1. 3 8) 80 + 29.6 25 109.6 9) 66. - 38.3 10) 78.9 - 55.779 11) 73 + 48.7 12) 41.3 - 20.65 13) 46 + 39.5 14) 72 - 67.01 15) 65 + 56.8 16) 58 - 45.183 17) 79.3 + 10.21 18) 17 - 1.2 26 19) 92 + 8.83 20) 67.15 - 24.302 21) 96 + 37.367 22) Jerry bought 6.95 lbs of cherry and lime jelly beans for his birthday party. If 1.75 lbs were cherry flavor, how many pounds were lime flavor 23) Paige was measuring how much taller she got over two years. In the first year she grew 4.62 cm. In the second year she grew 7.7 cm. How much taller did she get altogether? 27 (Lesson 11 pt 1 Do Now) 1) Vanessa downloaded two apps which were 17.73 kb total. If one app was 8.63 kb, how big was the other app? 2) Nancy was buying food for her birthday party. She bought a 52.93 oz bag of barbeque chips and a 79.6 oz bag of regular chips. How many ounces did she buy all together? 3) Tom was weighing the amount of candy he received for Halloween. If he received 8.30 kg and his brother received 1.8 kg, how much candy did they get all together? 28 (Lesson 11 pt 4 Do Now) 27) John ate a snack with 80.79 total calories. If the chips he ate were 43.39 calories, how many calories were in the rest of his snack? 28) A computer programmer had two files with a total size of 93 gigabytes. If one of the files was 50.30 gigabytes, how big is the second file? 29) A weatherman was measuring the amount of rain two cities received over a week. City A received 3.74 inches while City B received 9.8 inches. How much rain did they get total? 29 30) During a science experiment, Mary found the mass of two rocks to be 41.4 grams and 74.3 grams. What is the total mass of these two rocks? 31) Ned and Sarah were running a relay race. The race was 22.01 kilometers total. If Ned ran 9.41 kilometers how far did Sarah run? 30 Addition and Subtraction of Decimals Rewrite each problem and then add or subtract. a. 0.45 + 0.34 = b. 1.06 + 2.32 = c. 7.8 + 0.46 = d. 2.54 + 10.8 = e. 1.76 + 6.3 = f. 2.865 + 93.71 = g. 0.65 – 0.24 = h. 1.24 – 0.17 = i. 3.08 – 2.6 = j. 3.62 – 1.9 = k. 2 + 3.9 = l. 9 – 4.8 31 32 Adding and Subtracting Decimals When adding and subtracting decimals, make sure that you always line the number up using the decimal so that the same place values are being added together. Rewrite the problem vertically and then solve. a) 0.25 + 0.4 = b) 0.8 + 0.6 = c) 0.6 + 0.26 = d) 0.45 + 0.47 = e) 0.67 + 1.09 = f) 0.3 + 0.87 = g) 1.47 + 0.03 = h) 0.85 – 0.2 = i) 1.3 – 0.95 = j) 0.6 – 0.08 = 33 (Lesson 11 pt 3 Do Now) Adding and Subtracting Decimals a) 0.124 + 2.33 = b) 1.14 – 1.08 = c) 3.1 + 0.13 = d) 3.706 – 1.59 = e) There are 15.1 servings in a box of popular cereal. How many servings are there in two boxes? Show your work. 34 f) Andrew wants to buy a $5.00 binder for his notes. He has saved $3.60 so far. How much more money does Andrew need to save? g) Emily and Amanda pooled their money to buy some snacks. They had $9.57 altogether. If Amanda gave $4.65, how much money did Emily give? h) 42.34 + 87.9 = i) Lesson 11 pt1 35 1.79 - .99 = Application Problem – After school, Marcus ran 3.2km and Cindy ran 1.95km. Who ran farther? How much farther? 36 Multiply Whole Numbers using the algorithm 1 Example 42 X 8 336 First Multiply the ones place (2 x 8) You get 16 so place the 6 in the ones place and carry the 1 on top of the 4 Then multiply the 8 times the 4 in the tens place You get 32 and then add the 1 that you carried from the 16 so you get 33 Solve using the algorithm A) 20 × 9 B) 58 x 3 C) 71 x 6 D) 61 x 7 37 E) 76 x 5 F) 91 x 5 G) 78 x 8 H) 76 x 2 I) 75 x 2 J) 83 x 3 K) 18 x 5 L) 40 x 4 M) 84 x 5 N) 13 x 2 38 O) 46 x 3 P) 20 x 3 Q) 81 × 4 R) 37 x 9 S) 52 x 9 T) 84 x 4 39 A) 763 × 3 B) 440 x 3 C) 222 x 9 D) 721 x 2 Lesson 11 pt 1 H.W E) 839 x 2 F) 234 x 8 G) 899 x 7 H) 637 x 6 I) 936 x 5 J) 442 x 7 40 Lesson 11 pt2 Do Now K) 135 x 8 L) 406 x 2 M) 830 x 3 N) 840 x 5 O) 405 x 2 P) 702 x 6 Q) 294 x 9 R) 302 x 2 S) 583 x 3 T) 400 x 7 41 A) 57 x 7.1 B) 3.3 x 5.8 C) .97 x 45 D) 3.7 x .42 E) 7.7 x .56 F) 4.7 x 67 G) 74 x 9.9 H) .26 x 1.7 42 Lesson 11 pt2 Multiplying Whole Numbers using the algorithm A) 27 x 39 B) 74 x 92 C) 13 x 52 D) 63 x 86 E) 64 x 90 F) 92 x 20 G) 73 x 60 H) 34 x 48 43 Lesson 11 pt 2 H.W. I) 74 x 94 J) 78 x 10 K) 51 x 11 L) 97 x 60 44 Lesson 11 pt 3 A) 164 x 39 B) 459 x 15 C) 224 x 92 D) 862 x 79 E) 261 x 76 F) 667 x 89 45 G) 360 x 11 H) 631 x 43 I) 155 x 51 J) 165 x 73 K) 630 x 35 L) 927 x 86 M) 519 x 30 N) 527 x 33 46 Lesson 11 pt3 H.W. O) 808 x 54 P) 625 x 93 Q) 230 x 82 R) 630 x 38 S) 670 x 44 T) 401 x 44 47 Lesson 11 Pt 4 Notes Multiplying with decimals When multiplying decimals you multiply the numbers without the decimals. Then you count the number of digits in each of the factors. The product should have the same number of total digits in the decimal place as the factors. 48 Multiplying Decimals A) 63.9 × 7 B) 44.8 × .84 C) 88 x 5.1 D) 7.9 x 4 E) 14.3 x .49 F) 80.1 x 2.8 (Additional decimal multiplication work on page 42) 49 G) 5.9 x 3.9 H) 5.6 x .62 Lesson 11 Pt 4 H.W. I) 63.1 x .42 J) 7.5 x 8 K) 325 x .78 L) 39.6 x 8 50 Lesson 11 pt 5 Application Problem Louis buys 4 chocolates. Each chocolate costs $2.35. Louis multiplies 4 x 235 and gets 940. Place the decimal to show the cost of the chocolates. 51 Divide Whole Numbers by 1 digit Divisors with or without Remainders D - Divide M – Multiply S - Subtract B – Bring Down C – Circle 44 ÷ 2 = 22 86 ÷ 2 = 43 27 ÷ 2 = 13 47 ÷ 5 = 9 r2 32 ÷ 3 = 61 ÷ 9 = 6 52 31 ÷ 3 = 96 ÷ 2 = 20 ÷ 8 = 2 40 ÷ 6 = 98 ÷ 2 = 72 ÷ 2 = 53 804 ÷ 7 = 695 ÷ 7 = 458 ÷ 7 = 393 ÷ 9 = 509 ÷ 6 = 622 ÷ 8 = 496 ÷ 9 = 680 ÷ 3 = 54 Lesson 11 pt 5 H.W. 869 ÷ 8 = 162 ÷ 8 = 438 ÷ 8 = 991 ÷ 2 = 55 Lessons 14 and 15 – Division of Decimals Application Problem Lesson 14 A bag of potato chips contains 0.96 grams of sodium. If the bag is split into 8 equal servings, how many grams of sodium will each serving contain? 56 NOTES Dividing with decimals Dividing with decimals (rounding the answer). 57 There can be no remainders when you divide decimals 6.72 ÷ 3 = ___ 5.16 ÷ 4 = ____________ 6.72 ÷ 4 = ________ 20.08 ÷ 8 = _________ 6.372 ÷ 6 = _________ 4.236 ÷ 3 = ______ 58 What is different with the following two division problems? 1.7 ÷ 2 2.6 ÷ 4 Solve the division problems 17 ÷ 4 22 ÷ 8 7.7 ÷ 4 0.84 ÷ 4 59 1.324 ÷ 2 = ______ 0.78 ÷ 3 = 7.28 ÷ 4 = ______ 17.45 ÷ 5 = _____ 0.5 ÷ 2 = _______ 5.7 ÷ 4 = _______ 60 0.9 ÷ 2 = 9.1 ÷ 5= 9÷6= 0.98 ÷ 4 = 9.3 ÷ 6 = 91 ÷ 4 = 61 Mrs. Nguyen used 1.48 meters of netting to make 4 identical mini hockey goals. How much netting did she use per goal? Esperanza usually buys avocados for $0.94 apiece. During a sale, she gets 5 avocados for $4.10. How much money did she save per avocado? Use a tape diagram and show your calculations. Six bakers shared 7.5 kg of flour equally. How much flour did they each receive? 62 Mrs. Henderson makes punch by mixing 10.9 liters of apple juice, 600 milliliters of orange juice, and 8 liters of ginger ale. She pours the mixture equally into 6 large punch bowls. How much punch is in each bowl? Express your answer in liters. 63 Homework Lessons 14 and 15 Solve 5.241 ÷ 3 = _______ 3.445 ÷ 5 = _______ 0.64 ÷ 4 = 6.45 ÷ 5 = _____ 64 16.404 ÷ 6 = 0.7 ÷ 4 = _______ 8.1 ÷ 5 = _______ 0.7 ÷ 2 = 3.9 ÷ 6 = 9÷4= 65 0.92 ÷ 2 = 9.4 ÷ 4 = 91 ÷ 8 = Mrs. Mayuko paid $40.68 for 3 kg of shrimp. What’s the cost of 1 kg of shrimp? 66 Lesson 14 & 15 Pt 2 The total weight of 6 pieces of butter and a bag of sugar is 3.8 lb. If the weight of the bag of sugar is 1.4 lb., what’s the weight of each piece of butter? A rope 8.7 m long is cut into 5 equal pieces. How long is each piece? Yasmine bought 6 gallons of apple juice. After filling up 4 bottles of the same size with apple juice, she had 0.3 gallon of apple juice left. What’s the amount of apple juice in each bottle? 67 Word Problems 1) Mr. Frye distributed $126 equally among his 4 children for their weekly allowance. How much money did each child receive? 2) Brandon mixed 6.83 lbs. of cashews with 3.57 lbs. of pistachios. After filling up 6 bags that were the same size with the mixture, he had 0.35 lbs. of nuts left. What was the weight of each bag? 3) Ava is 23 cm taller than Olivia, and Olivia is half the height of Lucas. If Lucas is 1.78 m tall, how tall are Ava and Olivia? Express their heights in centimeters. 68 4) Mr. Hower can buy a computer with a down payment of $510 and 8 monthly payments of $35.75. If he pays cash for the computer, the cost is $699.99. How much money will he save if he pays cash for the computer instead of paying for it in monthly payments? 5) The bakery bought 4 bags of flour containing 3.5 kg each. 475 g of flour are needed to make a batch of muffins and 0.65 kg is needed to make a loaf of bread. a. If 4 batches of muffins and 5 loaves of bread are baked, how much flour will be left? Give your answer in kilograms. b. The remaining flour is stored in bins that hold 3 kg each. How many bins will be needed to store the flour? Explain your answer. 69 Decimal Division 392.58 ÷ 9 = 1404 ÷ 6 = 31.77 ÷ 5 = 347.9 ÷ 7 = 1404.9 ÷ 3 = 217.04 ÷ 4 = 70 Lesson 14 & 15 pt 2 H.W. 122.76 ÷ 2 = 392.44 ÷ 4 = 195.2 ÷ 8 = 748.2 ÷ 6 = You and three of your friends spend Saturday morning running the bake school at the school basketball tournament. After the bake sale there were 94 cupcakes that just didn’t sell so you and your friends decide to split them evenly. How many cupcakes will you each get? 71 At the end of Module 1 you should be able to do the following: Add decimals using place value strategies and relate those strategies to a written method. Subtract decimals using place value strategies and relate those strategies to a written method. Multiply a decimal fraction by a single digit whole number, relate to a written method through application of the area model and place value understanding and explain the reasoning used. Multiply a decimal fraction by single-digit whole numbers, including using estimation to confirm the placement of the decimal point. Divide decimals by single-digit whole numbers involving easily identifiable multiples using place value understanding and relate to a written method. Divide decimals with a remainder. Solve word problems using decimal operations. 72 Module 1 –Review 1) 5.582 x 100 = a) 55.82 b) 558.2 c) 0.0582 d) 5,582 2) 465.84 ÷ 100 = a) 4.6584 b) 46.584 c) 465.84 d) 46,584 3) 4) Which multiplication sentence is equivalent to 10000? a) 10 x 10 b) 10 x 10 x 10 c) 10 x 10 x 10 x 10 d) 10 x 10 x 10 x 10 x 10 What is the standard form of 7.65 x 102 a) 7.65 b) 76.5 c) 765 d) 7650 73 5) Convert 8 meters to centimeters a) 888 centimeters b) 800 centimeters c) .008 centimeters d) 8,000 centimeters 6) Convert 400 milliliters to liters a) 4 liters b) 400,000 liters c) 0.4 liters d) 40 liters 7) What is three thousandths as a decimal? a) 0.0003 b) 3,000.0 c) 0.03 d) 0.003 8) What is 67.43 in words? a) (6 x 10) + 7 + (4 x 0.1) + (3 x 0.01) b) sixty seven and forty three c) sixty seven and forty three tenths d) sixty seven and forty three hundredths 74 9) What is the expanded form of 67.43 using decimals? a) (6 x 10) + 7 +(4 x 0.1) + (3 x 0.01) b) 6 + 7 + (4 x 0.1) + (3 x 0.01) c) (6 x 10) + 7 + (4 x 10) + 3 d) (6 x 100) + (7 x 10) + 4 + (3 x 0.1) 10) What is the expanded form of 67.43 using fractions? a) (6 x 10) + 7 + (4 x 1/10) + (3 x 1/100) b) (6 x 1000) + (7 x 100) + (4 x 10) + 3 c) (6 x 1/10) + (7 x 1/10) + (4 x 1/10) + (3 x 1/10) d) (6 x 10) + 7 + (4 x 1/100) + (3 x 1/1000) 11) Compare 632.4 to 632.35 a) 632.4 = 632.35 b) 632.4 > 632.35 c) 632.4 < 632.35 12) Which list is in descending order? (greatest to least) a) 64.2, 64.1, 67.0 b) 67.0, 68.4, 65.2 c) 840.1, 840.01, 840.001 d) 8.2, 8.01, 8.21 75 13) Round 8.43 to the nearest tenth. a) 8 b) 8.4 c) 8.5 d) 8.42 14) Round 78.383 to the nearest hundredth. a) .100 b) 78.38 c) 78.40 d) 78.4 15) Solve. 8.54 + 3.5 a) 8.89 b) 12.04 c) 120.4 d) 11.104 16) Solve. 5.4 – 0.6 a) 6.0 b) 5.2 c) 4.8 d) 5.6 76 17) Which word problem matches the problem 5.01 ÷ 3? a) Jeff has 3 pails of water. Each pail holds 5.01 liters. How many liters of water are in all three pails? b) Craig has a box of candy that weighs 5.01 ounces. He wants to eat the candy over three days. If he eats the same amount of candy every day, how much candy will he eat each day? c) Alexis bikes 5.01 miles to her friend’s house. Then she bikes another 3 miles to the store. How far does she bike in all? d) Maggie has 5.01 kilograms of gravel. She used 3 kilograms of the gravel for a project at her school. How much gravel does she have left? 18) Complete the number sentence: 3.55 ÷ 5 = a) 355 hundredths ÷ 5 = 71 hundredths = .71 b) 355 tenths ÷ 5 = 71 tenths = .71 c) 355 hundredths ÷ 5 = 61 hundredths = .61 d) 355 hundredths ÷ 5 = 72 hundredths = .72 19) Solve. 5.15 ÷ 5. a) 1.03 b) 10.3 c) 103 d) 1.05 77 20) Which number sentence is not true? a) 0.3 > 0.25 b) 45 tenths > 0.45 c) 6 tens, 6 tenths and 8 hundredths = 6.68 d) 6 thousandths and 6 hundredths < .73 78 79 80 81 82