Blue - Divide by Whole Numbers and Powers of 10 Metric Conversions 1. The thickness of a book, including the covers, is 2.1 cm. The front and back cover are each 0.5 cm thick. The book has 230 pages, numbered from 1 to 460, because each page has two sides. Calculate the thickness of each page. Give your answer in mm correct to 2 sf. Applying Decimal Operations 2. In August 1992 Hurricane Andrew cut a path of destruction across Florida in the United States and Gulf of Mexico, killing an estimated 9 400 000 fish. This is onethousandth of the fish killed by shrimp trawlers every year in the Gulf of Mexico. a. Fill the gaps in this sentence. To calculate the estimated number of fish killed by shrimp trawlers every year in the Gulf of Mexico I will 9,400,000 by. b. What is the place value of the 4 in the estimated number of fish killed by i. Hurricane Andrew? ii. Shrimp trawlers every year? How many fish are estimated to be killed by shrimp trawlers every year in the c. Gulf of Mexico? Write your answer in billions. 3. Campers Cider Karin made pressed cider with a group of campers for the evening festivities. They wanted the counselors to have one-quarter of the cider, so they split the cider into four equal parts and put one of them aside for the counselors. The campers had 4.2 gallons of cider to drink themselves. Question: How much cider was squeezed from the apples in the first place? Extra: A third of a bushel contains about 15 pounds of apples and makes about a gallon of cider. Approximately how many bushels and how many pounds of apples did Karin's campers use for the cider? Scientific Notation (continued from last lesson) For a number to be in scientific notation, the digit in front of the decimal must be between 1 and 10. Example Write each number in scientific notation. a. 453.1 x 10 8 453.1 x 10 8 = 4.531 x 10 2 x 10 8 Write 453.1 as 4.531 x 10 2 = 4.531 x 10 10 Add the exponents.
Write each number in scientific notation. 4. 16 x 10 5 5. 0.203 x 10 6 6. 7,243 x 10 12 You can compare and order numbers using scientific notation. First compare the powers of 10, and then compare the decimals. Example Order 0.064 x 10 8, 312 x 10 2, and 0.58 x 10 7 from least to greatest. Write each number in scientific notation. 0.064 x 10 8 312 x 10 2 0.58 x 10 7 6.4 x 10 6 3.12 x 10 4 5.8 x 10 6 Order the powers of 10. Arrange the decimals with the same power of 10 in order. 3.12 x 10 4 5.8 x 10 6 6.4 x 10 6 Write the original numbers in order. 312 x 10 2, 0.58 x 10 7, 0.064 x 10 8 Write these in scientific notation and then order from least to greatest. 7. 526 x 10 7, 18.3 x 10 6, 0.098 x 10 9 Computations with scientific notation often occur in real-world situations that involve very large or very small numbers. Example Measurement. The Great Pyramid of Giza in Egypt contains about 2.3 x 10 6 blocks of stone. On average, each block weighs about 5 x 10 3 lb. About how many pounds of stone does the Great Pyramid contain? (2.3 x 10 6 )(5 x 10 3 ) Write a multiplication problem. = 2.3 x 5 x 10 6 x 10 3 Use the Commutative Property of Multiplication. = 11.5 x 10 6 x 10 3 Simplify. = 11.5 x 10 9 Add the exponents. = 1.15 x 10 1 x 10 9 Write 11.5 as 1.15 x 10 1 = 1.15 x 10 10 Add the exponents. The Great Pyramid contains more than 1.15 x 10 10 lb of stone. Multiply. Express the result in scientific notation. 8. (4 x 10 4 )(6 x 10 6 )
Use a calculator to enter these numbers in standard form, and work out the problems. Leave the answer in Scientific Notation. 9. (6 x 10 4 ) x (4 x 10 5 ) 10. (3 x 10 8 ) x (1.99312 x 10 57 ) 11. (5.3 x 10 17 ) ' (1.2 x 10 5 ) 12. Cat Walk A dog takes three steps to walk the same distance for which a cat takes four steps. Suppose one step of the dog covers 1/2 foot. How many feet would the cat cover in taking 24 steps? 13. Back-to-School Shopping In order to get ready for the new school year, Mrs. Bender took her three children shopping. Edward selected a jacket that cost $48.78. His sister, Stephanie, found a pair of shoes for $63.58 that she really liked. Devin thought that was a lot to spend on one pair of shoes. He selected two pairs of jeans. Mrs. Bender noticed that the total cost of the items before tax was exactly $155. How much did one pair of Devin's jeans cost? Remember that your solution should include enough information to help another student understand the steps that you took and the decisions that you made in solving the problem. Extra: What was the total of Mrs. Bender's bill after the 7% sales tax was added? 14. Chantelle is going on an 8-day hike of 82.5 miles. She plans to hike 8.25 hours every day for each of those 8 days. How many miles will she cover each hour of her trip? 15. Red blood cells do not reproduce. They are created in bone marrow at the rate of approximately 150,000 per minute. How many red blood cells would be created in.125 seconds? 16. If a 50-gallon water heater leaks.4 gallons of water every 17 minutes, how long until it is completely empty?
Solutions 1. 0.048 mm 2. a. b. c. Multiply, 1000 i. hundred thousands ii. hundred millions 9.4 billion 3. The amount of cider made was 5.6 gallons. The campers had 4.2 gallons of cider to themselves. Because 4.2 ¾ of the cider, you divide 4.2 by the numerator (3). 4.2 divided by 3 = 1.4 1.4 = ¼ of the cider made. ¾(4.2) plus ¼(1.4) = 1(5.6). 5.6 gallons is how much cider the campers made. They made 5.6 gallons. For each gallon it took 15 pounds of apples. 5.6 gallons times 15 pounds of apples = 84 pounds of apples to make the cider. 1/3 of a bushel is 15 pounds. 1 bushel is 45 pounds. (15*3) They used 84 pounds of apples. They need approximately 2 bushels of apples (90 pounds). 4. 1.6 x 10 6 5. 2.03 x 10 5 6. 7.243 x 10 15 7. 1.83 x 10 7, 9.8 x 10 7, 5.26 x 10 9 8. 4 x 6 x 10 4 x 10 6 = 24 x 10 10 = 2.4 x 10 11 9. 6 x 4 x 10 4 x 10 5 = 24 x 10 9 = 2.4 x 10 10 10. 3 x 1.99312 x 10 8 x 10 57 = 5.97936 x 10 65 11. 5.3 x 1.2 x 10 17 x 10 5 = 6.36 x 10 22 12. In 24 steps a cat can walk 9 feet. If a dog has steps of 1/2 of a foot and he took three steps to equal a cats four steps, they must have walked 1/2+1/2+1/2 feet=1.5 feet. I did 1.5 divided by 4 to figure out how big a cat s steps were (.375 feet long). Then I multiplied.375 feet times 24 = 9 feet. 13. One pair of Devin's jeans cost $21.32. The total of Mrs. Bender's bill after the 7% tax is added is $165.85 The cost of the 2 purchases together was $112.36. By subtracting that number from $155.00 we know that the two pairs of jeans cost $42.64. Dividing that by 2 gives us the answer = $21.32.
Extra: To find the total bill I first found the tax by doing 155*7/100 = $10.85. Then I added that to $155. 155+10.85=$165.85 14. 1.25 miles Chantelle will hike 8.25 hours x 8 days = 66 hours of hiking. 82.5 miles 66 hours = 1.25 miles. 15. 312.5 blood cells How many.125 second parts are in one minute? 60 seconds.125 seconds = 480 parts.125 of a second is 1/480 of a full minute. 150,000 480 = 312.5 red blood cells in.125 seconds. OR 150,000 60 = 2500 red blood cells per second 2500 * 0.125 = 312.5 red blood cells in 0.125 seconds 16. 35 hours and 25 minutes How many.4 gallon parts are in 50 gallons? 50.4 = 125 parts 17 minutes for each part to leak out. 125 x 17 minutes per part = 2125 minutes for the tank to empty. 2125 60 = 35 hours and 25 minutes
Bibliography Information Teachers attempted to cite the sources for the problems included in this problem set. In some cases, sources may not have been known. Problems Bibliography Information 3, 12-13 The Math Forum @ Drexel (http://mathforum.org/) 14-16 Zaccaro, Edward. Challenge Math (Second Edition): Hickory Grove Press, 2005.