1. 8 x 10-9, 14.7 x 10-7, 0.22 x 10

Transcription

1 Black - Divide by Whole Numbers and Powers of 10 Scientific Notation (continued from last lesson) Order from least to greatest x 10-9, 14.7 x 10-7, 0.22 x You can multiply numbers in scientific notation using the rule for Multiplying Powers with the Same Base. Example Multiply 3 x 10-7 and 9 x Express the result in scientific notation. (3 x 10-7 )(9 x 10 3 ) = 3 x 9 x 10-7 x 10 3 Use the Commutative Property of Multiplication. = 27 x 10-7 x 10 3 Multiply 3 and 9. = 27 x 10-4 Add the exponents. = 2.7 x 10 1 x 10-4 Write 27 as 2.7 x 10 1 = 2.7 x 10-3 Add the exponents. Multiply. Express the result in scientific notation. 2. (7.1 x 10-8 )(8 x 10 4 ) 3. Chemistry. A hydrogen atom has a mass of 1.67 x kg. What is the mass of 6 x 10 3 hydrogen atoms? Express the result in scientific notation. Use a calculator to enter these numbers in standard form, and work out the problems. Leave the answer in Scientific Notation. 4. (2.9 x ) x (7.8 x 10 8 ) 5. (1.532 x 10 4 ) x (9.883 x 10-5 ) 6. (6.982 x 10 8 )/(3.118 x 10-4 ) 7. (4.86 x 10-3 )/(2.04 x 10 8 ) 8. ( x 10 2 )/(9.318 x ) More Problems 9. Scientific Sums. Mathematicians and scientists often use scientific notation when working with very large or very small numbers. The number 25,700,000,000,000,000 can be written in scientific notation as 2.57 x Now isn't that a space saver?

2 When it comes to adding numbers written in scientific notation, you must be very careful with place value. Please help me to find the sum of the following numbers: 2.57 x x x x Don't forget to write your final answer in a complete sentence. Also, be sure that your sum is written in scientific notation. Bonus: When working with very large or very small numbers, mathematicians and scientists will also consider significant digits.* Explain what is meant by significant digits and state your answer to the sum using significant digits. 10. The speed of light is 186,000 miles per second. How many miles per hour is the speed of light? Express your answer in scientific notation to one decimal place. Problem Involving Really Big or Small Numbers 11. Clothing Industry Problem. There are about 230 million people in the United States. Assume that each person buys 6 pairs of socks a year and that socks cost about $4 a pair. How much money can the clothing industry expect to take in each year from selling socks? 12. Automotive Batteries Problem. There are about 120 million cars and trucks in the United States. Each one uses a battery, which needs replacing about once every 3 years. If an average battery costs $80, how much money can the battery manufacturing industry expect to make each year? 13. Glacier Problem. A typical glacier moves downhill at about 5 inches per day. Suppose that the glacier is 4 miles long. a. Recalling that 1 mile is 5280 feet, how many days will it take for snow that falls at the top of the glacier to move downhill to the bottom? How many years in this? 14. Numbers on a Calculator Problem. A normal calculator can handle numbers as big as 9.99 x To see how big a number this is, answer the following questions. a. The volume of the earth is 2.59 x cubic miles. One cubic mile is cubic feet. What is the volume of the earth in cubic feet? One grain of sand has a volume of about 1.3 x 10-9 cubic feet. Divide the answer in part (a) by 1.3 x 10-9 to find the number of grains of sand the earth could hold. c. Which is bigger, the number of grains of sand the earth could hold or the largest number a calculator can hold?

3 15. Sahara Desert Problem. The Sahara Desert covers about 3 million square miles. a. c. d. Write this number in scientific notation. One square mile is square feet. About how many square feet in the Sahara Desert? Assume that the Sahara Desert is covered with sand to an average depth of 200 feet. The volume of this sand in cubic feet is the area in square feet times the depth in feet. How many cubic feet of sand are there? A grain of sand has a volume of about 1.3 x 10-9 cubic foot. Divide the volume in cubic feet by 1.3 x 10-9 to find out approximately how many grains of sand there are in the Sahara Desert. 16. Sizing Up Sequoias. A sequoia tree seed weighs only 1/(5 x 10 3 ) of an ounce. If a mature sequoia tree weighs an average of 2.16 x times as much, how much does the average mature sequoia weigh? Give the weight in pounds; there are 16 ounces in a pound. Extra: If I weigh 100 lbs, how many seeds would it take to equal my weight? How many of me would it take to equal the weight of the tree? 17. If a circle has a radius of 4.5 inches, what is the length of 1 of its circumference? (Round to the nearest hundredth.) 18. A square piece of paper has a perimeter of after it is folded in half. What was the length of each side of the square before it was folded? 19. An Isosceles triangle with a height of inches is folded along its only line of symmetry. The perimeter of the folded triangle is inches. What is the perimeter of the original, triangle?

4 Solutions x10,8x10,1.47x x8x10 x10 = 56.8x10 = 5.68x x6x10 x10 = 10.02x10 = 1.002x x7.8x10 x10 = 22.62x10 = 2.262x x9.883x10 x10 = 15.14x10 = 1.514x x3.118x10 x10 = 21.77x10 = 2.177x x2.04x10 x10 = x x9.318x10 x10 = 81.58x10 = 8.518x10 9. Scientific Sums. The sum of the four numbers in scientific notation is X Bonus: The sum using significant digits is X We changed all the numbers in scientific notation to Then we added them X X X X X Since in scientific notation you can only have one number in front of the decimal, we moved the decimal two places to the left. We also added two exponents because we moved the decimal two places. Our final answer was X Bonus: Significant digits are digits you can trust to be accurate. We redid the original problem. We put a variable for the decimal places that we didn't know. 25.7xx X x X xx X x X xx X Because there are X's in the hundredths place, we don't know the result of the hundredths place, so we dropped the seven. We once again moved the decimal two places to the left and added two exponents. Our answer in significant digits is X

5 10. If light travels 186,000 miles in 1 second, then it travels 186,000 x 3600 = 669,600,000 or 6.7 x 10 8 miles per hour ,520,000, About 3.2 billion dollars! 13. a. 14. a. c. 15. a. c. d days 139 years x x calculator 3 x x sq ft 1.7 x cu ft 1.3 x grains 16. Sizing Up Sequoias. First of all, I figured out that 1/(5 x 10 3 ) was 1/5000 of an ounce. If one seed only weighs 1/5000 of an ounce then 5000 seeds would make an ounce. To figure out what an average sequoia tree weighs I did: 1/5000x(2.16 x ) 43,200,000 oz. To convert that to pounds I did: 43,200,000 divided by 16 because there are sixteen oz. in a pound. That equals 2,700,000. To convert that to tons I did: 2,700,000 divided by 2000 because there are 2000 lbs in a ton. That equals 1,350. Therefore, the average mature sequoia weighs 1,350 tons. EXTRA: To find how many seeds it would take to equal 100 pounds I did 5000(seeds to an ounce)x16(to make a pound) x 100 (to make 100 pounds) 5,000x16x100 80,000x100 8,000,000 It would take 8,000,000 seeds to equal 100 pounds. Since the tree weighs 2,700,000 pounds and you weigh 100 pounds, I found the answer by dividing 2,700,000 by ,700, = w ,000=w It would take 27,000 of you to equal the weight of a sequoia tree inches

6 A circle with a 4.5 inch radius has a 9 inch diameter. The formula for the circumference of a circle is pi x diameter: 9 x 3.14 = inch circumference. Because there are 360 degrees in a circle, the length of one degree is inches 360 =.0785 inches 18. When the paper is folded in half, its short sides are equal to half of the original side of the square. Add up the sides of the folded rectangle: 3n = n = inches inches When the triangle is folded in half, its perimeter is inches. Because the height is known, the remaining two sides of the triangle must equal = inches. The original triangle was twice this length: 2 x = inches.

7 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 9, 16 The Math Drexel ( Zaccaro, Edward. Challenge Math (Second Edition): Hickory Grove Press, 2005.