8.2 Orders of Magnitude: The Universe in Powers of Ten, Exercises of Science education

Download 8.2 Orders of Magnitude: The Universe in Powers of Ten and more Exercises Science education in PDF only on Docsity! 154 The Sourcebook for Teaching Science ACTIVITY 8.1.2 Advance Organizers in Your Science Text Textbook authors and publishers use “ traffi c signs ” to inform readers about the structure and content of the book. Research has shown that these advance organizers help students learn and remember new material by developing structures or schemas into which new information can be placed. Sadly, many students ignore these signs and spend much more time reading than necessary, yet with minimal understanding and retention. Before reading a textbook, you should study its structure and features. Complete the following activity for a chapter that your science instructor assigns. By understanding the structure of the text, you will understand the structure of the discipline and be better able to integrate new ideas into your existing mental outline. Organization of the Book Special features: What are the unique or special features of this book? Most authors write a preface to explain their purpose in writing and describe the special features of their work. Themes: What are the major themes of your text- book? Most authors group chapters in units with names that refl ect the major themes of the book. Topics: What are the main topics of the unit you are studying? This can generally be deduced from the chapter titles. Organization of the Chapter Objectives: What are the goals or objectives of the chapter you are studying? These are frequently listed at the beginning of the chapter. Subtopics: What are the subtopics of the chap- ter? The subtopics are the division headings within chapters, often shown in BOLDFACE CAPITALS . Major points: What are the major points of the section you are now studying? The major points are generally shown in lowercase bold letters . Key terms: What are the key terms of the section you are now studying? In most textbooks, the key terms are shown in italics or bold letters. 8.2 Orders of Magnitude: The Universe in Powers of Ten “ How wide is the Milky Way galaxy? ” “ How small is a carbon atom? ” These questions may sound simple, but their answers are virtually impos- sible to comprehend since nothing in our realm of experience approximates either of these meas- ures. To grasp the magnitude of such dimensions is perhaps impossible, but it is relatively easy to express such dimensions by scaling up or down (expressing them in orders of magnitude greater or smaller) from things with whose dimensions we are familiar. An order of magnitude is the number of powers of 10 contained in the number and gives a shorthand way to describe scale. An understand- ing of scale allows us to organize our thinking and experience in terms of size and gives us a sense of dimension within the universe. ACTIVITY 8.2.1 Understanding Powers of Ten Note: This is an Internet - based activity. To simplify the expression of very large and small numbers, scientists often use scientifi c nota- tion. Scientifi c notation involves writing a number as the product of two numbers. The fi rst one, the digit value, is always more than 1 and less than 10. The other, the exponential term, is expressed as a power of 10. Table 8.3 compares decimal and sci- entifi c notation. The diameter of the Milky Way Galaxy is believed to be about 1,000,000,000,000,000,000,000 meters. By contrast, the diameter of the nucleus of a carbon atom is only approximately 0.000 000 000 000 01 meters. In scientifi c notation, the diameter of the Milky Way is 1
10 21 m, and the diameter of the carbon nucleus is 1
10  14 m. The Milky Way is therefore approximately 10 35 times (35 orders of magnitude) larger than the carbon atom. Calculators and computers may express the dimensions of the Milky Way and the carbon nucleus as 1.0E21 and 1.0E - 14, where E stands for the exponential term. The speed of light, approximately 300 million (299,792,458) m c08.indd 154 5/9/08 5:57:33 PM Organizing Science Information and Concepts 155 per second, is expressed in scientifi c notation as approximately 3.0
10 8 m/s (3.0E8). Avogadro ’ s number, the number of molecules in a mole (602 213670000000000000000), is expressed as 6.02
10 23 (6.02E23). Scientifi c notation is particularly helpful when trying to express the scale of the universe. In 1957, Dutch educator Kees Boeke published Cosmic View: The Universe in 40 Jumps, in which he helped readers visualize the size of things in the known universe with reference to a square meter (10 0 m 2 = 1 m 2 ). 2 In this book, Boeke showed successively smaller pictures, each one a tenth the dimension of the previous (10  1 m, 10  2 m, 10  3 m, and so on) as well as successively larger pictures, each ten times larger than the previous (10 1 m, 10 2 m, 10 3 m, and so on). A number of moviemakers 3 and Web developers have followed Boeke ’ s idea in an effort to help people understand the scale of things in the universe. After examining “ powers of ten ” resources online (look on sciencesourcebook. com or www.powersof10.com , or search “ powers of ten ” ), perform the following investigation. Figure 8.2 displays millimeter graph paper. The tiny black square in the upper left corner is 1 mm on a side, (10  3 meters). The sides of the gray square in the upper left corner are an order of magnitude greater than the black square (10 mm per side, 10  2 m). Finally, the sides of the entire sheet, with 100 mm per side (10  1 m), are two orders of magnitude greater than the black square and one order of magnitude greater than the gray square. Working with your classmates, create a square meter (1000 mm on a side) by tap- ing 100 of these squares together in a 10
10 square. This is 1 square meter with sides and area three orders of magnitude greater than the square millimeter represented by the tiny black box. Measuring with a meter stick, place mark- ers at the four corners of a 10 m square in one corner of your school ’ s football field. This is four orders of magnitude greater than the origi- nal black square (1
10 4 times larger). If space permits, mark out a 100 m square as shown in Figure 8.3 . This square has sides that are five orders of magnitude larger (1
10 5 ) than the original black square. You may continue to increase the order of magnitude by using satellite photos of your cam- pus that are available on the Internet (look on sciencesourcebook.com , satellite view at maps. google.com , or earth.google.com ). By zooming out of the satellite photo such that the football fi eld represents approximately only one - tenth of Table 8.3 Decimal and Scientifi c Notation Decimal Notation Scientifi c Notation Order of Magnitude Decimal Notation Scientifi c Notation Order of Magnitude .001 1
10  3  3 10 1
10 1 1 .01 1
10  2  2 100 1
10 2 2 .1 1
10  1  1 1,000 1
10 3 3 1 1
10 0 0 10,000 1
10 4 4 103m 102m 101m O rd er o f M ag ni tu de –1 –2 –3 Dimension (m) Figure 8.2 Orders of Magnitude  3,  2,  1 c08.indd 155 5/9/08 5:57:33 PM