15 R.2 Sets and Real Numbers Write each percent as a decimal. See Examples 12(a)–12(c). Write each percent as a fraction. Give answers in lowest terms. See Example 13. 171. 51% 172. 47% 173. 15% 174. 35% 175. 2% 176. 8% 177. 140% 178. 180% 179. 7.5% 180. 2.5% Write each fraction as a percent. See Example 14. 181. 4 5 182. 3 25 183. 7 50 184. 9 20 185. 2 11 186. 4 9 187. 9 4 188. 8 5 189. 13 6 190. 31 9 R.2 Sets and Real Numbers ■ %DVLF 'HıQLWLRQV ■ Operations on Sets ■ Sets of Numbers and the Number Line Basic Definitions A set is a collection of objects. The objects that belong to a set are its elements, or members. In algebra, the elements of a set are usually numbers. Sets are commonly written using set braces, 5 6. 51, 2, 3, 46 The set containing the elements 1, 2, 3, and 4 The order in which the elements are listed is not important. This set can also be written 54, 3, 2, 16 or with any other arrangement of the four numbers. To show that 4 is an element of the set 51, 2, 3, 46, we use the symbol ∈. 4∈51, 2, 3, 46 Since 5 is not an element of this set, we place a slash through the symbol ∈. 5 ∉51, 2, 3, 46 It is customary to name sets with capital letters. S = 51, 2, 3, 46 S is used to name the set. Set S was written above by listing its elements. Set S might also be described as “the set containing the first four counting numbers.” The set F, consisting of all fractions between 0 and 1, is an example of an infinite set—one that has an unending list of distinct elements. A finite set is one that has a limited number of elements. The process of counting its elements comes to an end. Some infinite sets can be described by listing. For example, the set of numbers N used for counting, which are the natural numbers or the counting numbers, can be written as follows. N= 51, 2, 3, 4, N6 Natural (counting) numbers The three dots (ellipsis points) show that the list of elements of the set continues according to the established pattern. 151. 54% 152. 39% 153. 7% 154. 4% 155. 117% 156. 189% 157. 2.4% 158. 3.1% 159. 6 1 4 % 160. 5 1 2 % Write each decimal as a percent. See Examples 12(d)–12(f). 161. 0.79 162. 0.83 163. 0.02 164. 0.08 165. 0.004 166. 0.005 167. 1.28 168. 2.35 169. 0.4 170. 0.6
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