{"id":4436,"date":"2016-10-03T21:12:40","date_gmt":"2016-10-03T21:12:40","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/intermediatealgebra\/?post_type=chapter&p=4436"},"modified":"2023-11-08T13:18:42","modified_gmt":"2023-11-08T13:18:42","slug":"introduction-8","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/cuny-hunter-collegealgebra\/chapter\/introduction-8\/","title":{"raw":"Introduction","rendered":"Introduction"},"content":{"raw":"
\r\n

Why learn how to use exponents?<\/h2>\r\n<\/div>\r\n\r\n[caption id=\"attachment_2270\" align=\"alignleft\" width=\"440\"]\"Artist's Artist's concept of Voyager in flight.[\/caption]\r\n\r\nMathematicians, scientists, and economists commonly encounter very large and very small numbers. \u00a0For example, Star Wars fans may remember Han Solo bragging about the Millennium Falcon<\/em>'s ability to make the Kessel Run in less than 12 parsecs in Episode IV. \u00a0He was referring to a smuggler's route with sections\u00a0that were flown in hyperspace, making length an important factor in how quickly a ship could make the run.\r\n\r\nIn reality, a parsec is a unit of length used to measure large distances to objects outside the solar system. A parsec is equal to about 31 trillion kilometers, or 19 trillion miles\u00a0in length. Rather than writing all the zeros associated with the number 1 trillion (1,000,000,000,000) we commonly use the written words or scientific notation. Scientific notation uses exponents to represent the number of zeros that come before or after the important digits of a very small or large number. Using scientific notation, 19 trillion miles would be written [latex]{1.9}\\times{10}^{13}[\/latex] miles.\r\n\r\nThe most distant space probe, Voyager 1, was 0.0006 parsecs from Earth as of March 2015. It took Voyager 37 years to cover that distance. Voyager 1 was launched by NASA on September 5, 1977. As of 2013, the probe was moving with a relative velocity to the sun of about 17030\u00a0m\/s. With the velocity the probe is currently maintaining, Voyager 1 is traveling about 325 million miles per year, or 520 million kilometers per year. Here are some more distances to well-known astronomical objects in parsecs:\r\n
    \r\n \t
  • The distance to the open cluster Pleiades is 130\u00a0parsecs from Earth. That's [latex]{1.7}\\times{10}^{15}[\/latex] miles.<\/li>\r\n \t
  • The center of the Milky Way is more than 8 kiloparsecs (a kiloparsec is 1000 parsecs) from Earth, and the Milky Way is roughly 34 kiloparsecs across.<\/li>\r\n \t
  • The nearest star to Earth, Proxima Centauri, is about 1.3 parsecs from the sun.<\/li>\r\n \t
  • Most of the stars visible to the unaided eye in the nighttime sky are within 500 parsecs of the sun.<\/li>\r\n<\/ul>","rendered":"
    \n

    Why learn how to use exponents?<\/h2>\n<\/div>\n
    \"Artist's<\/p>\n

    Artist’s concept of Voyager in flight.<\/p>\n<\/div>\n

    Mathematicians, scientists, and economists commonly encounter very large and very small numbers. \u00a0For example, Star Wars fans may remember Han Solo bragging about the Millennium Falcon<\/em>‘s ability to make the Kessel Run in less than 12 parsecs in Episode IV. \u00a0He was referring to a smuggler’s route with sections\u00a0that were flown in hyperspace, making length an important factor in how quickly a ship could make the run.<\/p>\n

    In reality, a parsec is a unit of length used to measure large distances to objects outside the solar system. A parsec is equal to about 31 trillion kilometers, or 19 trillion miles\u00a0in length. Rather than writing all the zeros associated with the number 1 trillion (1,000,000,000,000) we commonly use the written words or scientific notation. Scientific notation uses exponents to represent the number of zeros that come before or after the important digits of a very small or large number. Using scientific notation, 19 trillion miles would be written [latex]{1.9}\\times{10}^{13}[\/latex] miles.<\/p>\n

    The most distant space probe, Voyager 1, was 0.0006 parsecs from Earth as of March 2015. It took Voyager 37 years to cover that distance. Voyager 1 was launched by NASA on September 5, 1977. As of 2013, the probe was moving with a relative velocity to the sun of about 17030\u00a0m\/s. With the velocity the probe is currently maintaining, Voyager 1 is traveling about 325 million miles per year, or 520 million kilometers per year. Here are some more distances to well-known astronomical objects in parsecs:<\/p>\n

      \n
    • The distance to the open cluster Pleiades is 130\u00a0parsecs from Earth. That’s [latex]{1.7}\\times{10}^{15}[\/latex] miles.<\/li>\n
    • The center of the Milky Way is more than 8 kiloparsecs (a kiloparsec is 1000 parsecs) from Earth, and the Milky Way is roughly 34 kiloparsecs across.<\/li>\n
    • The nearest star to Earth, Proxima Centauri, is about 1.3 parsecs from the sun.<\/li>\n
    • Most of the stars visible to the unaided eye in the nighttime sky are within 500 parsecs of the sun.<\/li>\n<\/ul>\n","protected":false},"author":21,"menu_order":1,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4436","chapter","type-chapter","status-web-only","hentry"],"part":774,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/cuny-hunter-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/4436","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/cuny-hunter-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/cuny-hunter-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/cuny-hunter-collegealgebra\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":3,"href":"https:\/\/courses.lumenlearning.com\/cuny-hunter-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/4436\/revisions"}],"predecessor-version":[{"id":4847,"href":"https:\/\/courses.lumenlearning.com\/cuny-hunter-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/4436\/revisions\/4847"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/cuny-hunter-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/774"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/cuny-hunter-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/4436\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/cuny-hunter-collegealgebra\/wp-json\/wp\/v2\/media?parent=4436"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/cuny-hunter-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=4436"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/cuny-hunter-collegealgebra\/wp-json\/wp\/v2\/contributor?post=4436"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/cuny-hunter-collegealgebra\/wp-json\/wp\/v2\/license?post=4436"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}