{"id":200,"date":"2019-06-26T22:59:52","date_gmt":"2019-06-26T22:59:52","guid":{"rendered":"http:\/\/funfacts.104.42.120.246.xip.io\/?page_id=200"},"modified":"2019-12-11T17:05:34","modified_gmt":"2019-12-11T17:05:34","slug":"powers-of-ten-in-base-two-and-five","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/funfacts\/powers-of-ten-in-base-two-and-five\/","title":{"rendered":"Powers of Ten in Base Two and Five"},"content":{"rendered":"\n<p>Make two lists; one consists of all powers of 10 in base 2, and the other all powers of 10 in base 5. (Powers of 10 are 10, 100, 1000, etc.)<\/p>\n\n\n\n<p>Fun Fact: for any integer N > 1, there is exactly one number in exactly one of the lists that is exactly N\u00a0digits\u00a0long!<\/p>\n\n\n\n<p><strong>Presentation&nbsp;Suggestions:<\/strong><br>Show students the first terms in each list: they are&nbsp;<br>(base 2) 1010, 1100100, 1111101000, &#8230;&nbsp;<br>(base 5) 20, 400, 13000, 310000, &#8230;<\/p>\n\n\n\n<p><strong>The&nbsp;Math&nbsp;Behind&nbsp;the&nbsp;Fact:<\/strong><br>This fact is quite startling when you first see it. Proving it makes a great exercise for a Putnam problem-solving seminar&#8230;<\/p>\n\n\n\n<p><strong>How to Cite this Page:<\/strong>&nbsp;<br>Su, Francis E., et al. &#8220;Powers of Ten in Base Two and Five.&#8221;&nbsp;<em>Math Fun Facts<\/em>. &lt;http:\/\/www.math.hmc.edu\/funfacts&gt;.<\/p>\n\n\n\n<p><strong>References:<\/strong><br>R. Vakil, <em><a href=\"https:\/\/www.amazon.com\/exec\/obidos\/ASIN\/1895997046\/ref=nosim\/mathfunfacts-20\">A Mathematical Mosaic<\/a><\/em>, 1996. p.131.<\/p>\n\n\n\n<p><strong>Fun Fact suggested by:   <\/strong><br>Ravi Vakil<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Make two lists; one consists of all powers of 10 in base 2, and the other all powers of 10&#46;&#46;&#46;<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[3,10,12],"class_list":["post-200","page","type-page","status-publish","hentry","tag-easy","tag-numtheory","tag-other"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/200","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/comments?post=200"}],"version-history":[{"count":4,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/200\/revisions"}],"predecessor-version":[{"id":1577,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/200\/revisions\/1577"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=200"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=200"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}