{"id":628670,"date":"2023-06-25T08:20:15","date_gmt":"2023-06-25T02:50:15","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/since-1-0-doesnt-exist-hence-0-has-no-____\/"},"modified":"2025-06-26T14:48:39","modified_gmt":"2025-06-26T09:18:39","slug":"since-1-0-doesnt-exist-hence-0-has-no-____","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/since-----------1----0--------doesnt-exist-hence\/","title":{"rendered":"Since           1    0       \u00a0 doesn&#8217;t exist, hence 0 has no ____."},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Since 1 0 \u00a0 doesn't exist, hence 0 has no ____.","custom_permalink":"question\/mathematics\/since-----------1----0--------doesnt-exist-hence\/"},"categories":[],"acf":{"question":"<p style=\"margin-top:0pt; margin-bottom:0pt; line-height:115%; font-size:12pt\"><span>Since <\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mrow>\r\n   <m:mfrac>\r\n    <m:mn>1<\/m:mn>\r\n    <m:mn>0<\/m:mn>\r\n   <\/m:mfrac>\r\n   <\/m:mrow>\r\n <\/m:semantics><\/math>&nbsp;<span> doesn't exist, hence 0 has no ____.<\/span><\/p><br><pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:115%;font-size:12pt\"><spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><p><\/p><pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:115%;font-size:12pt\"><spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><p><\/p><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:115%;font-size:12pt\"><\/spanstyle=\"font-family:'timesnewroman';-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt;line-height:115%;font-size:12pt\">","options":null,"solution":"<span>Since <\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mrow>\r\n   <m:mfrac>\r\n    <m:mn>1<\/m:mn>\r\n    <m:mn>0<\/m:mn>\r\n   <\/m:mfrac>\r\n   <\/m:mrow>\r\n <\/m:semantics><\/math>&nbsp;<span> doesn't exist, hence 0 has no reciprocal.<\/span><br><span>By definition, the reciprocal of a number <\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mi>x<\/m:mi>\r\n <\/m:semantics><\/math>&nbsp;<span> is a number <\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mi>y<\/m:mi>\r\n <\/m:semantics><\/math>&nbsp;<span> <\/span><span>such that <\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mrow>\r\n   <m:mi>x<\/m:mi><m:mi>y<\/m:mi><m:mo>=<\/m:mo><m:mn>1<\/m:mn><\/m:mrow>\r\n <\/m:semantics><\/math>&nbsp;<span>.<\/span><br><span>There is no such number that exists that we can multiply by 0 and get 1. So, <\/span>\r\n<math>\r\n <m:semantics>\r\n  <m:mn>0<\/m:mn>\r\n <\/m:semantics><\/math>&nbsp;<span> <\/span><span>does not have a reciprocal.<\/span><br><span>Therefore, the correct answer is reciprocal.<\/span><br><span>&nbsp;<\/span>","subject":"Mathematics"},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Since      1  0    \u00a0 doesn&#039;t exist, hence 0 has no ____. - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Since 1 0 \u00a0 doesn&#039;t exist, hence 0 has no ____.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/since-----------1----0--------doesnt-exist-hence\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Since      1  0    \u00a0 doesn&#039;t exist, hence 0 has no ____. - 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