{"id":252794,"date":"2025-07-11T12:26:10","date_gmt":"2025-07-11T12:26:10","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=252794"},"modified":"2025-07-11T12:26:12","modified_gmt":"2025-07-11T12:26:12","slug":"the-following-is-a-base-60-sexagesimal-number-written-in-modern-form","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/11\/the-following-is-a-base-60-sexagesimal-number-written-in-modern-form\/","title":{"rendered":"The following is a base 60 (sexagesimal) number written in modern form"},"content":{"rendered":"\n

The following is a base 60 (sexagesimal) number written in modern form: Find its value in the base-10 system. Round your answer to three decimal places, if necessary. (15,18,46; 31, 49) 60 Answer: In base-10, (15,18,46; 31,49_ (Round to 3 places) Recall that the notation (12, 34)60 means you have the number 12,34 in base 60_<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To convert the base-60 (sexagesimal) number (15,18,46; 31,49)\\\u2086\u2080 into base-10, we break it into two parts: the whole number part<\/strong> and the fractional part<\/strong>.<\/p>\n\n\n\n

Step 1: Understand the notation<\/h3>\n\n\n\n

In base-60, the notation (15,18,46; 31,49)\\\u2086\u2080 means:<\/p>\n\n\n\n

    \n
  • Whole number part = 15 \u00d7 60\u00b2 + 18 \u00d7 60\u00b9 + 46 \u00d7 60\u2070<\/li>\n\n\n\n
  • Fractional part = 31 \u00d7 60\u207b\u00b9 + 49 \u00d7 60\u207b\u00b2<\/li>\n<\/ul>\n\n\n\n

    Step 2: Convert the whole number part<\/h3>\n\n\n\n
      \n
    • 15 \u00d7 60\u00b2 = 15 \u00d7 3600 = 54000<\/li>\n\n\n\n
    • 18 \u00d7 60\u00b9 = 18 \u00d7 60 = 1080<\/li>\n\n\n\n
    • 46 \u00d7 1 = 46<\/li>\n<\/ul>\n\n\n\n

      Adding them together:
      54000 + 1080 + 46 = 55126<\/strong><\/p>\n\n\n\n

      Step 3: Convert the fractional part<\/h3>\n\n\n\n
        \n
      • 31 \u00d7 (1\/60) = 31 \u00f7 60 = 0.516666…<\/li>\n\n\n\n
      • 49 \u00d7 (1\/3600) = 49 \u00f7 3600 = 0.013611…<\/li>\n<\/ul>\n\n\n\n

        Adding them together:
        0.516666… + 0.013611… = 0.530278<\/strong><\/p>\n\n\n\n

        Step 4: Add both parts<\/h3>\n\n\n\n

        55126 + 0.530278 = 55126.530<\/strong><\/p>\n\n\n\n

        Final Answer:<\/h3>\n\n\n\n

        In base-10, (15,18,46; 31,49)\\\u2086\u2080 = 55126.530<\/strong><\/p>\n\n\n\n

        Explanation<\/h3>\n\n\n\n

        The base-60 number system, also called sexagesimal, was used by ancient Mesopotamians and is still used today in measuring time and angles. It operates similarly to our familiar base-10 system but uses powers of 60 instead of powers of 10. Each position in a sexagesimal number represents a multiple of a power of 60.<\/p>\n\n\n\n

        In the number (15,18,46; 31,49)\\\u2086\u2080, the digits to the left of the semicolon represent the whole number part, and those to the right represent the fractional part. To convert this to base-10, we multiply each digit by 60 raised to a specific power, starting with the leftmost digit. For example, the leftmost 15 is in the \u201c60 squared\u201d place, so we multiply 15 by 3600. The next digit, 18, is multiplied by 60. The last digit of the whole part, 46, is in the ones place.<\/p>\n\n\n\n

        The fractional part uses negative powers of 60. The first digit after the semicolon, 31, is in the 1\/60 place, and the next digit, 49, is in the 1\/3600 place. Each is converted to decimal and added to the whole number.<\/p>\n\n\n\n

        Finally, we add the decimal equivalents of both the whole and fractional parts to get the base-10 value. Rounding to three decimal places gives the final result: 55126.530<\/strong>.<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        The following is a base 60 (sexagesimal) number written in modern form: Find its value in the base-10 system. Round your answer to three decimal places, if necessary. (15,18,46; 31, 49) 60 Answer: In base-10, (15,18,46; 31,49_ (Round to 3 places) Recall that the notation (12, 34)60 means you have the number 12,34 in base […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-252794","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/252794","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=252794"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/252794\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=252794"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=252794"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=252794"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}