{"id":167264,"date":"2024-11-15T14:38:48","date_gmt":"2024-11-15T14:38:48","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=167264"},"modified":"2024-11-15T14:38:50","modified_gmt":"2024-11-15T14:38:50","slug":"how-many-factors-of-10-are-in-each-power","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/15\/how-many-factors-of-10-are-in-each-power\/","title":{"rendered":"How many factors of 10 are in each power"},"content":{"rendered":"\n

How many factors of 10 are in each power? Number of factors of 10 in 10^(2) : ? Number of factors of 10 in 10^(3) : ? 10^(2)=1010 10^(3)=10<\/em>10*10<\/p>\n\n\n\n

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

To understand the number of factors of 10 in each power of 10, let’s first break down the powers of 10 and their components.<\/p>\n\n\n\n

Understanding Powers of 10:<\/h3>\n\n\n\n
    \n
  • ( 10^2 ) means ( 10 \\times 10 ), which is ( 100 ).<\/li>\n\n\n\n
  • ( 10^3 ) means ( 10 \\times 10 \\times 10 ), which is ( 1000 ).<\/li>\n<\/ul>\n\n\n\n

    Breaking Down Factors of 10:<\/h3>\n\n\n\n

    A factor of 10<\/strong> can be expressed as the product of 10, which itself can be written as:
    [
    10 = 2 \\times 5
    ]
    Thus, every factor of 10 contains both the prime factors 2 and 5. Now, we need to figure out how many times 10 divides into a given number.<\/p>\n\n\n\n

    Number of Factors of 10 in ( 10^2 ):<\/h3>\n\n\n\n

    We start with the expression for ( 10^2 ):
    [
    10^2 = 10 \\times 10 = 100
    ]
    Since ( 100 = 2^2 \\times 5^2 ), it contains exactly two 10s<\/strong> (i.e., two factors of 10). This is because each 10 can be broken into one factor of 2 and one factor of 5. So, in ( 10^2 ), there are exactly 2 factors of 10<\/strong>.<\/p>\n\n\n\n

    Number of Factors of 10 in ( 10^3 ):<\/h3>\n\n\n\n

    Now, let’s consider ( 10^3 ):
    [
    10^3 = 10 \\times 10 \\times 10 = 1000
    ]
    Since ( 1000 = 2^3 \\times 5^3 ), it contains exactly three 10s<\/strong> (i.e., three factors of 10). This means that in ( 10^3 ), there are exactly 3 factors of 10<\/strong>.<\/p>\n\n\n\n

    Conclusion:<\/h3>\n\n\n\n
      \n
    • The number of factors of 10 in ( 10^2 ) is 2<\/strong>.<\/li>\n\n\n\n
    • The number of factors of 10 in ( 10^3 ) is 3<\/strong>.<\/li>\n<\/ul>\n\n\n\n

      This relationship holds generally: the number of factors of 10 in ( 10^n ) is exactly n<\/strong> because ( 10^n ) is the product of ( n ) tens, and each of those tens contributes one factor of 10. Therefore, ( 10^n ) contains ( n ) factors of 10.<\/p>\n","protected":false},"excerpt":{"rendered":"

      How many factors of 10 are in each power? Number of factors of 10 in 10^(2) : ? Number of factors of 10 in 10^(3) : ? 10^(2)=1010 10^(3)=1010*10 The Correct Answer and Explanation is: To understand the number of factors of 10 in each power of 10, let’s first break down the powers of […]<\/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-167264","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167264","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=167264"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167264\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=167264"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=167264"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=167264"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}