{"id":2785,"date":"2024-08-25T12:19:26","date_gmt":"2024-08-25T12:19:26","guid":{"rendered":"https:\/\/workhouse.sweetdishy.com\/?p=2785"},"modified":"2024-08-25T12:19:27","modified_gmt":"2024-08-25T12:19:27","slug":"measuring-errors","status":"publish","type":"post","link":"https:\/\/workhouse.sweetdishy.com\/index.php\/2024\/08\/25\/measuring-errors\/","title":{"rendered":"MEASURING ERRORS"},"content":{"rendered":"\n<p id=\"para-107\">Measurement is essentially an act by which a comparison is made between a given quantity and a quantity of the same kind chosen as a unit of measurement, that is, standard quantity. To make this comparison, a device is used called measuring instrument. When an unknown quantity is measured, the value thus obtained is considered to be a true value but it is seldom true. There is always some difference between the measured value and the true or exact value of the unknown quantity.<\/p>\n\n\n\n<p id=\"para-108\">The difference between the measured value (<em>A<\/em><sub>m<\/sub>) and the actual or true value&nbsp;<em>A<\/em>&nbsp;of the unknown quantity is called absolute error of measurement (<em>\u03b4<\/em><em>A<\/em>).<\/p>\n\n\n\n<p id=\"para-109\">i.e.,<em><\/em><\/p>\n\n\n\n<p id=\"para-110\">&nbsp;<\/p>\n\n\n\n<p><em>\u03b5<\/em><sub>0<\/sub>&nbsp;=<em>&nbsp;<\/em><em>\u03b4<\/em>&nbsp;<em>A<\/em>&nbsp;=&nbsp;<em>A<\/em><sub>m<\/sub><em>&nbsp;<\/em>\u2013&nbsp;<em>A<\/em><\/p>\n\n\n\n<p id=\"para-111\">The absolute value of error&nbsp;<em>\u03b4<\/em><em>A<\/em>&nbsp;does not indicate precisely the accuracy of measurement. For example, while measuring the circumference of earth if the absolute error is 1 cm, it is&nbsp;<a><\/a>considered to be negligible; however, if this error occurs while measuring the circumference of a cricket ball, then it is quite significant. Therefore, it is preferred to represent the error in terms of relative error than to represent in absolute form.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"h4-007\">9.6.1&nbsp;&nbsp;Relative Error<\/h4>\n\n\n\n<p id=\"para-112\">The ratio of absolute error to the true value of quantity to be measured is termed as relative error.<\/p>\n\n\n\n<p id=\"para-113\">i.e.,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332558311\/files\/images\/page445_1.png\" alt=\"image\"\/><\/figure>\n\n\n\n<p id=\"para-114\">When the absolute error&nbsp;<em>\u03b5<\/em><sub>0<\/sub>&nbsp;or&nbsp;<em>\u03b4<\/em><em>A<\/em>&nbsp;is negligible, that is, when the difference between measured value&nbsp;<em>A<\/em><sub>m<\/sub>&nbsp;and true value&nbsp;<em>A<\/em>&nbsp;is negligible, then relative error may be expressed as<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332558311\/files\/images\/page445_2.png\" alt=\"image\"\/><\/figure>\n\n\n\n<p id=\"para-115\">The relative error may be represented as a fraction or as a percentage.<\/p>\n\n\n\n<p id=\"para-116\">i.e.,<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/learning.oreilly.com\/api\/v2\/epubs\/urn:orm:book:9789332558311\/files\/images\/page445_3.png\" alt=\"image\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Measurement is essentially an act by which a comparison is made between a given quantity and a quantity of the same kind chosen as a unit of measurement, that is, standard quantity. To make this comparison, a device is used called measuring instrument. When an unknown quantity is measured, the value thus obtained is considered [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":2483,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[412],"tags":[],"class_list":["post-2785","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-measuring-instruments"],"jetpack_featured_media_url":"https:\/\/workhouse.sweetdishy.com\/wp-content\/uploads\/2024\/08\/download-4.jpeg","_links":{"self":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2785","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/comments?post=2785"}],"version-history":[{"count":1,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2785\/revisions"}],"predecessor-version":[{"id":2786,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/posts\/2785\/revisions\/2786"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media\/2483"}],"wp:attachment":[{"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/media?parent=2785"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/categories?post=2785"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/workhouse.sweetdishy.com\/index.php\/wp-json\/wp\/v2\/tags?post=2785"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}