![\"Q=](\"https:\/\/www.bellevuecollege.edu\/wp-content\/uploads\/sites\/166\/2014\/11\/H-Draft1.gif\")
<\/p>\nSuppose we calculate a quantity Q based on the measured values x,y, and z. Then Q is a function of three variables.<\/p>\n
<\/p>\n
<\/p>\n
<\/p>\n
Each of the measured values will have an associated uncertainty Suppose that Q is given by the function shown, , where k = 0.3872 is a constant. Also assume that we have the measured values<\/p>\n . (We will round after the uncertainty has been found)<\/p>\n Now find the partial derivatives<\/p>\n and finally compute the uncertainty in Q using the expression above.<\/p>\n So rounding to one significant figure. Combining with the computed value for Q and rounding so that it agrees with the uncertainty gives .<\/p>\n If you apply the simpler rules described in section G, you will find to give for the final result. You can see that the simpler rules slightly overestimate the uncertainty.<\/p>\n","protected":false},"excerpt":{"rendered":" Suppose we calculate a quantity Q based on the measured values x,y, and z. Then Q is a function of three variables. Each of the measured values will have an associated uncertainty , , and . Then the formal uncertainty in Q is given by the expression This expression may seem intimidating at ...more about H. Precision of Computed Results (Formal Method)<\/a><\/p>\n","protected":false},"author":86,"featured_media":0,"parent":46,"menu_order":8,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-165","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.bellevuecollege.edu\/physics\/wp-json\/wp\/v2\/pages\/165","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.bellevuecollege.edu\/physics\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.bellevuecollege.edu\/physics\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.bellevuecollege.edu\/physics\/wp-json\/wp\/v2\/users\/86"}],"replies":[{"embeddable":true,"href":"https:\/\/www.bellevuecollege.edu\/physics\/wp-json\/wp\/v2\/comments?post=165"}],"version-history":[{"count":2,"href":"https:\/\/www.bellevuecollege.edu\/physics\/wp-json\/wp\/v2\/pages\/165\/revisions"}],"predecessor-version":[{"id":221,"href":"https:\/\/www.bellevuecollege.edu\/physics\/wp-json\/wp\/v2\/pages\/165\/revisions\/221"}],"up":[{"embeddable":true,"href":"https:\/\/www.bellevuecollege.edu\/physics\/wp-json\/wp\/v2\/pages\/46"}],"wp:attachment":[{"href":"https:\/\/www.bellevuecollege.edu\/physics\/wp-json\/wp\/v2\/media?parent=165"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"X+-AX\"](\"https:\/\/www.bellevuecollege.edu\/wp-content\/uploads\/sites\/166\/2014\/11\/H-Draft2.gif\")
<\/a>,![\"math\"](\"https:\/\/www.bellevuecollege.edu\/wp-content\/uploads\/sites\/166\/2014\/11\/H-Draft3a.gif\")
<\/a> , and ![\"math\"](\"https:\/\/www.bellevuecollege.edu\/wp-content\/uploads\/sites\/166\/2014\/11\/H-Draft4.gif\")
<\/a>. Then the formal uncertainty in Q is given by the expression<\/p>\n<\/a>
\nThis expression may seem intimidating at first but is rather easy to interpret. The “curly d” derivative used, is called the partial derivative of f with respect to x. It is easy to compute since you simply pretend that y and z are constant and find the ordinary derivative with respect to x. The following example will illustrate the method and all of the details.<\/p>\n
\nFirst compute Q<\/p>\n