{"id":1065,"date":"2012-12-07T18:14:45","date_gmt":"2012-12-07T18:14:45","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=1065"},"modified":"2012-12-07T22:41:03","modified_gmt":"2012-12-07T22:41:03","slug":"significant-figures-zeros","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/significant-figures-zeros\/","title":{"rendered":"Significant Figures: Zeros"},"content":{"rendered":"

Tutoring\u00a0physics or chemistry, significant figures are part of the landscape.\u00a0 Knowing when zero is significant can be tricky.<\/h1>\n

In this, our second installment on significant figures (see the first one here<\/a>), we start on\u00a0the practical question,\u00a0 “What digits are significant?”\u00a0 However, that question might be a bit ambitious for one post.\u00a0 We’ll restrict today’s article to “When is zero significant?”<\/p>\n

Numbers that result from calculations have other factors to consider.\u00a0 For the purpose of this talk, we’ll assume we know nothing about how the number came about; we only know it “by sight”.<\/p>\n

Case 1:\u00a0\u00a0a zero between two nonzero digits.<\/p>\n

Simple:\u00a0 Always significant.<\/p>\n

Example:\u00a0 In the number 502, zero is significant.<\/p>\n

Case 2:\u00a0 a zero after a nonzero digit but before an unwritten<\/em> decimal.<\/p>\n

Simple:\u00a0 Not significant.<\/p>\n

Example:\u00a0 In 7600 the zeros are not significant.<\/p>\n

Case 3:\u00a0 a zero\u00a0after a nonzero digit, but before\u00a0a written<\/em> decimal.<\/p>\n

Simple:\u00a0 Always significant.<\/p>\n

Example:\u00a0 In 7600.<\/strong> the zeros are<\/em> significant.<\/p>\n

Yes, indeed:\u00a0 120 and 120.<\/strong> are not<\/em> the same, from a science point of view.\u00a0 Their values are equal from\u00a0the point of view of doing calculations, but the results of the calculations have different meaning.<\/p>\n

Case 4:\u00a0 Zeros to the left of the first nonzero digit.<\/p>\n

Simple:\u00a0 Never significant.<\/p>\n

Example:\u00a0 in 0.0035, the zeros are not significant.<\/p>\n

Case 5:\u00a0 Zeros following a nonzero digit\u00a0and<\/strong> a decimal point:<\/p>\n

Simple:\u00a0 Always significant.<\/p>\n

Example:\u00a0 in 0.003 500 00, the four zeros\u00a0following the five are<\/em> significant.<\/p>\n

Example:\u00a0 in 13.0, the zero is<\/em> significant.<\/p>\n

We have another situation unique to significant figures:\u00a0 12 and 12.0 are not the same.\u00a0 80.1 and 80.100 are not the same, either, from the point of view of sig figs.<\/p>\n

Let’s say you want a zero to be significant, but normal rules say it’s not.\u00a0 Consider the following number:<\/p>\n

23 000<\/p>\n

We know that, since the decimal is unwritten<\/em>, the three zeros are not significant.\u00a0 However, what if, from the measurement itself, you know that\u00a0the first zero actually is<\/em> significant?<\/p>\n

You can put a dash over the 0 that normally wouldn’t be significant to show that it is:
\n\"\"<\/p>\n

Now that people use\u00a0scientific notation (which we’ll need to discuss in a future post), you rarely see the dashes anymore.<\/p>\n

Jack of Oracle Tutoring by Jack and Diane<\/a>, Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"

Tutoring\u00a0physics or chemistry, significant figures are part of the landscape.\u00a0 Knowing when zero is significant can be tricky. In this, our second installment on significant figures (see the first one here), we start on\u00a0the practical question,\u00a0 “What digits are significant?”\u00a0 …<\/p>\n

Significant Figures: Zeros<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11,7,10],"tags":[],"class_list":["post-1065","post","type-post","status-publish","format-standard","hentry","category-chemistry","category-physics","category-sciences"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/1065","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=1065"}],"version-history":[{"count":39,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/1065\/revisions"}],"predecessor-version":[{"id":1104,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/1065\/revisions\/1104"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=1065"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=1065"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=1065"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}