{"id":11758,"date":"2018-12-14T12:32:15","date_gmt":"2018-12-14T04:32:15","guid":{"rendered":"https:\/\/www.intmath.com\/blog\/?p=11758"},"modified":"2018-12-17T20:16:00","modified_gmt":"2018-12-17T12:16:00","slug":"units-calories-and-kilograms","status":"publish","type":"post","link":"https:\/\/www.intmath.com\/blog\/mathematics\/units-calories-and-kilograms-11758","title":{"rendered":"Units: Calories and kilograms"},"content":{"rendered":"<p>Two related stories about units came my way recently. <\/p>\n<h3>(a) Calorie or calorie?<\/h3>\n<p>Reader <em class=\"textem\">goldierocks<\/em> recently commented on an  article I wrote some years ago (<a href=\"https:\/\/www.intmath.com\/blog\/mathematics\/google-calculator-handy-but-not-always-correct-1314\">Google calculator - handy, but not always correct<\/a>) when Google began incorporating calculator answers into search. The calculator had scientific options (trigonometric calculations, logs, and so on) and was a good tool, especially as it was free.<\/p>\n<p>However, it didn't handle large number calculations well - the inevitable product of  computers thinking in binary digits, while we humans ask it to calculate things in the decimal system.<\/p>\n<p>My article pointed out what some of those large number calculation errors were, and I pointed to a longer article with more detail. <\/p>\n<p>Back to the <em class=\"textem\">goldierocks<\/em> comment, where (s)he said:<\/p>\n<blockquote>\n<p>Google calculator can be hopelessly wrong. For energy calculations it can be out by a factor of 1000 times (e.g. calorie to kilojoules - they have confused calories and kilocalories) <\/p>\n<\/blockquote>\n<p>I did a bit more investigation before I replied. <\/p>\n<p>On this <a href=\"https:\/\/www.checkyourmath.com\/convert\/energy\/kj_calories.php\">Convert calories to kJ<\/a> page by CheckYourMath, which provides a calculator for conversions in both directions, it says: <\/p>\n<blockquote>\n<p>A calorie is measured as the quantity of heat required to raise the temperature of 1 gram of water by 1&deg;C from a standard initial temperature at a pressure of 1 atmosphere. A calorie is also called a &quot;small calorie&quot; or &quot;gram calorie&quot;.<\/p>\n<\/blockquote>\n<p>For most people, the first thing that comes to mind when we hear &quot;calorie&quot; is the size of our wasteline and the need to cut food consumption. (The word &quot;calorie&quot; is derived from the French word &quot;<em class=\"textem\">calor&quot;<\/em> which means &quot;heat&quot;). <\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/www.intmath.com\/blog\/wp-content\/images\/2018\/12\/obesity.jpg\" alt=\"Obesity\" width=\"300\" height=\"219\" \/><\/p>\n<p>This <a href=\"https:\/\/www.britannica.com\/science\/calorie\">Britannica article on Calorie<\/a> points out the (small &quot;c&quot;) calorie ranges from 4.1855 joules to 4.19002 joules (it varies depending on the ambient temperature and pressure), while the (upper case &quot;C&quot;) Calorie (or &quot;kilogram calorie&quot;) used by food scientists, is really a kilocalorie, or 1,000 calories. For example: <\/p>\n<blockquote>\n<p>If a peach is listed as having 40 Calories, this indicates that that peach has actually 40,000 calories<\/p>\n<\/blockquote>\n<p>The CheckYourMath page  correctly used the lower-case &quot;c&quot;.<\/p>\n<p>So as I said to <em>goldierocks<\/em>, the Google calculator is addressing their most likely audience of obesity worriers - not the smaller number of science majors. However, the search result should point out they are using &quot;food Calories&quot; and use upper-case &quot;C&quot;, wherever that is the case . <\/p>\n<h4>Interesting search results<\/h4>\n<p>I noticed some interesting  differences in the Google results with what seems like almost identical search terms.<\/p>\n<p>(1) 1 calorie in kj<\/p>\n<p>Here I'm using lower-case &quot;j&quot; in &quot;kj&quot;. The result (in the drop-down list in the address bar, before going on to the search results page) is the &quot;food Calorie&quot; case: <\/p>\n<p class=\"indent\"><img loading=\"lazy\" src=\"https:\/\/www.intmath.com\/blog\/wp-content\/images\/2018\/12\/calorie-kj-2.png\" alt=\"Search result - 1 calorie in kj\" width=\"180\" height=\"118\" \/><\/p>\n<p>(2) 1 calorie in kJ<\/p>\n<p>When I do the same thing using upper-case &quot;J&quot; as in &quot;kJ&quot;, it appears to assume I have more scientific intent and so gives the &quot;small c&quot; answer in the address bar. Note the icon that indicates it's giving the answer using the &quot;scientific calculator&quot;: <\/p>\n<p class=\"indent\"><img loading=\"lazy\" src=\"https:\/\/www.intmath.com\/blog\/wp-content\/images\/2018\/12\/calorie-kj-1.png\" alt=\"Search result - 1 calorie in kJ\" width=\"180\" height=\"133\" \/><\/p>\n<p>(3) Opening the actual search result page<\/p>\n<p>This time, it gives a &quot;kilocalorie to kilojoules&quot; result: <\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/www.intmath.com\/blog\/wp-content\/images\/2018\/12\/calorie-kj-3.png\" alt=\"SERP result\" width=\"348\" height=\"171\" \/><\/p>\n<h3>(b) The kilogram is changing <\/h3>\n<p>The <strong>kilogram<\/strong> is one of the base units in the metric system, along with the meter, second, Ampere, Kelvin, Mole, candela.<\/p>\n<p>For over 200 years, the &quot;standard kilogram&quot;, used to compare and calibrate scales all over the world, has been a metalic cylinder kept in France. In <a href=\"https:\/\/aperiodical.com\/2018\/11\/kilogram-definition-to-be-changed-to-be-based-on-plancks-constant\/\">Kilogram definition to be changed  based on Planck&rsquo;s constant<\/a> we learn the problem with this cylinder is that over time, it's weight has actually dropped by around 50 &micro;g, about the mass of an eyelash) and that means the precision of anything that is compared to it, becomes inaccurate over time.<\/p>\n<p>In the Vox article, <a href=\"https:\/\/www.vox.com\/science-and-health\/2018\/11\/14\/18072368\/kilogram-kibble-redefine-weight-science\">The world just redefined the kilogram<\/a> they point out there are several copies of the &quot;kilogram cylinder&quot;, including in the US. Instead of (sensibly) using it as-is and producing metric scales, they do a conversion (in the US, 1 pound is defined as 0.45359237 kilograms. A foot is defined as 0.3048 meters.)<\/p>\n<p>They also describe the Kibble balance, a machine that can make use of Planck's constant to very precisely weigh objects.<\/p>\n<p>As a result of the recent meeting, the <a href=\"https:\/\/www.bipm.org\/utils\/common\/pdf\/CGPM-2018\/26th-CGPM-Resolutions.pdf\">Resolutions<\/a> (PDF) of the General Conference on Weights and Measures state: <\/p>\n<blockquote>\n<p>The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant <em>h<\/em> to be 6.626 070 15 &times; 10<sup>&ndash;34<\/sup> when expressed in the unit J s, which is equal to kg m<sup>2<\/sup> s<sup>&ndash;1<\/sup>, where the metre and the second are defined in terms of <em>c<\/em> and [the caesium frequency] &Delta;<em>v<\/em><sub>Cs<\/sub>. <\/p>\n<\/blockquote>\n<h4>Irony<\/h4>\n<p>There is an image on the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Kilogram\">Wikipedia Kilogram page<\/a> of <em>Le Grand K<\/em>, the cylinder made of platinum-iridium alloy  which has represented the kg since 1799.<\/p>\n<p>Strangely, it uses an <strong>inch<\/strong> ruler for size comparison! <\/p>\n<p><img loading=\"lazy\" src=\"https:\/\/www.intmath.com\/blog\/wp-content\/images\/2018\/12\/le-grand-k.jpg\" alt=\"Le Grand K - with inch ruler!\" width=\"300\" height=\"157\" \/><\/p>\n<p class=\"alt\">See the <a href=\"https:\/\/www.intmath.com\/blog\/mathematics\/units-calories-and-kilograms-11758#comments\" id=\"comms\">1 Comment<\/a> below.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>  <a href=\"https:\/\/www.intmath.com\/blog\/mathematics\/units-calories-and-kilograms-11758\"><img loading=\"lazy\" src=\"https:\/\/www.intmath.com\/blog\/wp-content\/images\/2018\/12\/le-grand-k_th.jpg\" alt=\"Le Grand K with inch ruler\" width=\"128\" height=\"100\" class=\"imgRt\" \/><\/a><br \/>\nHow many calories? and the way the kilogram was defined has been in place since 1799. It recently got a makeover. <\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mo_disable_npp":""},"categories":[4],"tags":[130],"_links":{"self":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/11758"}],"collection":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/comments?post=11758"}],"version-history":[{"count":3,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/11758\/revisions"}],"predecessor-version":[{"id":11774,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/11758\/revisions\/11774"}],"wp:attachment":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/media?parent=11758"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/categories?post=11758"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/tags?post=11758"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}