{"id":3411,"date":"2021-04-29T20:52:20","date_gmt":"2021-04-29T18:52:20","guid":{"rendered":"https:\/\/agora.xtec.cat\/cfacanovelles\/?p=3411"},"modified":"2021-04-29T20:52:20","modified_gmt":"2021-04-29T18:52:20","slug":"sistema-metric-decimal-longitud-massa-capacitat-superficie-i-volum","status":"publish","type":"post","link":"https:\/\/agora.xtec.cat\/cfacanovelles\/matematiques-ii\/sistema-metric-decimal-longitud-massa-capacitat-superficie-i-volum\/","title":{"rendered":"Sistema m\u00e8tric decimal: longitud, massa, capacitat, superf\u00edcie i volum"},"content":{"rendered":"<p>Per fer mesuraments, cal un sistema d&#8217;unitats, \u00e9s a dir un conjunt de magnituds amb les que es comparen les coses que es volen mesurar.<\/p>\n<p>El sistema m\u00e8tric decimal \u00e9s un sistema d&#8217;unitats en els quals els m\u00faltiples i els subm\u00faltiples de la unitat de mesura estan relacionats entre si per m\u00faltiples o subm\u00faltiples de\u00a010.<\/p>\n<p>Per exemple, pertanyen al sistema m\u00e8tric decimal: el gram i el quilogram (per mesurar la massa), el metro i el cent\u00edmetre (per mesurar longitud) o el litre (per mesurar capacitat).<\/p>\n<p>A banda del sistema m\u00e8tric decimal, hi ha altres sistemes d&#8217;unitats: el sistema sax\u00f3, les anomenades mesures tradicionals, etc.<\/p>\n<h2>Mesures de longitud<\/h2>\n<p>La unitat principal per mesurar longituds \u00e9s el metre. No obstant aix\u00f2, hi ha altres unitats:<\/p>\n<table>\n<thead>\n<tr>\n<th>Nom<\/th>\n<th>S\u00edmbol<\/th>\n<th>Equival\u00e8ncia<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>kil\u00f2metre<\/td>\n<td>km<\/td>\n<td>1000 m<\/td>\n<\/tr>\n<tr>\n<td>hect\u00f2metre<\/td>\n<td>hm<\/td>\n<td>100 m<\/td>\n<\/tr>\n<tr>\n<td>dec\u00e0metre<\/td>\n<td>dam<\/td>\n<td>10 m<\/td>\n<\/tr>\n<tr>\n<td>metre<\/td>\n<td>m<\/td>\n<td>1 m<\/td>\n<\/tr>\n<tr>\n<td>dec\u00edmetre<\/td>\n<td>dm<\/td>\n<td>0.1 m<\/td>\n<\/tr>\n<tr>\n<td>cent\u00edmetre<\/td>\n<td>cm<\/td>\n<td>0.01 m<\/td>\n<\/tr>\n<tr>\n<td>mil\u00edmetre<\/td>\n<td>mm<\/td>\n<td>0.001 m<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Per passar una quantitat d&#8217;una unitat a una altra:<\/p>\n<ul>\n<li>Si la unitat original \u00e9s menor que la que es vol obtenir, es dividir\u00e0 la quantitat per\u00a010\u00a0tantes vegades com files s&#8217;hagi de &#8220;pujar&#8221; a la taula anterior.<\/li>\n<li>Si la unitat original \u00e9s m\u00e9s gran que la que es vol obtenir, es multiplicar\u00e0 la quantitat per\u00a010\u00a0tantes vegades com files s&#8217;hagi de &#8220;baixar&#8221; a la taula anterior.<\/li>\n<\/ul>\n<div class=\"ejemplo\">\n<table style=\"border-color: #000000; background-color: #26c7f0;\">\n<tbody>\n<tr>\n<td style=\"width: 819px;\"><strong><em><span style=\"font-family: inherit; font-size: 1em;\">Exemple<\/span><\/em><\/strong><\/p>\n<div class=\"ejemplo\">\n<p>Si es vol passar\u00a01.400\u00a0metres a dec\u00e0metre es fa:<\/p>\n<p>Un metre \u00e9s menor que un dec\u00e0metre, per tant s&#8217;ha de dividir\u00a01.400\u00a0per\u00a010\u00a0una vegada (perqu\u00e8 de metre a dec\u00e0metre hem de pujar una vegada). Es t\u00e9:<\/p>\n<p>140010=140\u00a0dec\u00e0metres.<\/p>\n<p>\u00c9s a dir,\u00a01.400\u00a0metres s\u00f3n\u00a0140\u00a0dec\u00e0metres.<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h2>Mesures de massa<\/h2>\n<p>La unitat principal per mesurar massa \u00e9s el gram. Les altres unitats que hi ha s\u00f3n:<\/p>\n<table>\n<thead>\n<tr>\n<th>Nom<\/th>\n<th>S\u00edmbol<\/th>\n<th>Equival\u00e8ncia<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>kilogram<\/td>\n<td>kg<\/td>\n<td>1000 g<\/td>\n<\/tr>\n<tr>\n<td>hectogram<\/td>\n<td>hg<\/td>\n<td>100 g<\/td>\n<\/tr>\n<tr>\n<td>decagram<\/td>\n<td>dag<\/td>\n<td>10 g<\/td>\n<\/tr>\n<tr>\n<td>gram<\/td>\n<td>g<\/td>\n<td>1 g<\/td>\n<\/tr>\n<tr>\n<td>decigram<\/td>\n<td>dg<\/td>\n<td>0.1 g<\/td>\n<\/tr>\n<tr>\n<td>centigram<\/td>\n<td>cg<\/td>\n<td>0.01 g<\/td>\n<\/tr>\n<tr>\n<td>miligram<\/td>\n<td>mg<\/td>\n<td>0.001 g<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Per passar una quantitat d&#8217;una unitat a una altra:<\/p>\n<ul>\n<li>Si la unitat original \u00e9s menor que la que es vol obtenir, es dividir\u00e0 la quantitat per\u00a010\u00a0tantes vegades com files s&#8217;hagi de &#8220;pujar&#8221; a la taula anterior.<\/li>\n<li>Si la unitat original \u00e9s m\u00e9s gran que la que es vol obtenir, es multplicar\u00e1 la quantitat per\u00a010\u00a0tantes vegades com files s&#8217;hagi de &#8220;baixar&#8221; a la taula anterior.<\/li>\n<\/ul>\n<div class=\"ejemplo\">\n<table style=\"border-color: #000000; background-color: #26c7f0;\">\n<tbody>\n<tr>\n<td style=\"width: 819px;\"><strong><em><span style=\"font-family: inherit; font-size: 1em;\">Exemple<\/span><\/em><\/strong><\/p>\n<div class=\"ejemplo\">\n<p>Si es vol passar\u00a023,4\u00a0hectograms a decigrams es fa: Un hectogram \u00e9s m\u00e9s gran que un decigram, per tant s&#8217;ha de multiplicar\u00a023,4\u00a0per\u00a010\u00a0tres vegades, ja que en la taula anterior s&#8217;han de baixar tres files per anar de hectogram a decigram.<\/p>\n<p>Per tant:<\/p>\n<p>23,4\u22c510\u22c510\u22c510=23400decigrams.<\/p>\n<p>\u00c9s a dir\u00a023,4\u00a0hectograms s\u00f3n\u00a023400\u00a0decigrams.<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h2>Mesures de capacitat<\/h2>\n<p>Per mesurar la capacitat, es fa servir com a unitat principal el litre. La seg\u00fcent taula mostra les altres mesures de capacitat m\u00e9s comuns:<\/p>\n<table>\n<thead>\n<tr>\n<th>Nom<\/th>\n<th>S\u00edmbol<\/th>\n<th>Equival\u00e8ncia<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>kilolitre<\/td>\n<td>kl<\/td>\n<td>1000 l<\/td>\n<\/tr>\n<tr>\n<td>hectolitre<\/td>\n<td>hl<\/td>\n<td>100 l<\/td>\n<\/tr>\n<tr>\n<td>decalitre<\/td>\n<td>dal<\/td>\n<td>10 l<\/td>\n<\/tr>\n<tr>\n<td>litre<\/td>\n<td>l<\/td>\n<td>1 l<\/td>\n<\/tr>\n<tr>\n<td>decilitre<\/td>\n<td>dl<\/td>\n<td>0.1 l<\/td>\n<\/tr>\n<tr>\n<td>centilitre<\/td>\n<td>cl<\/td>\n<td>0.01 l<\/td>\n<\/tr>\n<tr>\n<td>mililitre<\/td>\n<td>ml<\/td>\n<td>0.001 l<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Per passar una quantitat d&#8217;una unitat a una altra:<\/p>\n<ul>\n<li>Si la unitat original \u00e9s menor que la que es vol obtenir, es dividir\u00e0 la quantitat per\u00a010\u00a0tantes vegades com files s&#8217;hagi de &#8220;pujar&#8221; a la taula anterior.<\/li>\n<li>Si la unitat original \u00e9s m\u00e9s gran que la que es vol obtenir, es multiplicar\u00e0 la quantitat per 10 tantes vegades com files s&#8217;hagi de &#8220;baixar&#8221; a la taula anterior.<\/li>\n<\/ul>\n<div class=\"ejemplo\">\n<table style=\"border-color: #000000; background-color: #26c7f0;\">\n<tbody>\n<tr>\n<td style=\"width: 819px;\"><strong><em><span style=\"font-family: inherit; font-size: 1em;\">Exemple<\/span><\/em><\/strong><\/p>\n<div class=\"ejemplo\">\n<p>Si es vol passar\u00a0400\u00a0mil\u00b7lilitres a litres es fa:<\/p>\n<p>Com que per passar de mil\u00b7lilitres a litres es pugen tres files, s&#8217;ha de dividir per\u00a010\u00a0tres vegades (o el que \u00e9s el mateix, per\u00a01000). Per tant:<\/p>\n<p>400:1000=0,4\u00a0litres.<\/p>\n<p>\u00c9s a dir,\u00a0400\u00a0mil\u00b7lilitres s\u00f3n\u00a00,4\u00a0litres.<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h2>Mesures de superf\u00edcie<\/h2>\n<p>Per mesurar superf\u00edcies, la unitat b\u00e0sica \u00e9s el metre quadrat, encara que tamb\u00e9 s&#8217;utilitzen les seg\u00fcents unitats:<\/p>\n<table>\n<thead>\n<tr>\n<th>Nom<\/th>\n<th>S\u00edmbol<\/th>\n<th>Equival\u00e8ncia<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>kil\u00f3metre cuadrat<\/td>\n<td>km<sup>2<\/sup><\/td>\n<td>1.000.000 m<sup>2<\/sup><\/td>\n<\/tr>\n<tr>\n<td>hect\u00f3metre cuadrat<\/td>\n<td>hm<sup>2<\/sup><\/td>\n<td>10.000 m<sup>2<\/sup><\/td>\n<\/tr>\n<tr>\n<td>dec\u00e0metre cuadrat<\/td>\n<td>dam<sup>2<\/sup><\/td>\n<td>100 m<sup>2<\/sup><\/td>\n<\/tr>\n<tr>\n<td>metre cuadrat<\/td>\n<td>m<sup>2<\/sup><\/td>\n<td>1 m<sup>2<\/sup><\/td>\n<\/tr>\n<tr>\n<td>dec\u00edmetre cuadrat<\/td>\n<td>dm<sup>2<\/sup><\/td>\n<td>0.01 m<sup>2<\/sup><\/td>\n<\/tr>\n<tr>\n<td>cent\u00edmetre cuadrat<\/td>\n<td>cm<sup>2<\/sup><\/td>\n<td>0.0001 m<sup>2<\/sup><\/td>\n<\/tr>\n<tr>\n<td>mil\u00edmetre cuadrat<\/td>\n<td>mm<sup>2<\/sup><\/td>\n<td>0.000001 m<sup>2<\/sup><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Per passar una quantitat d&#8217;una unitat a una altra:<\/p>\n<ul>\n<li>Si la unitat original \u00e9s menor que la que es vol obtenir, es dividir\u00e0 la quantitat per\u00a0100\u00a0tantes vegades com files s&#8217;hagi de &#8220;pujar&#8221; a la taula anterior.<\/li>\n<li>Si la unitat original \u00e9s m\u00e9s gran que la que es vol obtenir, es multplicar\u00e1 la quantitat per\u00a0100\u00a0tantes vegades com files s&#8217;hagi de &#8220;baixar&#8221; a la taula anterior.<\/li>\n<\/ul>\n<div class=\"ejemplo\">\n<table style=\"border-color: #000000; background-color: #26c7f0;\">\n<tbody>\n<tr>\n<td style=\"width: 819px;\"><strong><em><span style=\"font-family: inherit; font-size: 1em;\">Exemple<\/span><\/em><\/strong><\/p>\n<div class=\"ejemplo\">\n<p>Si es vol passar\u00a00,003\u00a0quil\u00f2metres quadrats a dec\u00e0metres quadrats, llavors, com per passar de quil\u00f2metres quadrats a dec\u00e0metres quadrats es baixen dues files de la taula anterior, s&#8217;ha de multiplicar per\u00a0100\u00a0dues vegades (o el que \u00e9s el mateix, per\u00a010.000) . Per tant:<\/p>\n<p>0,003\u22c510000=30\u00a0dec\u00e0metres quadrats.<\/p>\n<p>\u00c9s a dir,\u00a00,003\u00a0quil\u00f2metres quadrats s\u00f3n\u00a030\u00a0dec\u00e0metres quadrats.<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h2>Mesures de volum<\/h2>\n<p>La unitat m\u00e9s utilitzada per a la mesura de volum \u00e9s el metre c\u00fabic. Altres unitats freq\u00fcentment utilitzades s\u00f3n:<\/p>\n<table>\n<thead>\n<tr>\n<th>Nom<\/th>\n<th>S\u00edmbol<\/th>\n<th>Equival\u00e8ncia<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>kil\u00f3metre c\u00fabic<\/td>\n<td>km<sup>3<\/sup><\/td>\n<td>1.000.000.000 m<sup>3<\/sup><\/td>\n<\/tr>\n<tr>\n<td>hect\u00f3metre c\u00fabic<\/td>\n<td>hm<sup>3<\/sup><\/td>\n<td>1.000.000 m<sup>3<\/sup><\/td>\n<\/tr>\n<tr>\n<td>dec\u00e1metre c\u00fabic<\/td>\n<td>dam<sup>3<\/sup><\/td>\n<td>1000 m<sup>3<\/sup><\/td>\n<\/tr>\n<tr>\n<td>metre c\u00fabic<\/td>\n<td>m<sup>3<\/sup><\/td>\n<td>1 m<sup>3<\/sup><\/td>\n<\/tr>\n<tr>\n<td>dec\u00edmetre c\u00fabic<\/td>\n<td>dm<sup>3<\/sup><\/td>\n<td>0.001 m<sup>3<\/sup><\/td>\n<\/tr>\n<tr>\n<td>cent\u00edmetre c\u00fabic<\/td>\n<td>cm<sup>3<\/sup><\/td>\n<td>0.000001 m<sup>3<\/sup><\/td>\n<\/tr>\n<tr>\n<td>mil\u00edmetre c\u00fabic<\/td>\n<td>mm<sup>3<\/sup><\/td>\n<td>0.000000001 m<sup>3<\/sup><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Per passar una quantitat d&#8217;una unitat a una altra:<\/p>\n<ul>\n<li>Si la unitat original \u00e9s menor que la que es vol obtenir, es dividir\u00e0 la quantitat per\u00a01000\u00a0tantes vegades com files s&#8217;hagi de &#8220;pujar&#8221; a la taula anterior.<\/li>\n<li>Si la unitat original \u00e9s m\u00e9s gran que la que es vol obtenir, es multplicar\u00e1 la quantitat per 1000 tantes vegades com files s&#8217;hagi de &#8220;baixar&#8221; a la taula anterior.<\/li>\n<\/ul>\n<div class=\"ejemplo\">\n<table style=\"border-color: #000000; background-color: #26c7f0;\">\n<tbody>\n<tr>\n<td style=\"width: 819px;\"><strong><em><span style=\"font-family: inherit; font-size: 1em;\">Exemple<\/span><\/em><\/strong><\/p>\n<div class=\"ejemplo\">\n<p>Per exemple, si es vol passar\u00a06.000.000\u00a0cent\u00edmetres c\u00fabics a dec\u00edmetres c\u00fabics, com per passar dels primers als segons s&#8217;ha de pujar nom\u00e9s una fila, llavors s&#8217;ha de dividir una vegada per\u00a01.000:<\/p>\n<p>6.000.000:1.000=6.000\u00a0dec\u00edmetres c\u00fabics.<\/p>\n<p>Per tant\u00a06.000.000\u00a0cent\u00edmetres c\u00fabics s\u00f3n\u00a06.000\u00a0dec\u00edmetres c\u00fabics.<\/p>\n<\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Ara que segur ja tens tota la teoria clara, practiquem una mica com mesurar fent la seg\u00fcent activitat:<br \/>\n<a href=\"https:\/\/www.thatquiz.org\/tq\/classtest?3RBAVLO4\">https:\/\/www.thatquiz.org\/tq\/classtest?3RBAVLO4<\/a><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><em>Llic\u00e8ncia i APA: Sangaku S.L. (2021) Sistema m\u00e8tric decimal: longitud, massa, capacitat, superf\u00edcie i volum.\u00a0<a href=\"https:\/\/www.sangakoo.com\/\">sangakoo.com<\/a>.<\/em><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Per fer mesuraments, cal un sistema d&#8217;unitats, \u00e9s a dir un conjunt de magnituds amb les que es comparen les coses que es volen mesurar.<br \/>\nEl sistema m\u00e8tric decimal \u00e9s un sistema d&#8217;unitats en els quals els m\u00faltiples i els subm\u00faltiples de la unitat de mesura&hellip;  <a href=\"https:\/\/agora.xtec.cat\/cfacanovelles\/matematiques-ii\/sistema-metric-decimal-longitud-massa-capacitat-superficie-i-volum\/\" title=\"Read Sistema m\u00e8tric decimal: longitud, massa, capacitat, superf\u00edcie i volum\">Llegeix m\u00e9s\u00bb<\/a><\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0,"footnotes":""},"categories":[116],"tags":[],"class_list":["post-3411","post","type-post","status-publish","format-standard","hentry","category-matematiques-ii"],"post_mailing_queue_ids":[],"_links":{"self":[{"href":"https:\/\/agora.xtec.cat\/cfacanovelles\/wp-json\/wp\/v2\/posts\/3411","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/agora.xtec.cat\/cfacanovelles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/agora.xtec.cat\/cfacanovelles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/agora.xtec.cat\/cfacanovelles\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/agora.xtec.cat\/cfacanovelles\/wp-json\/wp\/v2\/comments?post=3411"}],"version-history":[{"count":2,"href":"https:\/\/agora.xtec.cat\/cfacanovelles\/wp-json\/wp\/v2\/posts\/3411\/revisions"}],"predecessor-version":[{"id":3413,"href":"https:\/\/agora.xtec.cat\/cfacanovelles\/wp-json\/wp\/v2\/posts\/3411\/revisions\/3413"}],"wp:attachment":[{"href":"https:\/\/agora.xtec.cat\/cfacanovelles\/wp-json\/wp\/v2\/media?parent=3411"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/agora.xtec.cat\/cfacanovelles\/wp-json\/wp\/v2\/categories?post=3411"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/agora.xtec.cat\/cfacanovelles\/wp-json\/wp\/v2\/tags?post=3411"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}