{"id":1243,"date":"2020-06-18T14:07:58","date_gmt":"2020-06-18T12:07:58","guid":{"rendered":"https:\/\/blogs.futura-sciences.com\/lehning\/?p=1243"},"modified":"2021-11-05T18:47:07","modified_gmt":"2021-11-05T17:47:07","slug":"les-grands-nombres-et-les-petits","status":"publish","type":"post","link":"https:\/\/blogs.futura-sciences.com\/lehning\/2020\/06\/18\/les-grands-nombres-et-les-petits\/","title":{"rendered":"Les grands nombres … et les petits"},"content":{"rendered":"

Dans la vie courante, nous avons rarement besoin d\u2019aller au-del\u00e0 des mille milliards qui, forc\u00e9ment, font penser aux mille milliards de mille sabords<\/em> du capitaine Haddock, le c\u00e9l\u00e8bre compagnon de Tintin.<\/p>\n

\"\"<\/p>\n

Nicolas Chuquet (1445\u00a0\u2013\u00a01500) inventa pourtant un syst\u00e8me pouvant aller bien au-del\u00e0. Dans son livre Triparty en la science des nombres<\/em>, il forgea de nouveaux noms de nombres sur des pr\u00e9fixes correspondants \u00e0 deux, trois,\u2026, neuf\u00a0: billion, trillion, quatrillion, quintillion, sextillion, septillion, octillion, nonillion. Le premier (un billion) est un million de millions, chacun est ensuite \u00e9gal \u00e0 un million de fois le pr\u00e9c\u00e9dent. Ce syst\u00e8me est appliqu\u00e9 en Europe sauf dans les pays de langue anglaise car, malheureusement, les \u00c9tats-Unis ont adopt\u00e9 un syst\u00e8me diff\u00e9rent o\u00f9 chaque quantit\u00e9 est \u00e9gale \u00e0 mille fois la pr\u00e9c\u00e9dente. Ainsi, un billion am\u00e9ricain vaut mille millions fran\u00e7ais donc \u00e0 un milliard et ainsi de suite. D\u2019autre part, on utilise aussi des pr\u00e9fixes comme d\u00e9ca, hecto, kilo, m\u00e9ga, etc. (voir le tableau syst\u00e8me de noms des grands nombres<\/em>). Ainsi, un kilogramme vaut 1000 grammes, etc. Les premiers ont un sens qui vient du grec o\u00f9 d\u00e9ka signifie dix, \u00e9katon, d\u2019o\u00f9 viennent les h\u00e9catombes, cent, kilo, mille, m\u00e9gas, d\u2019o\u00f9 vient m\u00e9galomane, grand, gigas, d\u2019o\u00f9 vient gigantesque, g\u00e9ant, t\u00e9ras d\u2019o\u00f9 vient la t\u00e9ratologie, monstre. Les autres donnent, toujours en grec, la puissance de 1000 utilis\u00e9e. Ainsi p\u00e9ta vient de pent\u00e9<\/em>, qui signifie 5 et qui a donn\u00e9 pentagone, mais pas P\u00e9taouchnock qui, bien qu\u2019imaginaire est cens\u00e9e \u00eatre une ville tr\u00e8s \u00e9loign\u00e9e, quelque part au fin fond de la Sib\u00e9rie. Exa vient de hexa<\/em>, qui signifie 6 et qui a donn\u00e9 hexagone. Les derniers sont l\u00e0 pour 7 (zetta) et 8 (yotta) mais sont artificiels.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Nom fran\u00e7ais<\/td>\nNom am\u00e9ricain<\/td>\nPr\u00e9fixe<\/td>\nSymbole<\/td>\nValeur<\/td>\n<\/tr>\n
dix<\/td>\n<\/td>\nd\u00e9ca<\/td>\nda<\/td>\n10<\/td>\n<\/tr>\n
cent<\/td>\n<\/td>\nhecto<\/td>\nh<\/td>\n100<\/td>\n<\/tr>\n
mille<\/td>\n<\/td>\nkilo<\/td>\nk<\/td>\n1000<\/td>\n<\/tr>\n
million<\/td>\n<\/td>\nm\u00e9ga<\/td>\nM<\/td>\n1\u00a0000\u00a0000<\/td>\n<\/tr>\n
milliard<\/td>\nbillion<\/td>\ngiga<\/td>\nG<\/td>\n1\u00a0000\u00a0000\u00a0000<\/td>\n<\/tr>\n
billion<\/td>\ntrillion<\/td>\nt\u00e9ra<\/td>\nT<\/td>\n1\u00a0000\u00a0000\u00a0000\u00a0000<\/td>\n<\/tr>\n
billiard<\/td>\nquadrillon<\/td>\np\u00e9ta<\/td>\nP<\/td>\n1\u00a0000\u00a0000\u00a0000\u00a0000\u00a0000<\/td>\n<\/tr>\n
trillion<\/td>\nquintillion<\/td>\nexa<\/td>\nE<\/td>\n1\u00a0000\u00a0000\u00a0000\u00a0000\u00a0000\u00a0000<\/td>\n<\/tr>\n
trilliard<\/td>\nsextillion<\/td>\nzetta<\/td>\nZ<\/td>\n1\u00a0000\u00a0000\u00a0000\u00a0000\u00a0000\u00a0000\u00a0000<\/td>\n<\/tr>\n
quadrillon<\/td>\nseptillion<\/td>\nyotta<\/td>\nY<\/td>\n1\u00a0000\u00a0000\u00a0000\u00a0000\u00a0000\u00a0000\u00a0000\u00a0000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Le syst\u00e8me de noms des grands nombres va au-del\u00e0 mais les nombres deviennent alors sans v\u00e9ritable utilisation concr\u00e8te. On peut alors simplifier les mille milliards de mille sabords du capitaine Haddock en un seul p\u00e9ta sabord\u2026 mais ce serait moins musical et pourrait \u00eatre mal interpr\u00e9t\u00e9.<\/em><\/p>\n

Les financiers utilisent parfois des expressions telles que kiloeuros (k\u20ac) ou millions d\u2019euros (M\u20ac), qu\u2019ils seraient plus logique de nommer m\u00e9gaeuros vu le symbole M utilis\u00e9, mais cela n\u2019appara\u00eet pas normalement dans les comptes bancaires des particuliers. Sauf en p\u00e9riode d\u2019hyper inflation, comme en Allemagne en 1923 o\u00f9 on imprima des billets de 500 millions de marks, ou au Zimbabwe en 2009 o\u00f9 on alla jusqu\u2019\u00e0 100\u00a0000 milliards, soit 100 trillions au sens anglo-saxon (voir la photographie un billet sans valeur<\/em>), les particuliers n\u2019ont pas besoin d\u2019envisager des sommes sup\u00e9rieures au milliard fran\u00e7ais, donc au billion am\u00e9ricain\u2026 et les \u00c9tats, gu\u00e8re plus.<\/p>\n

\"\"
Un billet sans valeur<\/figcaption><\/figure>\n

En informatique, l\u2019usage du syst\u00e8me binaire fait que les pr\u00e9fixes ont un sens l\u00e9g\u00e8rement diff\u00e9rent. Kilo signifie alors 1024 car ce nombre est \u00e9gal \u00e0 2 \u00e0 la puissance 10, m\u00e9ga vaut 1024 kilo, giga, 1024 m\u00e9ga, t\u00e9ra, 1024 giga et p\u00e9ta, 1024 t\u00e9ra, etc.<\/p>\n

Les petits nombres<\/h2>\n

Pris \u00e0 l\u2019envers, ce syst\u00e8me permet \u00e9galement de visiter l\u2019infiniment petit (voir le tableau syst\u00e8me de noms des petits nombres<\/em>). Ici encore, les pr\u00e9fixes ont un sens. Les premiers viennent du grec o\u00f9 micro signifie petit et nano, nain. On passe ensuite \u00e0 l\u2019italien o\u00f9 piccolo, qui signifie petit, a donn\u00e9 pico. Les autres sont artificiels.<\/p>\n

 <\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Nom fran\u00e7ais<\/td>\nNom am\u00e9ricain<\/td>\nPr\u00e9fixe<\/td>\nSymbole<\/td>\nValeur<\/td>\n<\/tr>\n
dixi\u00e8me<\/td>\n<\/td>\nd\u00e9ci<\/td>\nd<\/td>\n0,1<\/td>\n<\/tr>\n
centi\u00e8me<\/td>\n<\/td>\ncenti<\/td>\nc<\/td>\n0,01<\/td>\n<\/tr>\n
milli\u00e8me<\/td>\n<\/td>\nmilli<\/td>\nm<\/td>\n0,001<\/td>\n<\/tr>\n
millioni\u00e8me<\/td>\n<\/td>\nmicro<\/td>\nm<\/td>\n0,000 001<\/td>\n<\/tr>\n
milliardi\u00e8me<\/td>\nbillioni\u00e8me<\/td>\nnano<\/td>\nn<\/td>\n0,000 000\u00a0001<\/td>\n<\/tr>\n
billioni\u00e8me<\/td>\ntrillioni\u00e8me<\/td>\npico<\/td>\np<\/td>\n0,000 000\u00a0000\u00a0001<\/td>\n<\/tr>\n
billiardi\u00e8me<\/td>\nquadrilloni\u00e8me<\/td>\nfemto<\/td>\nf<\/td>\n0,000 000\u00a0000\u00a0000\u00a0001<\/td>\n<\/tr>\n
trillioni\u00e8me<\/td>\nquintillioni\u00e8me<\/td>\natto<\/td>\na<\/td>\n0,000 000\u00a0000\u00a0000\u00a0000\u00a0001<\/td>\n<\/tr>\n
trilliardi\u00e8me<\/td>\nsextillioni\u00e8me<\/td>\nzepto<\/td>\nz<\/td>\n0,000 000\u00a0000\u00a0000\u00a0000\u00a0000\u00a0001<\/td>\n<\/tr>\n
quadrilloni\u00e8me<\/td>\nseptillioni\u00e8me<\/td>\nyocto<\/td>\ny<\/td>\n0,000 000\u00a0000\u00a0000\u00a0000\u00a0000\u00a0000\u00a0001<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Syst\u00e8me de noms des petits nombres. Le syst\u00e8me va au-del\u00e0 mais les nombres deviennent alors sans v\u00e9ritable utilisation concr\u00e8te.<\/em><\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Dans la vie courante, nous avons rarement besoin d\u2019aller au-del\u00e0 des mille milliards qui, forc\u00e9ment, font penser aux mille milliards de mille sabords du capitaine Haddock, le c\u00e9l\u00e8bre compagnon de Tintin. Nicolas Chuquet (1445\u00a0\u2013\u00a01500) inventa pourtant un syst\u00e8me pouvant aller bien au-del\u00e0. Dans son livre Triparty en la science des nombres, il forgea de nouveaux … Continuer la lecture de Les grands nombres … et les petits<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":12,"featured_media":1248,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[63,434,29,10],"tags":[443,445,444,446,442],"class_list":["post-1243","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-histoire","category-informatique","category-maths-2","category-voyages","tag-billets-de-banque","tag-chuquet","tag-inflation","tag-nicolas-chuquet","tag-zimbabwe"],"yoast_head":"\nLes grands nombres ... et les petits, par Herv\u00e9 Lehning<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/blogs.futura-sciences.com\/lehning\/2020\/06\/18\/les-grands-nombres-et-les-petits\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Les grands nombres ... et les petits, par Herv\u00e9 Lehning\" \/>\n<meta property=\"og:description\" content=\"Dans la vie courante, nous avons rarement besoin d\u2019aller au-del\u00e0 des mille milliards qui, forc\u00e9ment, font penser aux mille milliards de mille sabords du capitaine Haddock, le c\u00e9l\u00e8bre compagnon de Tintin. Nicolas Chuquet (1445\u00a0\u2013\u00a01500) inventa pourtant un syst\u00e8me pouvant aller bien au-del\u00e0. 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