[{"data":1,"prerenderedAt":2001},["ShallowReactive",2],{"subject-categories-math":3,"formula-de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fpromille":546,"formula-related-de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fpromille":1991},[4,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,173,174,175,176,177,178,179,180,181,182,183,184,185,186,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545],{"category":5},"algebra",{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":5},{"category":65},"arithmetic",{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":65},{"category":101},"calculus",{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":101},{"category":172},"differential-equations",{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":172},{"category":187},"discrete-math",{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":187},{"category":208},"functions",{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":208},{"category":247},"geometry",{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":247},{"category":312},"linear-algebra",{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":312},{"category":368},"multivariable-calculus",{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":368},{"category":391},"numerics",{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":391},{"category":412},"sequences-series",{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":412},{"category":441},"stochastics",{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":441},{"category":518},"trigonometry",{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"category":518},{"id":547,"title":548,"aliases":549,"body":556,"category":65,"checks":1936,"conditions":1958,"conditionsHtml":1958,"deprecated":1958,"description":1930,"extension":1959,"figure":1958,"figureCaption":1958,"figureHtml":1958,"formulaId":1960,"latex":1961,"latexHtml":1962,"level":1963,"meta":1964,"navigation":1965,"path":1966,"redirectFrom":1967,"related":1968,"seo":1972,"stem":1973,"subject":581,"summary":1974,"tags":1975,"variables":1980,"__hash__":1990},"formulas_de\u002Fde\u002Fformulas\u002Fmath\u002Farithmetic\u002Fpromille.md","Promille",[550,551,552,553,554,555],"Promillerechnung","Promille berechnen","Promille in Prozent","von Tausend","‰","Promillewert",{"type":557,"value":558,"toc":1929},"minimark",[559,564,813,816,826,829,1122,1126,1216,1412,1415,1460,1643,1675,1678,1741,1911,1914,1918],[560,561,563],"h2",{"id":562},"erklärung","Erklärung",[565,566,567,570,571,752,753,782,783,812],"p",{},[568,569,548],"strong",{}," (‰) heißt „von Tausend\". 1 ‰ ist ein Tausendstel, also ",[572,573,576,612],"span",{"className":574},[575],"katex",[572,577,580],{"className":578},[579],"katex-mathml",[581,582,584],"math",{"xmlns":583},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[585,586,587,607],"semantics",{},[588,589,590,600,604],"mrow",{},[591,592,593,597],"mfrac",{},[594,595,596],"mn",{},"1",[594,598,599],{},"1000",[601,602,603],"mo",{},"=",[594,605,606],{},"0,001",[608,609,611],"annotation",{"encoding":610},"application\u002Fx-tex","\\frac{1}{1000} = 0{,}001",[572,613,617,729],{"className":614,"ariaHidden":616},[615],"katex-html","true",[572,618,621,626,717,722,726],{"className":619},[620],"base",[572,622],{"className":623,"style":625},[624],"strut","height:1.1901em;vertical-align:-0.345em;",[572,627,630,635,713],{"className":628},[629],"mord",[572,631],{"className":632},[633,634],"mopen","nulldelimiter",[572,636,638],{"className":637},[591],[572,639,643,704],{"className":640},[641,642],"vlist-t","vlist-t2",[572,644,647,699],{"className":645},[646],"vlist-r",[572,648,652,673,684],{"className":649,"style":651},[650],"vlist","height:0.8451em;",[572,653,655,660],{"style":654},"top:-2.655em;",[572,656],{"className":657,"style":659},[658],"pstrut","height:3em;",[572,661,667],{"className":662},[663,664,665,666],"sizing","reset-size6","size3","mtight",[572,668,670],{"className":669},[629,666],[572,671,599],{"className":672},[629,666],[572,674,676,679],{"style":675},"top:-3.23em;",[572,677],{"className":678,"style":659},[658],[572,680],{"className":681,"style":683},[682],"frac-line","border-bottom-width:0.04em;",[572,685,687,690],{"style":686},"top:-3.394em;",[572,688],{"className":689,"style":659},[658],[572,691,693],{"className":692},[663,664,665,666],[572,694,696],{"className":695},[629,666],[572,697,596],{"className":698},[629,666],[572,700,703],{"className":701},[702],"vlist-s","​",[572,705,707],{"className":706},[646],[572,708,711],{"className":709,"style":710},[650],"height:0.345em;",[572,712],{},[572,714],{"className":715},[716,634],"mclose",[572,718],{"className":719,"style":721},[720],"mspace","margin-right:0.2778em;",[572,723,603],{"className":724},[725],"mrel",[572,727],{"className":728,"style":721},[720],[572,730,732,736,740,748],{"className":731},[620],[572,733],{"className":734,"style":735},[624],"height:0.8389em;vertical-align:-0.1944em;",[572,737,739],{"className":738},[629],"0",[572,741,743],{"className":742},[629],[572,744,747],{"className":745},[746],"mpunct",",",[572,749,751],{"className":750},[629],"001",". Gerechnet wird genau wie in der Prozentrechnung, nur dass man durch ",[572,754,756,769],{"className":755},[575],[572,757,759],{"className":758},[579],[581,760,761],{"xmlns":583},[585,762,763,767],{},[588,764,765],{},[594,766,599],{},[608,768,599],{"encoding":610},[572,770,772],{"className":771,"ariaHidden":616},[615],[572,773,775,779],{"className":774},[620],[572,776],{"className":777,"style":778},[624],"height:0.6444em;",[572,780,599],{"className":781},[629]," statt durch ",[572,784,786,800],{"className":785},[575],[572,787,789],{"className":788},[579],[581,790,791],{"xmlns":583},[585,792,793,798],{},[588,794,795],{},[594,796,797],{},"100",[608,799,797],{"encoding":610},[572,801,803],{"className":802,"ariaHidden":616},[615],[572,804,806,809],{"className":805},[620],[572,807],{"className":808,"style":778},[624],[572,810,797],{"className":811},[629]," teilt.",[565,814,815],{},"Umrechnung zwischen Prozent und Promille:",[817,818,819,823],"ul",{},[820,821,822],"li",{},"1 % = 10 ‰",[820,824,825],{},"1 ‰ = 0,1 %",[565,827,828],{},"Promille verwendet man bei sehr kleinen Anteilen, z.B. beim Salzgehalt von Wasser, bei Gebühren und Versicherungsbeiträgen oder beim Blutalkohol.",[565,830,831,832,985,986,1121],{},"Die Formel lässt sich wie beim Prozentwert umstellen: ",[572,833,835,865],{"className":834},[575],[572,836,838],{"className":837},[579],[581,839,840],{"xmlns":583},[585,841,842,862],{},[588,843,844,847,849,857,860],{},[845,846,565],"mi",{},[601,848,603],{},[591,850,851,854],{},[845,852,853],{},"W",[845,855,856],{},"G",[601,858,859],{},"⋅",[594,861,599],{},[608,863,864],{"encoding":610},"p = \\frac{W}{G} \\cdot 1000",[572,866,868,888,976],{"className":867,"ariaHidden":616},[615],[572,869,871,875,879,882,885],{"className":870},[620],[572,872],{"className":873,"style":874},[624],"height:0.625em;vertical-align:-0.1944em;",[572,876,565],{"className":877},[629,878],"mathnormal",[572,880],{"className":881,"style":721},[720],[572,883,603],{"className":884},[725],[572,886],{"className":887,"style":721},[720],[572,889,891,895,965,969,973],{"className":890},[620],[572,892],{"className":893,"style":894},[624],"height:1.2173em;vertical-align:-0.345em;",[572,896,898,901,962],{"className":897},[629],[572,899],{"className":900},[633,634],[572,902,904],{"className":903},[591],[572,905,907,954],{"className":906},[641,642],[572,908,910,951],{"className":909},[646],[572,911,914,928,936],{"className":912,"style":913},[650],"height:0.8723em;",[572,915,916,919],{"style":654},[572,917],{"className":918,"style":659},[658],[572,920,922],{"className":921},[663,664,665,666],[572,923,925],{"className":924},[629,666],[572,926,856],{"className":927},[629,878,666],[572,929,930,933],{"style":675},[572,931],{"className":932,"style":659},[658],[572,934],{"className":935,"style":683},[682],[572,937,938,941],{"style":686},[572,939],{"className":940,"style":659},[658],[572,942,944],{"className":943},[663,664,665,666],[572,945,947],{"className":946},[629,666],[572,948,853],{"className":949,"style":950},[629,878,666],"margin-right:0.1389em;",[572,952,703],{"className":953},[702],[572,955,957],{"className":956},[646],[572,958,960],{"className":959,"style":710},[650],[572,961],{},[572,963],{"className":964},[716,634],[572,966],{"className":967,"style":968},[720],"margin-right:0.2222em;",[572,970,859],{"className":971},[972],"mbin",[572,974],{"className":975,"style":968},[720],[572,977,979,982],{"className":978},[620],[572,980],{"className":981,"style":778},[624],[572,983,599],{"className":984},[629]," und ",[572,987,989,1017],{"className":988},[575],[572,990,992],{"className":991},[579],[581,993,994],{"xmlns":583},[585,995,996,1014],{},[588,997,998,1000,1002],{},[845,999,856],{},[601,1001,603],{},[591,1003,1004,1012],{},[588,1005,1006,1008,1010],{},[845,1007,853],{},[601,1009,859],{},[594,1011,599],{},[845,1013,565],{},[608,1015,1016],{"encoding":610},"G = \\frac{W \\cdot 1000}{p}",[572,1018,1020,1039],{"className":1019,"ariaHidden":616},[615],[572,1021,1023,1027,1030,1033,1036],{"className":1022},[620],[572,1024],{"className":1025,"style":1026},[624],"height:0.6833em;",[572,1028,856],{"className":1029},[629,878],[572,1031],{"className":1032,"style":721},[720],[572,1034,603],{"className":1035},[725],[572,1037],{"className":1038,"style":721},[720],[572,1040,1042,1046],{"className":1041},[620],[572,1043],{"className":1044,"style":1045},[624],"height:1.3534em;vertical-align:-0.4811em;",[572,1047,1049,1052,1118],{"className":1048},[629],[572,1050],{"className":1051},[633,634],[572,1053,1055],{"className":1054},[591],[572,1056,1058,1109],{"className":1057},[641,642],[572,1059,1061,1106],{"className":1060},[646],[572,1062,1064,1078,1086],{"className":1063,"style":913},[650],[572,1065,1066,1069],{"style":654},[572,1067],{"className":1068,"style":659},[658],[572,1070,1072],{"className":1071},[663,664,665,666],[572,1073,1075],{"className":1074},[629,666],[572,1076,565],{"className":1077},[629,878,666],[572,1079,1080,1083],{"style":675},[572,1081],{"className":1082,"style":659},[658],[572,1084],{"className":1085,"style":683},[682],[572,1087,1088,1091],{"style":686},[572,1089],{"className":1090,"style":659},[658],[572,1092,1094],{"className":1093},[663,664,665,666],[572,1095,1097,1100,1103],{"className":1096},[629,666],[572,1098,853],{"className":1099,"style":950},[629,878,666],[572,1101,859],{"className":1102},[972,666],[572,1104,599],{"className":1105},[629,666],[572,1107,703],{"className":1108},[702],[572,1110,1112],{"className":1111},[646],[572,1113,1116],{"className":1114,"style":1115},[650],"height:0.4811em;",[572,1117],{},[572,1119],{"className":1120},[716,634],".",[560,1123,1125],{"id":1124},"beispiele","Beispiele",[565,1127,1128,1129,1215],{},"Meerwasser enthält etwa 35 ‰ Salz. In ",[572,1130,1132,1164],{"className":1131},[575],[572,1133,1135],{"className":1134},[579],[581,1136,1137],{"xmlns":583},[585,1138,1139,1161],{},[588,1140,1141,1144,1148,1151,1153,1156,1158],{},[594,1142,1143],{},"2",[1145,1146,1147],"mtext",{}," ",[1145,1149,1150],{},"kg",[601,1152,603],{},[594,1154,1155],{},"2000",[1145,1157,1147],{},[1145,1159,1160],{},"g",[608,1162,1163],{"encoding":610},"2\\,\\text{kg} = 2000\\,\\text{g}",[572,1165,1167,1197],{"className":1166,"ariaHidden":616},[615],[572,1168,1170,1174,1177,1181,1188,1191,1194],{"className":1169},[620],[572,1171],{"className":1172,"style":1173},[624],"height:0.8889em;vertical-align:-0.1944em;",[572,1175,1143],{"className":1176},[629],[572,1178],{"className":1179,"style":1180},[720],"margin-right:0.1667em;",[572,1182,1185],{"className":1183},[629,1184],"text",[572,1186,1150],{"className":1187},[629],[572,1189],{"className":1190,"style":721},[720],[572,1192,603],{"className":1193},[725],[572,1195],{"className":1196,"style":721},[720],[572,1198,1200,1203,1206,1209],{"className":1199},[620],[572,1201],{"className":1202,"style":735},[624],[572,1204,1155],{"className":1205},[629],[572,1207],{"className":1208,"style":1180},[720],[572,1210,1212],{"className":1211},[629,1184],[572,1213,1160],{"className":1214},[629]," Meerwasser sind",[572,1217,1220],{"className":1218},[1219],"katex-display",[572,1221,1223,1264],{"className":1222},[575],[572,1224,1226],{"className":1225},[579],[581,1227,1229],{"xmlns":583,"display":1228},"block",[585,1230,1231,1261],{},[588,1232,1233,1235,1237,1239,1241,1243,1245,1252,1254,1257,1259],{},[845,1234,853],{},[601,1236,603],{},[594,1238,1155],{},[1145,1240,1147],{},[1145,1242,1160],{},[601,1244,859],{},[591,1246,1247,1250],{},[594,1248,1249],{},"35",[594,1251,599],{},[601,1253,603],{},[594,1255,1256],{},"70",[1145,1258,1147],{},[1145,1260,1160],{},[608,1262,1263],{"encoding":610},"W = 2000\\,\\text{g} \\cdot \\frac{35}{1000} = 70\\,\\text{g}",[572,1265,1267,1285,1312,1394],{"className":1266,"ariaHidden":616},[615],[572,1268,1270,1273,1276,1279,1282],{"className":1269},[620],[572,1271],{"className":1272,"style":1026},[624],[572,1274,853],{"className":1275,"style":950},[629,878],[572,1277],{"className":1278,"style":721},[720],[572,1280,603],{"className":1281},[725],[572,1283],{"className":1284,"style":721},[720],[572,1286,1288,1291,1294,1297,1303,1306,1309],{"className":1287},[620],[572,1289],{"className":1290,"style":735},[624],[572,1292,1155],{"className":1293},[629],[572,1295],{"className":1296,"style":1180},[720],[572,1298,1300],{"className":1299},[629,1184],[572,1301,1160],{"className":1302},[629],[572,1304],{"className":1305,"style":968},[720],[572,1307,859],{"className":1308},[972],[572,1310],{"className":1311,"style":968},[720],[572,1313,1315,1319,1385,1388,1391],{"className":1314},[620],[572,1316],{"className":1317,"style":1318},[624],"height:2.0074em;vertical-align:-0.686em;",[572,1320,1322,1325,1382],{"className":1321},[629],[572,1323],{"className":1324},[633,634],[572,1326,1328],{"className":1327},[591],[572,1329,1331,1373],{"className":1330},[641,642],[572,1332,1334,1370],{"className":1333},[646],[572,1335,1338,1350,1358],{"className":1336,"style":1337},[650],"height:1.3214em;",[572,1339,1341,1344],{"style":1340},"top:-2.314em;",[572,1342],{"className":1343,"style":659},[658],[572,1345,1347],{"className":1346},[629],[572,1348,599],{"className":1349},[629],[572,1351,1352,1355],{"style":675},[572,1353],{"className":1354,"style":659},[658],[572,1356],{"className":1357,"style":683},[682],[572,1359,1361,1364],{"style":1360},"top:-3.677em;",[572,1362],{"className":1363,"style":659},[658],[572,1365,1367],{"className":1366},[629],[572,1368,1249],{"className":1369},[629],[572,1371,703],{"className":1372},[702],[572,1374,1376],{"className":1375},[646],[572,1377,1380],{"className":1378,"style":1379},[650],"height:0.686em;",[572,1381],{},[572,1383],{"className":1384},[716,634],[572,1386],{"className":1387,"style":721},[720],[572,1389,603],{"className":1390},[725],[572,1392],{"className":1393,"style":721},[720],[572,1395,1397,1400,1403,1406],{"className":1396},[620],[572,1398],{"className":1399,"style":735},[624],[572,1401,1256],{"className":1402},[629],[572,1404],{"className":1405,"style":1180},[720],[572,1407,1409],{"className":1408},[629,1184],[572,1410,1160],{"className":1411},[629],[565,1413,1414],{},"Salz gelöst.",[565,1416,1417,1418,1459],{},"Eine Gebäudeversicherung kostet im Jahr 1,5 ‰ der Versicherungssumme von ",[572,1419,1421,1441],{"className":1420},[575],[572,1422,1424],{"className":1423},[579],[581,1425,1426],{"xmlns":583},[585,1427,1428,1438],{},[588,1429,1430,1433,1435],{},[594,1431,1432],{},"240",[1145,1434,1147],{},[594,1436,1437],{},"000",[608,1439,1440],{"encoding":610},"240\\,000",[572,1442,1444],{"className":1443,"ariaHidden":616},[615],[572,1445,1447,1450,1453,1456],{"className":1446},[620],[572,1448],{"className":1449,"style":778},[624],[572,1451,1432],{"className":1452},[629],[572,1454],{"className":1455,"style":1180},[720],[572,1457,1437],{"className":1458},[629]," €:",[572,1461,1463],{"className":1462},[1219],[572,1464,1466,1502],{"className":1465},[575],[572,1467,1469],{"className":1468},[579],[581,1470,1471],{"xmlns":583,"display":1228},[585,1472,1473,1499],{},[588,1474,1475,1477,1479,1481,1483,1485,1487,1494,1496],{},[845,1476,853],{},[601,1478,603],{},[594,1480,1432],{},[1145,1482,1147],{},[594,1484,1437],{},[601,1486,859],{},[591,1488,1489,1492],{},[594,1490,1491],{},"1,5",[594,1493,599],{},[601,1495,603],{},[594,1497,1498],{},"360",[608,1500,1501],{"encoding":610},"W = 240\\,000 \\cdot \\frac{1{,}5}{1000} = 360",[572,1503,1505,1523,1547,1634],{"className":1504,"ariaHidden":616},[615],[572,1506,1508,1511,1514,1517,1520],{"className":1507},[620],[572,1509],{"className":1510,"style":1026},[624],[572,1512,853],{"className":1513,"style":950},[629,878],[572,1515],{"className":1516,"style":721},[720],[572,1518,603],{"className":1519},[725],[572,1521],{"className":1522,"style":721},[720],[572,1524,1526,1529,1532,1535,1538,1541,1544],{"className":1525},[620],[572,1527],{"className":1528,"style":778},[624],[572,1530,1432],{"className":1531},[629],[572,1533],{"className":1534,"style":1180},[720],[572,1536,1437],{"className":1537},[629],[572,1539],{"className":1540,"style":968},[720],[572,1542,859],{"className":1543},[972],[572,1545],{"className":1546,"style":968},[720],[572,1548,1550,1553,1625,1628,1631],{"className":1549},[620],[572,1551],{"className":1552,"style":1318},[624],[572,1554,1556,1559,1622],{"className":1555},[629],[572,1557],{"className":1558},[633,634],[572,1560,1562],{"className":1561},[591],[572,1563,1565,1614],{"className":1564},[641,642],[572,1566,1568,1611],{"className":1567},[646],[572,1569,1571,1582,1590],{"className":1570,"style":1337},[650],[572,1572,1573,1576],{"style":1340},[572,1574],{"className":1575,"style":659},[658],[572,1577,1579],{"className":1578},[629],[572,1580,599],{"className":1581},[629],[572,1583,1584,1587],{"style":675},[572,1585],{"className":1586,"style":659},[658],[572,1588],{"className":1589,"style":683},[682],[572,1591,1592,1595],{"style":1360},[572,1593],{"className":1594,"style":659},[658],[572,1596,1598,1601,1607],{"className":1597},[629],[572,1599,596],{"className":1600},[629],[572,1602,1604],{"className":1603},[629],[572,1605,747],{"className":1606},[746],[572,1608,1610],{"className":1609},[629],"5",[572,1612,703],{"className":1613},[702],[572,1615,1617],{"className":1616},[646],[572,1618,1620],{"className":1619,"style":1379},[650],[572,1621],{},[572,1623],{"className":1624},[716,634],[572,1626],{"className":1627,"style":721},[720],[572,1629,603],{"className":1630},[725],[572,1632],{"className":1633,"style":721},[720],[572,1635,1637,1640],{"className":1636},[620],[572,1638],{"className":1639,"style":778},[624],[572,1641,1498],{"className":1642},[629],[565,1644,1645,1646,1674],{},"Der Beitrag beträgt also ",[572,1647,1649,1662],{"className":1648},[575],[572,1650,1652],{"className":1651},[579],[581,1653,1654],{"xmlns":583},[585,1655,1656,1660],{},[588,1657,1658],{},[594,1659,1498],{},[608,1661,1498],{"encoding":610},[572,1663,1665],{"className":1664,"ariaHidden":616},[615],[572,1666,1668,1671],{"className":1667},[620],[572,1669],{"className":1670,"style":778},[624],[572,1672,1498],{"className":1673},[629]," €.",[565,1676,1677],{},"Umrechnen: 2,5 ‰ sind 0,25 %, und 0,4 % sind 4 ‰.",[565,1679,1680,1681,1710,1711,1740],{},"Promillesatz gesucht: Von ",[572,1682,1684,1698],{"className":1683},[575],[572,1685,1687],{"className":1686},[579],[581,1688,1689],{"xmlns":583},[585,1690,1691,1696],{},[588,1692,1693],{},[594,1694,1695],{},"8000",[608,1697,1695],{"encoding":610},[572,1699,1701],{"className":1700,"ariaHidden":616},[615],[572,1702,1704,1707],{"className":1703},[620],[572,1705],{"className":1706,"style":778},[624],[572,1708,1695],{"className":1709},[629]," Bauteilen sind ",[572,1712,1714,1728],{"className":1713},[575],[572,1715,1717],{"className":1716},[579],[581,1718,1719],{"xmlns":583},[585,1720,1721,1726],{},[588,1722,1723],{},[594,1724,1725],{},"12",[608,1727,1725],{"encoding":610},[572,1729,1731],{"className":1730,"ariaHidden":616},[615],[572,1732,1734,1737],{"className":1733},[620],[572,1735],{"className":1736,"style":778},[624],[572,1738,1725],{"className":1739},[629]," defekt. Das sind",[572,1742,1744],{"className":1743},[1219],[572,1745,1747,1777],{"className":1746},[575],[572,1748,1750],{"className":1749},[579],[581,1751,1752],{"xmlns":583,"display":1228},[585,1753,1754,1774],{},[588,1755,1756,1758,1760,1766,1768,1770,1772],{},[845,1757,565],{},[601,1759,603],{},[591,1761,1762,1764],{},[594,1763,1725],{},[594,1765,1695],{},[601,1767,859],{},[594,1769,599],{},[601,1771,603],{},[594,1773,1491],{},[608,1775,1776],{"encoding":610},"p = \\frac{12}{8000} \\cdot 1000 = 1{,}5",[572,1778,1780,1798,1875,1893],{"className":1779,"ariaHidden":616},[615],[572,1781,1783,1786,1789,1792,1795],{"className":1782},[620],[572,1784],{"className":1785,"style":874},[624],[572,1787,565],{"className":1788},[629,878],[572,1790],{"className":1791,"style":721},[720],[572,1793,603],{"className":1794},[725],[572,1796],{"className":1797,"style":721},[720],[572,1799,1801,1804,1866,1869,1872],{"className":1800},[620],[572,1802],{"className":1803,"style":1318},[624],[572,1805,1807,1810,1863],{"className":1806},[629],[572,1808],{"className":1809},[633,634],[572,1811,1813],{"className":1812},[591],[572,1814,1816,1855],{"className":1815},[641,642],[572,1817,1819,1852],{"className":1818},[646],[572,1820,1822,1833,1841],{"className":1821,"style":1337},[650],[572,1823,1824,1827],{"style":1340},[572,1825],{"className":1826,"style":659},[658],[572,1828,1830],{"className":1829},[629],[572,1831,1695],{"className":1832},[629],[572,1834,1835,1838],{"style":675},[572,1836],{"className":1837,"style":659},[658],[572,1839],{"className":1840,"style":683},[682],[572,1842,1843,1846],{"style":1360},[572,1844],{"className":1845,"style":659},[658],[572,1847,1849],{"className":1848},[629],[572,1850,1725],{"className":1851},[629],[572,1853,703],{"className":1854},[702],[572,1856,1858],{"className":1857},[646],[572,1859,1861],{"className":1860,"style":1379},[650],[572,1862],{},[572,1864],{"className":1865},[716,634],[572,1867],{"className":1868,"style":968},[720],[572,1870,859],{"className":1871},[972],[572,1873],{"className":1874,"style":968},[720],[572,1876,1878,1881,1884,1887,1890],{"className":1877},[620],[572,1879],{"className":1880,"style":778},[624],[572,1882,599],{"className":1883},[629],[572,1885],{"className":1886,"style":721},[720],[572,1888,603],{"className":1889},[725],[572,1891],{"className":1892,"style":721},[720],[572,1894,1896,1899,1902,1908],{"className":1895},[620],[572,1897],{"className":1898,"style":735},[624],[572,1900,596],{"className":1901},[629],[572,1903,1905],{"className":1904},[629],[572,1906,747],{"className":1907},[746],[572,1909,1610],{"className":1910},[629],[565,1912,1913],{},"also 1,5 ‰.",[560,1915,1917],{"id":1916},"typische-fehler","Typische Fehler",[817,1919,1920,1923,1926],{},[820,1921,1922],{},"Durch 100 statt durch 1000 teilen: 35 ‰ von 2000 g sind 70 g, nicht 700 g.",[820,1924,1925],{},"Beim Umrechnen in die falsche Richtung schieben: 2,5 ‰ sind 0,25 %, nicht 25 %.",[820,1927,1928],{},"Promille und Prozent verwechseln, weil die Zeichen ähnlich aussehen: ‰ hat drei kleine Kreise (passend zu den drei Nullen von 1000), % nur zwei.",{"title":1930,"searchDepth":1931,"depth":1931,"links":1932},"",2,[1933,1934,1935],{"id":562,"depth":1931,"text":563},{"id":1124,"depth":1931,"text":1125},{"id":1916,"depth":1931,"text":1917},[1937,1940,1944,1946,1949,1952,1955],{"lhs":1938,"rhs":1939},"G*p\u002F1000","G*(p\u002F10)\u002F100",{"lhs":1938,"rhs":1256,"where":1941},{"G":1942,"p":1943},2000,35,{"lhs":1945,"rhs":1498},"240000*1.5\u002F1000",{"lhs":1947,"rhs":1948},"2.5\u002F10","0.25",{"lhs":1950,"rhs":1951},"0.4*10","4",{"lhs":1953,"rhs":1954},"12\u002F8000*1000","1.5",{"lhs":1956,"rhs":1957},"2000*35\u002F100","700",null,"md","per-mille","W = G \\cdot \\frac{p}{1000}","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>W\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>G\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmfrac>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>1000\u003C\u002Fmn>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">W = G \\cdot \\frac{p}{1000}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">W\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">G\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003Cspan class=\"mbin\">⋅\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2222em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:1.7936em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.1076em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1000\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","middle",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Farithmetic\u002Fpromille",[],[1969,1970,1971],"percentage-value","percentage-rate","base-value",{"title":548,"description":1930},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fpromille","Promille bedeutet Tausendstel; der Promillewert ist der Grundwert mal p durch 1000.",[1976,1977,1978,1979],"promille","prozent","anteil","tausendstel",[1981,1984,1987],{"symbol":853,"meaning":1982,"symbolHtml":1983},"Promillewert, der Anteil","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>W\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">W\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">W\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":856,"meaning":1985,"symbolHtml":1986},"Grundwert, das Ganze (entspricht 1000 ‰)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>G\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">G\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">G\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":565,"meaning":1988,"symbolHtml":1989},"Promillesatz als Zahl, z.B. p = 35 bei 35 ‰","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>p\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","jhxTfJJjF0Egg-G5UQzmqsy5VjTeSgzKyJuuMOwMY-w",[1992,1995,1998],{"stem":1993,"title":1994,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fgrundwert","Grundwert",{"stem":1996,"title":1997,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fprozentsatz","Prozentsatz",{"stem":1999,"title":2000,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fprozentwert","Prozentwert",1793824259812]