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Danach bringt man das Ergebnis wieder in die richtige Form.",[560,1002,1004],{"id":1003},"beispiele","Beispiele",[565,1006,1007,1008,1068,1069,1098],{},"Die mittlere Entfernung Erde–Mond beträgt etwa ",[585,1009,1011,1038],{"className":1010},[588],[585,1012,1014],{"className":1013},[592],[594,1015,1016],{"xmlns":596},[598,1017,1018,1035],{},[601,1019,1020,1023,1027,1030,1032],{},[644,1021,1022],{},"384",[1024,1025,1026],"mtext",{}," ",[644,1028,1029],{},"000",[1024,1031,1026],{},[1024,1033,1034],{},"km",[608,1036,1037],{"encoding":610},"384\\,000\\,\\text{km}",[585,1039,1041],{"className":1040,"ariaHidden":615},[614],[585,1042,1044,1048,1051,1055,1058,1061],{"className":1043},[619],[585,1045],{"className":1046,"style":1047},[623],"height:0.6944em;",[585,1049,1022],{"className":1050},[628],[585,1052],{"className":1053,"style":1054},[684],"margin-right:0.1667em;",[585,1056,1029],{"className":1057},[628],[585,1059],{"className":1060,"style":1054},[684],[585,1062,1065],{"className":1063},[628,1064],"text",[585,1066,1034],{"className":1067},[628],". Das Komma wandert um ",[585,1070,1072,1086],{"className":1071},[588],[585,1073,1075],{"className":1074},[592],[594,1076,1077],{"xmlns":596},[598,1078,1079,1084],{},[601,1080,1081],{},[644,1082,1083],{},"5",[608,1085,1083],{"encoding":610},[585,1087,1089],{"className":1088,"ariaHidden":615},[614],[585,1090,1092,1095],{"className":1091},[619],[585,1093],{"className":1094,"style":724},[623],[585,1096,1083],{"className":1097},[628]," Stellen nach links:",[585,1100,1103],{"className":1101},[1102],"katex-display",[585,1104,1106,1140],{"className":1105},[588],[585,1107,1109],{"className":1108},[592],[594,1110,1112],{"xmlns":596,"display":1111},"block",[598,1113,1114,1137],{},[601,1115,1116,1118,1120,1122,1125,1128,1131],{},[644,1117,1022],{},[1024,1119,1026],{},[644,1121,1029],{},[648,1123,1124],{},"=",[644,1126,1127],{},"3,84",[648,1129,1130],{},"⋅",[748,1132,1133,1135],{},[644,1134,664],{},[644,1136,1083],{},[608,1138,1139],{"encoding":610},"384\\,000 = 3{,}84 \\cdot 10^5",[585,1141,1143,1167,1200],{"className":1142,"ariaHidden":615},[614],[585,1144,1146,1149,1152,1155,1158,1161,1164],{"className":1145},[619],[585,1147],{"className":1148,"style":724},[623],[585,1150,1022],{"className":1151},[628],[585,1153],{"className":1154,"style":1054},[684],[585,1156,1029],{"className":1157},[628],[585,1159],{"className":1160,"style":685},[684],[585,1162,1124],{"className":1163},[689],[585,1165],{"className":1166,"style":685},[684],[585,1168,1170,1174,1178,1185,1189,1193,1197],{"className":1169},[619],[585,1171],{"className":1172,"style":1173},[623],"height:0.8389em;vertical-align:-0.1944em;",[585,1175,1177],{"className":1176},[628],"3",[585,1179,1181],{"className":1180},[628],[585,1182,728],{"className":1183},[1184],"mpunct",[585,1186,1188],{"className":1187},[628],"84",[585,1190],{"className":1191,"style":1192},[684],"margin-right:0.2222em;",[585,1194,1130],{"className":1195},[1196],"mbin",[585,1198],{"className":1199,"style":1192},[684],[585,1201,1203,1207,1210],{"className":1202},[619],[585,1204],{"className":1205,"style":1206},[623],"height:0.8641em;",[585,1208,646],{"className":1209},[628],[585,1211,1213,1216],{"className":1212},[628],[585,1214,777],{"className":1215},[628],[585,1217,1219],{"className":1218},[781],[585,1220,1222],{"className":1221},[785],[585,1223,1225],{"className":1224},[789],[585,1226,1228],{"className":1227,"style":1206},[793],[585,1229,1231,1234],{"style":1230},"top:-3.113em;margin-right:0.05em;",[585,1232],{"className":1233,"style":801},[800],[585,1235,1237],{"className":1236},[805,806,807,808],[585,1238,1083],{"className":1239},[628,808],[565,1241,1242,1243,1272],{},"Eine kleine Zahl, das Komma wandert um ",[585,1244,1246,1260],{"className":1245},[588],[585,1247,1249],{"className":1248},[592],[594,1250,1251],{"xmlns":596},[598,1252,1253,1258],{},[601,1254,1255],{},[644,1256,1257],{},"4",[608,1259,1257],{"encoding":610},[585,1261,1263],{"className":1262,"ariaHidden":615},[614],[585,1264,1266,1269],{"className":1265},[619],[585,1267],{"className":1268,"style":724},[623],[585,1270,1257],{"className":1271},[628]," Stellen nach rechts:",[585,1274,1276],{"className":1275},[1102],[585,1277,1279,1317],{"className":1278},[588],[585,1280,1282],{"className":1281},[592],[594,1283,1284],{"xmlns":596,"display":1111},[598,1285,1286,1314],{},[601,1287,1288,1291,1293,1296,1298,1301,1303],{},[644,1289,1290],{},"0,000",[1024,1292,1026],{},[644,1294,1295],{},"72",[648,1297,1124],{},[644,1299,1300],{},"7,2",[648,1302,1130],{},[748,1304,1305,1307],{},[644,1306,664],{},[601,1308,1309,1312],{},[648,1310,1311],{},"−",[644,1313,1257],{},[608,1315,1316],{"encoding":610},"0{,}000\\,72 = 7{,}2 \\cdot 10^{-4}",[585,1318,1320,1353,1382],{"className":1319,"ariaHidden":615},[614],[585,1321,1323,1326,1329,1335,1338,1341,1344,1347,1350],{"className":1322},[619],[585,1324],{"className":1325,"style":1173},[623],[585,1327,777],{"className":1328},[628],[585,1330,1332],{"className":1331},[628],[585,1333,728],{"className":1334},[1184],[585,1336,1029],{"className":1337},[628],[585,1339],{"className":1340,"style":1054},[684],[585,1342,1295],{"className":1343},[628],[585,1345],{"className":1346,"style":685},[684],[585,1348,1124],{"className":1349},[689],[585,1351],{"className":1352,"style":685},[684],[585,1354,1356,1359,1363,1369,1373,1376,1379],{"className":1355},[619],[585,1357],{"className":1358,"style":1173},[623],[585,1360,1362],{"className":1361},[628],"7",[585,1364,1366],{"className":1365},[628],[585,1367,728],{"className":1368},[1184],[585,1370,1372],{"className":1371},[628],"2",[585,1374],{"className":1375,"style":1192},[684],[585,1377,1130],{"className":1378},[1196],[585,1380],{"className":1381,"style":1192},[684],[585,1383,1385,1388,1391],{"className":1384},[619],[585,1386],{"className":1387,"style":1206},[623],[585,1389,646],{"className":1390},[628],[585,1392,1394,1397],{"className":1393},[628],[585,1395,777],{"className":1396},[628],[585,1398,1400],{"className":1399},[781],[585,1401,1403],{"className":1402},[785],[585,1404,1406],{"className":1405},[789],[585,1407,1409],{"className":1408,"style":1206},[793],[585,1410,1411,1414],{"style":1230},[585,1412],{"className":1413,"style":801},[800],[585,1415,1417],{"className":1416},[805,806,807,808],[585,1418,1420,1423],{"className":1419},[628,808],[585,1421,1311],{"className":1422},[628,808],[585,1424,1257],{"className":1425},[628,808],[565,1427,1428],{},"Multiplizieren und danach normieren:",[585,1430,1432],{"className":1431},[1102],[585,1433,1435,1508],{"className":1434},[588],[585,1436,1438],{"className":1437},[592],[594,1439,1440],{"xmlns":596,"display":1111},[598,1441,1442,1505],{},[601,1443,1444,1448,1450,1452,1458,1461,1463,1465,1467,1469,1476,1478,1480,1483,1485,1491,1493,1496,1498],{},[648,1445,1447],{"stretchy":1446},"false","(",[644,1449,1177],{},[648,1451,1130],{},[748,1453,1454,1456],{},[644,1455,664],{},[644,1457,1257],{},[648,1459,1460],{"stretchy":1446},")",[648,1462,1130],{},[648,1464,1447],{"stretchy":1446},[644,1466,1083],{},[648,1468,1130],{},[748,1470,1471,1473],{},[644,1472,664],{},[644,1474,1475],{},"6",[648,1477,1460],{"stretchy":1446},[648,1479,1124],{},[644,1481,1482],{},"15",[648,1484,1130],{},[748,1486,1487,1489],{},[644,1488,664],{},[644,1490,664],{},[648,1492,1124],{},[644,1494,1495],{},"1,5",[648,1497,1130],{},[748,1499,1500,1502],{},[644,1501,664],{},[644,1503,1504],{},"11",[608,1506,1507],{"encoding":610},"(3 \\cdot 10^4) \\cdot (5 \\cdot 10^6) = 15 \\cdot 10^{10} = 1{,}5 \\cdot 10^{11}",[585,1509,1511,1533,1585,1606,1656,1674,1724,1751],{"className":1510,"ariaHidden":615},[614],[585,1512,1514,1517,1521,1524,1527,1530],{"className":1513},[619],[585,1515],{"className":1516,"style":699},[623],[585,1518,1447],{"className":1519},[1520],"mopen",[585,1522,1177],{"className":1523},[628],[585,1525],{"className":1526,"style":1192},[684],[585,1528,1130],{"className":1529},[1196],[585,1531],{"className":1532,"style":1192},[684],[585,1534,1536,1540,1543,1572,1576,1579,1582],{"className":1535},[619],[585,1537],{"className":1538,"style":1539},[623],"height:1.1141em;vertical-align:-0.25em;",[585,1541,646],{"className":1542},[628],[585,1544,1546,1549],{"className":1545},[628],[585,1547,777],{"className":1548},[628],[585,1550,1552],{"className":1551},[781],[585,1553,1555],{"className":1554},[785],[585,1556,1558],{"className":1557},[789],[585,1559,1561],{"className":1560,"style":1206},[793],[585,1562,1563,1566],{"style":1230},[585,1564],{"className":1565,"style":801},[800],[585,1567,1569],{"className":1568},[805,806,807,808],[585,1570,1257],{"className":1571},[628,808],[585,1573,1460],{"className":1574},[1575],"mclose",[585,1577],{"className":1578,"style":1192},[684],[585,1580,1130],{"className":1581},[1196],[585,1583],{"className":1584,"style":1192},[684],[585,1586,1588,1591,1594,1597,1600,1603],{"className":1587},[619],[585,1589],{"className":1590,"style":699},[623],[585,1592,1447],{"className":1593},[1520],[585,1595,1083],{"className":1596},[628],[585,1598],{"className":1599,"style":1192},[684],[585,1601,1130],{"className":1602},[1196],[585,1604],{"className":1605,"style":1192},[684],[585,1607,1609,1612,1615,1644,1647,1650,1653],{"className":1608},[619],[585,1610],{"className":1611,"style":1539},[623],[585,1613,646],{"className":1614},[628],[585,1616,1618,1621],{"className":1617},[628],[585,1619,777],{"className":1620},[628],[585,1622,1624],{"className":1623},[781],[585,1625,1627],{"className":1626},[785],[585,1628,1630],{"className":1629},[789],[585,1631,1633],{"className":1632,"style":1206},[793],[585,1634,1635,1638],{"style":1230},[585,1636],{"className":1637,"style":801},[800],[585,1639,1641],{"className":1640},[805,806,807,808],[585,1642,1475],{"className":1643},[628,808],[585,1645,1460],{"className":1646},[1575],[585,1648],{"className":1649,"style":685},[684],[585,1651,1124],{"className":1652},[689],[585,1654],{"className":1655,"style":685},[684],[585,1657,1659,1662,1665,1668,1671],{"className":1658},[619],[585,1660],{"className":1661,"style":724},[623],[585,1663,1482],{"className":1664},[628],[585,1666],{"className":1667,"style":1192},[684],[585,1669,1130],{"className":1670},[1196],[585,1672],{"className":1673,"style":1192},[684],[585,1675,1677,1680,1683,1715,1718,1721],{"className":1676},[619],[585,1678],{"className":1679,"style":1206},[623],[585,1681,646],{"className":1682},[628],[585,1684,1686,1689],{"className":1685},[628],[585,1687,777],{"className":1688},[628],[585,1690,1692],{"className":1691},[781],[585,1693,1695],{"className":1694},[785],[585,1696,1698],{"className":1697},[789],[585,1699,1701],{"className":1700,"style":1206},[793],[585,1702,1703,1706],{"style":1230},[585,1704],{"className":1705,"style":801},[800],[585,1707,1709],{"className":1708},[805,806,807,808],[585,1710,1712],{"className":1711},[628,808],[585,1713,664],{"className":1714},[628,808],[585,1716],{"className":1717,"style":685},[684],[585,1719,1124],{"className":1720},[689],[585,1722],{"className":1723,"style":685},[684],[585,1725,1727,1730,1733,1739,1742,1745,1748],{"className":1726},[619],[585,1728],{"className":1729,"style":1173},[623],[585,1731,646],{"className":1732},[628],[585,1734,1736],{"className":1735},[628],[585,1737,728],{"className":1738},[1184],[585,1740,1083],{"className":1741},[628],[585,1743],{"className":1744,"style":1192},[684],[585,1746,1130],{"className":1747},[1196],[585,1749],{"className":1750,"style":1192},[684],[585,1752,1754,1757,1760],{"className":1753},[619],[585,1755],{"className":1756,"style":1206},[623],[585,1758,646],{"className":1759},[628],[585,1761,1763,1766],{"className":1762},[628],[585,1764,777],{"className":1765},[628],[585,1767,1769],{"className":1768},[781],[585,1770,1772],{"className":1771},[785],[585,1773,1775],{"className":1774},[789],[585,1776,1778],{"className":1777,"style":1206},[793],[585,1779,1780,1783],{"style":1230},[585,1781],{"className":1782,"style":801},[800],[585,1784,1786],{"className":1785},[805,806,807,808],[585,1787,1789],{"className":1788},[628,808],[585,1790,1504],{"className":1791},[628,808],[565,1793,1794],{},"Dividieren:",[585,1796,1798],{"className":1797},[1102],[585,1799,1801,1881],{"className":1800},[588],[585,1802,1804],{"className":1803},[592],[594,1805,1806],{"xmlns":596,"display":1111},[598,1807,1808,1878],{},[601,1809,1810,1842,1844,1846,1848,1866,1868,1870,1872],{},[1811,1812,1813,1826],"mfrac",{},[601,1814,1815,1818,1820],{},[644,1816,1817],{},"8",[648,1819,1130],{},[748,1821,1822,1824],{},[644,1823,664],{},[644,1825,1177],{},[601,1827,1828,1830,1832],{},[644,1829,1372],{},[648,1831,1130],{},[748,1833,1834,1836],{},[644,1835,664],{},[601,1837,1838,1840],{},[648,1839,1311],{},[644,1841,1372],{},[648,1843,1124],{},[644,1845,1257],{},[648,1847,1130],{},[748,1849,1850,1852],{},[644,1851,664],{},[601,1853,1854,1856,1858,1860,1862,1864],{},[644,1855,1177],{},[648,1857,1311],{},[648,1859,1447],{"stretchy":1446},[648,1861,1311],{},[644,1863,1372],{},[648,1865,1460],{"stretchy":1446},[648,1867,1124],{},[644,1869,1257],{},[648,1871,1130],{},[748,1873,1874,1876],{},[644,1875,664],{},[644,1877,1083],{},[608,1879,1880],{"encoding":610},"\\frac{8 \\cdot 10^3}{2 \\cdot 10^{-2}} = 4 \\cdot 10^{3 - (-2)} = 4 \\cdot 10^5",[585,1882,1884,2065,2083,2149,2167],{"className":1883,"ariaHidden":615},[614],[585,1885,1887,1891,2056,2059,2062],{"className":1886},[619],[585,1888],{"className":1889,"style":1890},[623],"height:2.1771em;vertical-align:-0.686em;",[585,1892,1894,1898,2053],{"className":1893},[628],[585,1895],{"className":1896},[1520,1897],"nulldelimiter",[585,1899,1901],{"className":1900},[1811],[585,1902,1905,2044],{"className":1903},[785,1904],"vlist-t2",[585,1906,1908,2039],{"className":1907},[789],[585,1909,1912,1974,1985],{"className":1910,"style":1911},[793],"height:1.4911em;",[585,1913,1915,1919],{"style":1914},"top:-2.314em;",[585,1916],{"className":1917,"style":1918},[800],"height:3em;",[585,1920,1922,1925,1928,1931,1934,1937],{"className":1921},[628],[585,1923,1372],{"className":1924},[628],[585,1926],{"className":1927,"style":1192},[684],[585,1929,1130],{"className":1930},[1196],[585,1932],{"className":1933,"style":1192},[684],[585,1935,646],{"className":1936},[628],[585,1938,1940,1943],{"className":1939},[628],[585,1941,777],{"className":1942},[628],[585,1944,1946],{"className":1945},[781],[585,1947,1949],{"className":1948},[785],[585,1950,1952],{"className":1951},[789],[585,1953,1956],{"className":1954,"style":1955},[793],"height:0.7401em;",[585,1957,1959,1962],{"style":1958},"top:-2.989em;margin-right:0.05em;",[585,1960],{"className":1961,"style":801},[800],[585,1963,1965],{"className":1964},[805,806,807,808],[585,1966,1968,1971],{"className":1967},[628,808],[585,1969,1311],{"className":1970},[628,808],[585,1972,1372],{"className":1973},[628,808],[585,1975,1977,1980],{"style":1976},"top:-3.23em;",[585,1978],{"className":1979,"style":1918},[800],[585,1981],{"className":1982,"style":1984},[1983],"frac-line","border-bottom-width:0.04em;",[585,1986,1988,1991],{"style":1987},"top:-3.677em;",[585,1989],{"className":1990,"style":1918},[800],[585,1992,1994,1997,2000,2003,2006,2009],{"className":1993},[628],[585,1995,1817],{"className":1996},[628],[585,1998],{"className":1999,"style":1192},[684],[585,2001,1130],{"className":2002},[1196],[585,2004],{"className":2005,"style":1192},[684],[585,2007,646],{"className":2008},[628],[585,2010,2012,2015],{"className":2011},[628],[585,2013,777],{"className":2014},[628],[585,2016,2018],{"className":2017},[781],[585,2019,2021],{"className":2020},[785],[585,2022,2024],{"className":2023},[789],[585,2025,2028],{"className":2026,"style":2027},[793],"height:0.8141em;",[585,2029,2030,2033],{"style":796},[585,2031],{"className":2032,"style":801},[800],[585,2034,2036],{"className":2035},[805,806,807,808],[585,2037,1177],{"className":2038},[628,808],[585,2040,2043],{"className":2041},[2042],"vlist-s","​",[585,2045,2047],{"className":2046},[789],[585,2048,2051],{"className":2049,"style":2050},[793],"height:0.686em;",[585,2052],{},[585,2054],{"className":2055},[1575,1897],[585,2057],{"className":2058,"style":685},[684],[585,2060,1124],{"className":2061},[689],[585,2063],{"className":2064,"style":685},[684],[585,2066,2068,2071,2074,2077,2080],{"className":2067},[619],[585,2069],{"className":2070,"style":724},[623],[585,2072,1257],{"className":2073},[628],[585,2075],{"className":2076,"style":1192},[684],[585,2078,1130],{"className":2079},[1196],[585,2081],{"className":2082,"style":1192},[684],[585,2084,2086,2090,2093,2140,2143,2146],{"className":2085},[619],[585,2087],{"className":2088,"style":2089},[623],"height:0.938em;",[585,2091,646],{"className":2092},[628],[585,2094,2096,2099],{"className":2095},[628],[585,2097,777],{"className":2098},[628],[585,2100,2102],{"className":2101},[781],[585,2103,2105],{"className":2104},[785],[585,2106,2108],{"className":2107},[789],[585,2109,2111],{"className":2110,"style":2089},[793],[585,2112,2113,2116],{"style":1230},[585,2114],{"className":2115,"style":801},[800],[585,2117,2119],{"className":2118},[805,806,807,808],[585,2120,2122,2125,2128,2131,2134,2137],{"className":2121},[628,808],[585,2123,1177],{"className":2124},[628,808],[585,2126,1311],{"className":2127},[1196,808],[585,2129,1447],{"className":2130},[1520,808],[585,2132,1311],{"className":2133},[628,808],[585,2135,1372],{"className":2136},[628,808],[585,2138,1460],{"className":2139},[1575,808],[585,2141],{"className":2142,"style":685},[684],[585,2144,1124],{"className":2145},[689],[585,2147],{"className":2148,"style":685},[684],[585,2150,2152,2155,2158,2161,2164],{"className":2151},[619],[585,2153],{"className":2154,"style":724},[623],[585,2156,1257],{"className":2157},[628],[585,2159],{"className":2160,"style":1192},[684],[585,2162,1130],{"className":2163},[1196],[585,2165],{"className":2166,"style":1192},[684],[585,2168,2170,2173,2176],{"className":2169},[619],[585,2171],{"className":2172,"style":1206},[623],[585,2174,646],{"className":2175},[628],[585,2177,2179,2182],{"className":2178},[628],[585,2180,777],{"className":2181},[628],[585,2183,2185],{"className":2184},[781],[585,2186,2188],{"className":2187},[785],[585,2189,2191],{"className":2190},[789],[585,2192,2194],{"className":2193,"style":1206},[793],[585,2195,2196,2199],{"style":1230},[585,2197],{"className":2198,"style":801},[800],[585,2200,2202],{"className":2201},[805,806,807,808],[585,2203,1083],{"className":2204},[628,808],[560,2206,2208],{"id":2207},"typische-fehler","Typische Fehler",[574,2210,2211,2399,2672],{},[577,2212,2213,2214,2301,2302,2398],{},"Das Ergebnis nicht normieren: ",[585,2215,2217,2239],{"className":2216},[588],[585,2218,2220],{"className":2219},[592],[594,2221,2222],{"xmlns":596},[598,2223,2224,2236],{},[601,2225,2226,2228,2230],{},[644,2227,1482],{},[648,2229,1130],{},[748,2231,2232,2234],{},[644,2233,664],{},[644,2235,664],{},[608,2237,2238],{"encoding":610},"15 \\cdot 10^{10}",[585,2240,2242,2260],{"className":2241,"ariaHidden":615},[614],[585,2243,2245,2248,2251,2254,2257],{"className":2244},[619],[585,2246],{"className":2247,"style":724},[623],[585,2249,1482],{"className":2250},[628],[585,2252],{"className":2253,"style":1192},[684],[585,2255,1130],{"className":2256},[1196],[585,2258],{"className":2259,"style":1192},[684],[585,2261,2263,2266,2269],{"className":2262},[619],[585,2264],{"className":2265,"style":2027},[623],[585,2267,646],{"className":2268},[628],[585,2270,2272,2275],{"className":2271},[628],[585,2273,777],{"className":2274},[628],[585,2276,2278],{"className":2277},[781],[585,2279,2281],{"className":2280},[785],[585,2282,2284],{"className":2283},[789],[585,2285,2287],{"className":2286,"style":2027},[793],[585,2288,2289,2292],{"style":796},[585,2290],{"className":2291,"style":801},[800],[585,2293,2295],{"className":2294},[805,806,807,808],[585,2296,2298],{"className":2297},[628,808],[585,2299,664],{"className":2300},[628,808]," ist richtig gerechnet, aber erst ",[585,2303,2305,2327],{"className":2304},[588],[585,2306,2308],{"className":2307},[592],[594,2309,2310],{"xmlns":596},[598,2311,2312,2324],{},[601,2313,2314,2316,2318],{},[644,2315,1495],{},[648,2317,1130],{},[748,2319,2320,2322],{},[644,2321,664],{},[644,2323,1504],{},[608,2325,2326],{"encoding":610},"1{,}5 \\cdot 10^{11}",[585,2328,2330,2357],{"className":2329,"ariaHidden":615},[614],[585,2331,2333,2336,2339,2345,2348,2351,2354],{"className":2332},[619],[585,2334],{"className":2335,"style":1173},[623],[585,2337,646],{"className":2338},[628],[585,2340,2342],{"className":2341},[628],[585,2343,728],{"className":2344},[1184],[585,2346,1083],{"className":2347},[628],[585,2349],{"className":2350,"style":1192},[684],[585,2352,1130],{"className":2353},[1196],[585,2355],{"className":2356,"style":1192},[684],[585,2358,2360,2363,2366],{"className":2359},[619],[585,2361],{"className":2362,"style":2027},[623],[585,2364,646],{"className":2365},[628],[585,2367,2369,2372],{"className":2368},[628],[585,2370,777],{"className":2371},[628],[585,2373,2375],{"className":2374},[781],[585,2376,2378],{"className":2377},[785],[585,2379,2381],{"className":2380},[789],[585,2382,2384],{"className":2383,"style":2027},[793],[585,2385,2386,2389],{"style":796},[585,2387],{"className":2388,"style":801},[800],[585,2390,2392],{"className":2391},[805,806,807,808],[585,2393,2395],{"className":2394},[628,808],[585,2396,1504],{"className":2397},[628,808]," ist wissenschaftliche Schreibweise.",[577,2400,2401,2402,2430,2431,2434,2435,2578,2579,812],{},"Das Vorzeichen des Exponenten verwechseln: Zahlen kleiner als ",[585,2403,2405,2418],{"className":2404},[588],[585,2406,2408],{"className":2407},[592],[594,2409,2410],{"xmlns":596},[598,2411,2412,2416],{},[601,2413,2414],{},[644,2415,646],{},[608,2417,646],{"encoding":610},[585,2419,2421],{"className":2420,"ariaHidden":615},[614],[585,2422,2424,2427],{"className":2423},[619],[585,2425],{"className":2426,"style":724},[623],[585,2428,646],{"className":2429},[628]," haben einen ",[569,2432,2433],{},"negativen"," Exponenten, ",[585,2436,2438,2471],{"className":2437},[588],[585,2439,2441],{"className":2440},[592],[594,2442,2443],{"xmlns":596},[598,2444,2445,2469],{},[601,2446,2447,2449,2451,2453,2455,2457,2459],{},[644,2448,1290],{},[1024,2450,1026],{},[644,2452,1295],{},[648,2454,1124],{},[644,2456,1300],{},[648,2458,1130],{},[748,2460,2461,2463],{},[644,2462,664],{},[601,2464,2465,2467],{},[648,2466,1311],{},[644,2468,1257],{},[608,2470,1316],{"encoding":610},[585,2472,2474,2507,2534],{"className":2473,"ariaHidden":615},[614],[585,2475,2477,2480,2483,2489,2492,2495,2498,2501,2504],{"className":2476},[619],[585,2478],{"className":2479,"style":1173},[623],[585,2481,777],{"className":2482},[628],[585,2484,2486],{"className":2485},[628],[585,2487,728],{"className":2488},[1184],[585,2490,1029],{"className":2491},[628],[585,2493],{"className":2494,"style":1054},[684],[585,2496,1295],{"className":2497},[628],[585,2499],{"className":2500,"style":685},[684],[585,2502,1124],{"className":2503},[689],[585,2505],{"className":2506,"style":685},[684],[585,2508,2510,2513,2516,2522,2525,2528,2531],{"className":2509},[619],[585,2511],{"className":2512,"style":1173},[623],[585,2514,1362],{"className":2515},[628],[585,2517,2519],{"className":2518},[628],[585,2520,728],{"className":2521},[1184],[585,2523,1372],{"className":2524},[628],[585,2526],{"className":2527,"style":1192},[684],[585,2529,1130],{"className":2530},[1196],[585,2532],{"className":2533,"style":1192},[684],[585,2535,2537,2540,2543],{"className":2536},[619],[585,2538],{"className":2539,"style":2027},[623],[585,2541,646],{"className":2542},[628],[585,2544,2546,2549],{"className":2545},[628],[585,2547,777],{"className":2548},[628],[585,2550,2552],{"className":2551},[781],[585,2553,2555],{"className":2554},[785],[585,2556,2558],{"className":2557},[789],[585,2559,2561],{"className":2560,"style":2027},[793],[585,2562,2563,2566],{"style":796},[585,2564],{"className":2565,"style":801},[800],[585,2567,2569],{"className":2568},[805,806,807,808],[585,2570,2572,2575],{"className":2571},[628,808],[585,2573,1311],{"className":2574},[628,808],[585,2576,1257],{"className":2577},[628,808],", nicht ",[585,2580,2582,2604],{"className":2581},[588],[585,2583,2585],{"className":2584},[592],[594,2586,2587],{"xmlns":596},[598,2588,2589,2601],{},[601,2590,2591,2593,2595],{},[644,2592,1300],{},[648,2594,1130],{},[748,2596,2597,2599],{},[644,2598,664],{},[644,2600,1257],{},[608,2602,2603],{"encoding":610},"7{,}2 \\cdot 10^4",[585,2605,2607,2634],{"className":2606,"ariaHidden":615},[614],[585,2608,2610,2613,2616,2622,2625,2628,2631],{"className":2609},[619],[585,2611],{"className":2612,"style":1173},[623],[585,2614,1362],{"className":2615},[628],[585,2617,2619],{"className":2618},[628],[585,2620,728],{"className":2621},[1184],[585,2623,1372],{"className":2624},[628],[585,2626],{"className":2627,"style":1192},[684],[585,2629,1130],{"className":2630},[1196],[585,2632],{"className":2633,"style":1192},[684],[585,2635,2637,2640,2643],{"className":2636},[619],[585,2638],{"className":2639,"style":2027},[623],[585,2641,646],{"className":2642},[628],[585,2644,2646,2649],{"className":2645},[628],[585,2647,777],{"className":2648},[628],[585,2650,2652],{"className":2651},[781],[585,2653,2655],{"className":2654},[785],[585,2656,2658],{"className":2657},[789],[585,2659,2661],{"className":2660,"style":2027},[793],[585,2662,2663,2666],{"style":796},[585,2664],{"className":2665,"style":801},[800],[585,2667,2669],{"className":2668},[805,806,807,808],[585,2670,1257],{"className":2671},[628,808],[577,2673,2674,2675,2792,2793,812],{},"Die Mantisse statt der Zehn potenzieren: ",[585,2676,2678,2706],{"className":2677},[588],[585,2679,2681],{"className":2680},[592],[594,2682,2683],{"xmlns":596},[598,2684,2685,2703],{},[601,2686,2687,2690,2692,2698,2700],{},[644,2688,2689],{},"2,5",[648,2691,1130],{},[748,2693,2694,2696],{},[644,2695,664],{},[644,2697,1177],{},[648,2699,1124],{},[644,2701,2702],{},"2500",[608,2704,2705],{"encoding":610},"2{,}5 \\cdot 10^3 = 2500",[585,2707,2709,2736,2783],{"className":2708,"ariaHidden":615},[614],[585,2710,2712,2715,2718,2724,2727,2730,2733],{"className":2711},[619],[585,2713],{"className":2714,"style":1173},[623],[585,2716,1372],{"className":2717},[628],[585,2719,2721],{"className":2720},[628],[585,2722,728],{"className":2723},[1184],[585,2725,1083],{"className":2726},[628],[585,2728],{"className":2729,"style":1192},[684],[585,2731,1130],{"className":2732},[1196],[585,2734],{"className":2735,"style":1192},[684],[585,2737,2739,2742,2745,2774,2777,2780],{"className":2738},[619],[585,2740],{"className":2741,"style":2027},[623],[585,2743,646],{"className":2744},[628],[585,2746,2748,2751],{"className":2747},[628],[585,2749,777],{"className":2750},[628],[585,2752,2754],{"className":2753},[781],[585,2755,2757],{"className":2756},[785],[585,2758,2760],{"className":2759},[789],[585,2761,2763],{"className":2762,"style":2027},[793],[585,2764,2765,2768],{"style":796},[585,2766],{"className":2767,"style":801},[800],[585,2769,2771],{"className":2770},[805,806,807,808],[585,2772,1177],{"className":2773},[628,808],[585,2775],{"className":2776,"style":685},[684],[585,2778,1124],{"className":2779},[689],[585,2781],{"className":2782,"style":685},[684],[585,2784,2786,2789],{"className":2785},[619],[585,2787],{"className":2788,"style":724},[623],[585,2790,2702],{"className":2791},[628],", aber ",[585,2794,2796,2819],{"className":2795},[588],[585,2797,2799],{"className":2798},[592],[594,2800,2801],{"xmlns":596},[598,2802,2803,2816],{},[601,2804,2805,2811,2813],{},[748,2806,2807,2809],{},[644,2808,2689],{},[644,2810,1177],{},[648,2812,1124],{},[644,2814,2815],{},"15,625",[608,2817,2818],{"encoding":610},"2{,}5^3 = 15{,}625",[585,2820,2822,2876],{"className":2821,"ariaHidden":615},[614],[585,2823,2825,2829,2832,2838,2867,2870,2873],{"className":2824},[619],[585,2826],{"className":2827,"style":2828},[623],"height:1.0085em;vertical-align:-0.1944em;",[585,2830,1372],{"className":2831},[628],[585,2833,2835],{"className":2834},[628],[585,2836,728],{"className":2837},[1184],[585,2839,2841,2844],{"className":2840},[628],[585,2842,1083],{"className":2843},[628],[585,2845,2847],{"className":2846},[781],[585,2848,2850],{"className":2849},[785],[585,2851,2853],{"className":2852},[789],[585,2854,2856],{"className":2855,"style":2027},[793],[585,2857,2858,2861],{"style":796},[585,2859],{"className":2860,"style":801},[800],[585,2862,2864],{"className":2863},[805,806,807,808],[585,2865,1177],{"className":2866},[628,808],[585,2868],{"className":2869,"style":685},[684],[585,2871,1124],{"className":2872},[689],[585,2874],{"className":2875,"style":685},[684],[585,2877,2879,2882,2885,2891],{"className":2878},[619],[585,2880],{"className":2881,"style":1173},[623],[585,2883,1482],{"className":2884},[628],[585,2886,2888],{"className":2887},[628],[585,2889,728],{"className":2890},[1184],[585,2892,2894],{"className":2893},[628],"625",{"title":2896,"searchDepth":2897,"depth":2897,"links":2898},"",2,[2899,2900,2901],{"id":562,"depth":2897,"text":563},{"id":1003,"depth":2897,"text":1004},{"id":2207,"depth":2897,"text":2208},[2903,2906,2909,2912,2915,2917,2920,2923],{"lhs":2904,"rhs":2905},"a*10^m * b*10^n","a*b*10^(m+n)",{"lhs":2907,"rhs":2908},"3.84 * 10^5","384000",{"lhs":2910,"rhs":2911},"7.2 * 10^(-4)","0.00072",{"lhs":2913,"rhs":2914},"(3*10^4) * (5*10^6)","15 * 10^10",{"lhs":2914,"rhs":2916},"1.5 * 10^11",{"lhs":2918,"rhs":2919},"(8*10^3) \u002F (2*10^(-2))","4 * 10^5",{"lhs":2921,"rhs":2922},"2.5^3","15.625",{"lhs":2924,"rhs":2702},"2.5 * 10^3","1 \\leq |a| \u003C 10,\\ n \\in \\mathbb{Z}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmn>1\u003C\u002Fmn>\u003Cmo>≤\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmi>a\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmo><\u003C\u002Fmo>\u003Cmn>10\u003C\u002Fmn>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">1 \\leq |a| < 10,\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:0.7804em;vertical-align:-0.136em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\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:0.8389em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">10\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003Cmo>∈\u003C\u002Fmo>\u003Cmi mathvariant=\"double-struck\">Z\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n \\in \\mathbb{Z}\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:0.5782em;vertical-align:-0.0391em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\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:0.6889em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathbb\">Z\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","scientific-notation","x = a \\cdot 10^n","\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>x\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi>a\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsup>\u003Cmn>10\u003C\u002Fmn>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmsup>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x = a \\cdot 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style=\"height:0.7144em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.7144em;\">\u003Cspan style=\"top:-3.113em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mathnormal mtight\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","middle",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Farithmetic\u002Fwissenschaftliche-schreibweise",[],[2938,2939,2940],"power-product-rule","power-quotient-rule","negative-exponent",{"title":548,"description":2896},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fwissenschaftliche-schreibweise","Sehr große und sehr kleine Zahlen schreibt man als Zahl zwischen 1 und 10 mal einer Zehnerpotenz.",[2945,2946,2947,2948],"zehnerpotenz","gleitkomma","große zahlen","kleine zahlen",[2950,2954,2957],{"symbol":2951,"meaning":2952,"symbolHtml":2953},"x","die darzustellende Zahl (nicht null)","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x\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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":606,"meaning":2955,"symbolHtml":2956},"Mantisse, eine Zahl mit genau einer von null verschiedenen Stelle vor dem Komma","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>a\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">a\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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">a\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":754,"meaning":2958,"symbolHtml":2959},"ganzzahliger Exponent der Zehnerpotenz","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>n\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">n\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:0.4306em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">n\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","migubYwmS2szc8GU7SKWO_VGCOKiIBuNZmTCxLefewg",[2962,2965,2968],{"stem":2963,"title":2964,"category":5},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fnegative-exponenten","Negative Exponenten und Exponent null",{"stem":2966,"title":2967,"category":5},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fpotenzen-gleicher-basis-dividieren","Potenzen mit gleicher Basis dividieren",{"stem":2969,"title":2970,"category":5},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fpotenzen-gleicher-basis-multiplizieren","Potenzen mit gleicher Basis multiplizieren",1793824260390]