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3{,}14",[581,975,977,999],{"className":976,"ariaHidden":616},[615],[581,978,980,984,988,992,996],{"className":979},[620],[581,981],{"className":982,"style":983},[624],"height:0.4831em;",[581,985,964],{"className":986,"style":987},[629,633],"margin-right:0.0359em;",[581,989],{"className":990,"style":991},[722],"margin-right:0.2778em;",[581,993,967],{"className":994},[995],"mrel",[581,997],{"className":998,"style":991},[722],[581,1000,1002,1005,1009,1015],{"className":1001},[620],[581,1003],{"className":1004,"style":817},[624],[581,1006,1008],{"className":1007},[629],"3",[581,1010,1012],{"className":1011},[629],[581,1013,829],{"className":1014},[828],[581,1016,1018],{"className":1017},[629],"14",":",[581,1021,1024],{"className":1022},[1023],"katex-display",[581,1025,1027,1087],{"className":1026},[584],[581,1028,1030],{"className":1029},[588],[590,1031,1033],{"xmlns":592,"display":1032},"block",[594,1034,1035,1084],{},[597,1036,1037,1039,1041,1044,1047,1049,1051,1053,1055,1057,1060,1063,1065,1067,1074,1076,1079,1081],{},[600,1038,603],{"mathvariant":602},[600,1040,606],{},[789,1042,1043],{},"=",[600,1045,1046],{"mathvariant":602},"∣",[693,1048,970],{},[789,1050,802],{},[600,1052,964],{},[600,1054,1046],{"mathvariant":602},[789,1056,967],{},[693,1058,1059],{},"0,00159",[722,1061],{"width":1062},"2em",[600,1064,654],{},[789,1066,1043],{},[1068,1069,1070,1072],"mfrac",{},[693,1071,1059],{},[600,1073,964],{},[789,1075,967],{},[693,1077,1078],{},"0,051",[697,1080,699],{},[600,1082,1083],{"mathvariant":602},"%",[608,1085,1086],{"encoding":610},"\\Delta x = |3{,}14 - \\pi| \\approx 0{,}00159 \\qquad \\delta = \\frac{0{,}00159}{\\pi} \\approx 0{,}051\\,\\%",[581,1088,1090,1111,1140,1161,1197,1298],{"className":1089,"ariaHidden":616},[615],[581,1091,1093,1096,1099,1102,1105,1108],{"className":1092},[620],[581,1094],{"className":1095,"style":625},[624],[581,1097,603],{"className":1098},[629],[581,1100,606],{"className":1101},[629,633],[581,1103],{"className":1104,"style":991},[722],[581,1106,1043],{"className":1107},[995],[581,1109],{"className":1110,"style":991},[722],[581,1112,1114,1118,1122,1128,1131,1134,1137],{"className":1113},[620],[581,1115],{"className":1116,"style":1117},[624],"height:1em;vertical-align:-0.25em;",[581,1119,1121],{"className":1120},[629],"∣3",[581,1123,1125],{"className":1124},[629],[581,1126,829],{"className":1127},[828],[581,1129,1018],{"className":1130},[629],[581,1132],{"className":1133,"style":837},[722],[581,1135,802],{"className":1136},[841],[581,1138],{"className":1139,"style":837},[722],[581,1141,1143,1146,1149,1152,1155,1158],{"className":1142},[620],[581,1144],{"className":1145,"style":1117},[624],[581,1147,964],{"className":1148,"style":987},[629,633],[581,1150,1046],{"className":1151},[629],[581,1153],{"className":1154,"style":991},[722],[581,1156,967],{"className":1157},[995],[581,1159],{"className":1160,"style":991},[722],[581,1162,1164,1168,1171,1177,1181,1185,1188,1191,1194],{"className":1163},[620],[581,1165],{"className":1166,"style":1167},[624],"height:0.8889em;vertical-align:-0.1944em;",[581,1169,821],{"className":1170},[629],[581,1172,1174],{"className":1173},[629],[581,1175,829],{"className":1176},[828],[581,1178,1180],{"className":1179},[629],"00159",[581,1182],{"className":1183,"style":1184},[722],"margin-right:2em;",[581,1186,654],{"className":1187,"style":671},[629,633],[581,1189],{"className":1190,"style":991},[722],[581,1192,1043],{"className":1193},[995],[581,1195],{"className":1196,"style":991},[722],[581,1198,1200,1204,1289,1292,1295],{"className":1199},[620],[581,1201],{"className":1202,"style":1203},[624],"height:2.0074em;vertical-align:-0.686em;",[581,1205,1207,1212,1285],{"className":1206},[629],[581,1208],{"className":1209},[1210,1211],"mopen","nulldelimiter",[581,1213,1215],{"className":1214},[1068],[581,1216,1219,1276],{"className":1217},[868,1218],"vlist-t2",[581,1220,1222,1271],{"className":1221},[872],[581,1223,1226,1239,1250],{"className":1224,"style":1225},[876],"height:1.3214em;",[581,1227,1229,1233],{"style":1228},"top:-2.314em;",[581,1230],{"className":1231,"style":1232},[883],"height:3em;",[581,1234,1236],{"className":1235},[629],[581,1237,964],{"className":1238,"style":987},[629,633],[581,1240,1242,1245],{"style":1241},"top:-3.23em;",[581,1243],{"className":1244,"style":1232},[883],[581,1246],{"className":1247,"style":1249},[1248],"frac-line","border-bottom-width:0.04em;",[581,1251,1253,1256],{"style":1252},"top:-3.677em;",[581,1254],{"className":1255,"style":1232},[883],[581,1257,1259,1262,1268],{"className":1258},[629],[581,1260,821],{"className":1261},[629],[581,1263,1265],{"className":1264},[629],[581,1266,829],{"className":1267},[828],[581,1269,1180],{"className":1270},[629],[581,1272,1275],{"className":1273},[1274],"vlist-s","​",[581,1277,1279],{"className":1278},[872],[581,1280,1283],{"className":1281,"style":1282},[876],"height:0.686em;",[581,1284],{},[581,1286],{"className":1287},[1288,1211],"mclose",[581,1290],{"className":1291,"style":991},[722],[581,1293,967],{"className":1294},[995],[581,1296],{"className":1297,"style":991},[722],[581,1299,1301,1305,1308,1314,1318,1321],{"className":1300},[620],[581,1302],{"className":1303,"style":1304},[624],"height:0.9444em;vertical-align:-0.1944em;",[581,1306,821],{"className":1307},[629],[581,1309,1311],{"className":1310},[629],[581,1312,829],{"className":1313},[828],[581,1315,1317],{"className":1316},[629],"051",[581,1319],{"className":1320,"style":723},[722],[581,1322,1083],{"className":1323},[629],[565,1325,1326,1327,1371,1372,1425,1426,1470,1471,942],{},"Zwei Messungen im Vergleich: Ein Brett von ",[581,1328,1330,1350],{"className":1329},[584],[581,1331,1333],{"className":1332},[588],[590,1334,1335],{"xmlns":592},[594,1336,1337,1347],{},[597,1338,1339,1342,1344],{},[693,1340,1341],{},"2",[697,1343,699],{},[697,1345,1346],{},"m",[608,1348,1349],{"encoding":610},"2\\,\\text{m}",[581,1351,1353],{"className":1352,"ariaHidden":616},[615],[581,1354,1356,1359,1362,1365],{"className":1355},[620],[581,1357],{"className":1358,"style":715},[624],[581,1360,1341],{"className":1361},[629],[581,1363],{"className":1364,"style":723},[722],[581,1366,1368],{"className":1367},[629,727],[581,1369,1346],{"className":1370},[629]," Länge wird mit ",[581,1373,1375,1394],{"className":1374},[584],[581,1376,1378],{"className":1377},[588],[590,1379,1380],{"xmlns":592},[594,1381,1382,1391],{},[597,1383,1384,1387,1389],{},[693,1385,1386],{},"2,03",[697,1388,699],{},[697,1390,1346],{},[608,1392,1393],{"encoding":610},"2{,}03\\,\\text{m}",[581,1395,1397],{"className":1396,"ariaHidden":616},[615],[581,1398,1400,1403,1406,1412,1416,1419],{"className":1399},[620],[581,1401],{"className":1402,"style":817},[624],[581,1404,1341],{"className":1405},[629],[581,1407,1409],{"className":1408},[629],[581,1410,829],{"className":1411},[828],[581,1413,1415],{"className":1414},[629],"03",[581,1417],{"className":1418,"style":723},[722],[581,1420,1422],{"className":1421},[629,727],[581,1423,1346],{"className":1424},[629]," gemessen, ein Stift von ",[581,1427,1429,1449],{"className":1428},[584],[581,1430,1432],{"className":1431},[588],[590,1433,1434],{"xmlns":592},[594,1435,1436,1446],{},[597,1437,1438,1441,1443],{},[693,1439,1440],{},"15",[697,1442,699],{},[697,1444,1445],{},"cm",[608,1447,1448],{"encoding":610},"15\\,\\text{cm}",[581,1450,1452],{"className":1451,"ariaHidden":616},[615],[581,1453,1455,1458,1461,1464],{"className":1454},[620],[581,1456],{"className":1457,"style":715},[624],[581,1459,1440],{"className":1460},[629],[581,1462],{"className":1463,"style":723},[722],[581,1465,1467],{"className":1466},[629,727],[581,1468,1445],{"className":1469},[629]," mit ",[581,1472,1474,1493],{"className":1473},[584],[581,1475,1477],{"className":1476},[588],[590,1478,1479],{"xmlns":592},[594,1480,1481,1490],{},[597,1482,1483,1486,1488],{},[693,1484,1485],{},"15,3",[697,1487,699],{},[697,1489,1445],{},[608,1491,1492],{"encoding":610},"15{,}3\\,\\text{cm}",[581,1494,1496],{"className":1495,"ariaHidden":616},[615],[581,1497,1499,1502,1505,1511,1514,1517],{"className":1498},[620],[581,1500],{"className":1501,"style":817},[624],[581,1503,1440],{"className":1504},[629],[581,1506,1508],{"className":1507},[629],[581,1509,829],{"className":1510},[828],[581,1512,1008],{"className":1513},[629],[581,1515],{"className":1516,"style":723},[722],[581,1518,1520],{"className":1519},[629,727],[581,1521,1445],{"className":1522},[629],[581,1524,1526],{"className":1525},[1023],[581,1527,1529,1581],{"className":1528},[584],[581,1530,1532],{"className":1531},[588],[590,1533,1534],{"xmlns":592,"display":1032},[594,1535,1536,1578],{},[597,1537,1538,1541,1543,1545,1547,1550,1552,1554,1556,1559,1561,1563,1569,1571,1574,1576],{},[697,1539,1540],{},"Brett: ",[600,1542,603],{"mathvariant":602},[600,1544,606],{},[789,1546,1043],{},[693,1548,1549],{},"0,03",[697,1551,699],{},[697,1553,1346],{},[789,1555,829],{"separator":616},[697,1557,1558],{}," ",[600,1560,654],{},[789,1562,1043],{},[1068,1564,1565,1567],{},[693,1566,1549],{},[693,1568,1341],{},[789,1570,1043],{},[693,1572,1573],{},"1,5",[697,1575,699],{},[600,1577,1083],{"mathvariant":602},[608,1579,1580],{"encoding":610},"\\text{Brett: } \\Delta x = 0{,}03\\,\\text{m},\\ \\delta = \\frac{0{,}03}{2} = 1{,}5\\,\\%",[581,1582,1584,1611,1659,1745],{"className":1583,"ariaHidden":616},[615],[581,1585,1587,1590,1596,1599,1602,1605,1608],{"className":1586},[620],[581,1588],{"className":1589,"style":625},[624],[581,1591,1593],{"className":1592},[629,727],[581,1594,1540],{"className":1595},[629],[581,1597,603],{"className":1598},[629],[581,1600,606],{"className":1601},[629,633],[581,1603],{"className":1604,"style":991},[722],[581,1606,1043],{"className":1607},[995],[581,1609],{"className":1610,"style":991},[722],[581,1612,1614,1617,1620,1626,1629,1632,1638,1641,1644,1647,1650,1653,1656],{"className":1613},[620],[581,1615],{"className":1616,"style":1167},[624],[581,1618,821],{"className":1619},[629],[581,1621,1623],{"className":1622},[629],[581,1624,829],{"className":1625},[828],[581,1627,1415],{"className":1628},[629],[581,1630],{"className":1631,"style":723},[722],[581,1633,1635],{"className":1634},[629,727],[581,1636,1346],{"className":1637},[629],[581,1639,829],{"className":1640},[828],[581,1642,1558],{"className":1643},[722],[581,1645],{"className":1646,"style":723},[722],[581,1648,654],{"className":1649,"style":671},[629,633],[581,1651],{"className":1652,"style":991},[722],[581,1654,1043],{"className":1655},[995],[581,1657],{"className":1658,"style":991},[722],[581,1660,1662,1665,1736,1739,1742],{"className":1661},[620],[581,1663],{"className":1664,"style":1203},[624],[581,1666,1668,1671,1733],{"className":1667},[629],[581,1669],{"className":1670},[1210,1211],[581,1672,1674],{"className":1673},[1068],[581,1675,1677,1725],{"className":1676},[868,1218],[581,1678,1680,1722],{"className":1679},[872],[581,1681,1683,1694,1702],{"className":1682,"style":1225},[876],[581,1684,1685,1688],{"style":1228},[581,1686],{"className":1687,"style":1232},[883],[581,1689,1691],{"className":1690},[629],[581,1692,1341],{"className":1693},[629],[581,1695,1696,1699],{"style":1241},[581,1697],{"className":1698,"style":1232},[883],[581,1700],{"className":1701,"style":1249},[1248],[581,1703,1704,1707],{"style":1252},[581,1705],{"className":1706,"style":1232},[883],[581,1708,1710,1713,1719],{"className":1709},[629],[581,1711,821],{"className":1712},[629],[581,1714,1716],{"className":1715},[629],[581,1717,829],{"className":1718},[828],[581,1720,1415],{"className":1721},[629],[581,1723,1275],{"className":1724},[1274],[581,1726,1728],{"className":1727},[872],[581,1729,1731],{"className":1730,"style":1282},[876],[581,1732],{},[581,1734],{"className":1735},[1288,1211],[581,1737],{"className":1738,"style":991},[722],[581,1740,1043],{"className":1741},[995],[581,1743],{"className":1744,"style":991},[722],[581,1746,1748,1751,1754,1760,1763,1766],{"className":1747},[620],[581,1749],{"className":1750,"style":1304},[624],[581,1752,695],{"className":1753},[629],[581,1755,1757],{"className":1756},[629],[581,1758,829],{"className":1759},[828],[581,1761,833],{"className":1762},[629],[581,1764],{"className":1765,"style":723},[722],[581,1767,1083],{"className":1768},[629],[581,1770,1772],{"className":1771},[1023],[581,1773,1775,1825],{"className":1774},[584],[581,1776,1778],{"className":1777},[588],[590,1779,1780],{"xmlns":592,"display":1032},[594,1781,1782,1822],{},[597,1783,1784,1787,1789,1791,1793,1796,1798,1800,1802,1804,1806,1808,1814,1816,1818,1820],{},[697,1785,1786],{},"Stift: ",[600,1788,603],{"mathvariant":602},[600,1790,606],{},[789,1792,1043],{},[693,1794,1795],{},"0,3",[697,1797,699],{},[697,1799,1445],{},[789,1801,829],{"separator":616},[697,1803,1558],{},[600,1805,654],{},[789,1807,1043],{},[1068,1809,1810,1812],{},[693,1811,1795],{},[693,1813,1440],{},[789,1815,1043],{},[693,1817,1341],{},[697,1819,699],{},[600,1821,1083],{"mathvariant":602},[608,1823,1824],{"encoding":610},"\\text{Stift: } \\Delta x = 0{,}3\\,\\text{cm},\\ \\delta = \\frac{0{,}3}{15} = 2\\,\\%",[581,1826,1828,1855,1903,1989],{"className":1827,"ariaHidden":616},[615],[581,1829,1831,1834,1840,1843,1846,1849,1852],{"className":1830},[620],[581,1832],{"className":1833,"style":667},[624],[581,1835,1837],{"className":1836},[629,727],[581,1838,1786],{"className":1839},[629],[581,1841,603],{"className":1842},[629],[581,1844,606],{"className":1845},[629,633],[581,1847],{"className":1848,"style":991},[722],[581,1850,1043],{"className":1851},[995],[581,1853],{"className":1854,"style":991},[722],[581,1856,1858,1861,1864,1870,1873,1876,1882,1885,1888,1891,1894,1897,1900],{"className":1857},[620],[581,1859],{"className":1860,"style":1167},[624],[581,1862,821],{"className":1863},[629],[581,1865,1867],{"className":1866},[629],[581,1868,829],{"className":1869},[828],[581,1871,1008],{"className":1872},[629],[581,1874],{"className":1875,"style":723},[722],[581,1877,1879],{"className":1878},[629,727],[581,1880,1445],{"className":1881},[629],[581,1883,829],{"className":1884},[828],[581,1886,1558],{"className":1887},[722],[581,1889],{"className":1890,"style":723},[722],[581,1892,654],{"className":1893,"style":671},[629,633],[581,1895],{"className":1896,"style":991},[722],[581,1898,1043],{"className":1899},[995],[581,1901],{"className":1902,"style":991},[722],[581,1904,1906,1909,1980,1983,1986],{"className":1905},[620],[581,1907],{"className":1908,"style":1203},[624],[581,1910,1912,1915,1977],{"className":1911},[629],[581,1913],{"className":1914},[1210,1211],[581,1916,1918],{"className":1917},[1068],[581,1919,1921,1969],{"className":1920},[868,1218],[581,1922,1924,1966],{"className":1923},[872],[581,1925,1927,1938,1946],{"className":1926,"style":1225},[876],[581,1928,1929,1932],{"style":1228},[581,1930],{"className":1931,"style":1232},[883],[581,1933,1935],{"className":1934},[629],[581,1936,1440],{"className":1937},[629],[581,1939,1940,1943],{"style":1241},[581,1941],{"className":1942,"style":1232},[883],[581,1944],{"className":1945,"style":1249},[1248],[581,1947,1948,1951],{"style":1252},[581,1949],{"className":1950,"style":1232},[883],[581,1952,1954,1957,1963],{"className":1953},[629],[581,1955,821],{"className":1956},[629],[581,1958,1960],{"className":1959},[629],[581,1961,829],{"className":1962},[828],[581,1964,1008],{"className":1965},[629],[581,1967,1275],{"className":1968},[1274],[581,1970,1972],{"className":1971},[872],[581,1973,1975],{"className":1974,"style":1282},[876],[581,1976],{},[581,1978],{"className":1979},[1288,1211],[581,1981],{"className":1982,"style":991},[722],[581,1984,1043],{"className":1985},[995],[581,1987],{"className":1988,"style":991},[722],[581,1990,1992,1996,1999,2002],{"className":1991},[620],[581,1993],{"className":1994,"style":1995},[624],"height:0.8056em;vertical-align:-0.0556em;",[581,1997,1341],{"className":1998},[629],[581,2000],{"className":2001,"style":723},[722],[581,2003,1083],{"className":2004},[629],[565,2006,2007,2008,2050,2051,2093],{},"Der absolute Fehler beim Stift ist mit ",[581,2009,2011,2029],{"className":2010},[584],[581,2012,2014],{"className":2013},[588],[590,2015,2016],{"xmlns":592},[594,2017,2018,2026],{},[597,2019,2020,2022,2024],{},[693,2021,1008],{},[697,2023,699],{},[697,2025,702],{},[608,2027,2028],{"encoding":610},"3\\,\\text{mm}",[581,2030,2032],{"className":2031,"ariaHidden":616},[615],[581,2033,2035,2038,2041,2044],{"className":2034},[620],[581,2036],{"className":2037,"style":715},[624],[581,2039,1008],{"className":2040},[629],[581,2042],{"className":2043,"style":723},[722],[581,2045,2047],{"className":2046},[629,727],[581,2048,702],{"className":2049},[629]," zehnmal kleiner als beim Brett (",[581,2052,2054,2072],{"className":2053},[584],[581,2055,2057],{"className":2056},[588],[590,2058,2059],{"xmlns":592},[594,2060,2061,2069],{},[597,2062,2063,2065,2067],{},[693,2064,1008],{},[697,2066,699],{},[697,2068,1445],{},[608,2070,2071],{"encoding":610},"3\\,\\text{cm}",[581,2073,2075],{"className":2074,"ariaHidden":616},[615],[581,2076,2078,2081,2084,2087],{"className":2077},[620],[581,2079],{"className":2080,"style":715},[624],[581,2082,1008],{"className":2083},[629],[581,2085],{"className":2086,"style":723},[722],[581,2088,2090],{"className":2089},[629,727],[581,2091,1445],{"className":2092},[629],"), relativ ist die Stiftmessung aber ungenauer.",[560,2095,2097],{"id":2096},"typische-fehler","Typische Fehler",[569,2099,2100,2103,2106],{},[572,2101,2102],{},"Das Vorzeichen behalten: Der absolute Fehler ist ein Abstand und deshalb nie negativ.",[572,2104,2105],{},"Absolute Fehler verschiedener Größen direkt vergleichen. Aussagekräftig für die Genauigkeit ist der relative Fehler.",[572,2107,2108,2109,2326],{},"Beim relativen Fehler die Einheit stehen lassen: ",[581,2110,2112,2155],{"className":2111},[584],[581,2113,2115],{"className":2114},[588],[590,2116,2117],{"xmlns":592},[594,2118,2119,2152],{},[597,2120,2121,2139,2141,2144,2146,2148,2150],{},[1068,2122,2123,2131],{},[597,2124,2125,2127,2129],{},[693,2126,1549],{},[697,2128,699],{},[697,2130,1346],{},[597,2132,2133,2135,2137],{},[693,2134,1341],{},[697,2136,699],{},[697,2138,1346],{},[789,2140,1043],{},[693,2142,2143],{},"0,015",[789,2145,1043],{},[693,2147,1573],{},[697,2149,699],{},[600,2151,1083],{"mathvariant":602},[608,2153,2154],{"encoding":610},"\\frac{0{,}03\\,\\text{m}}{2\\,\\text{m}} = 0{,}015 = 1{,}5\\,\\%",[581,2156,2158,2274,2302],{"className":2157,"ariaHidden":616},[615],[581,2159,2161,2165,2265,2268,2271],{"className":2160},[620],[581,2162],{"className":2163,"style":2164},[624],"height:1.2422em;vertical-align:-0.345em;",[581,2166,2168,2171,2262],{"className":2167},[629],[581,2169],{"className":2170},[1210,1211],[581,2172,2174],{"className":2173},[1068],[581,2175,2177,2253],{"className":2176},[868,1218],[581,2178,2180,2250],{"className":2179},[872],[581,2181,2184,2209,2217],{"className":2182,"style":2183},[876],"height:0.8972em;",[581,2185,2187,2190],{"style":2186},"top:-2.655em;",[581,2188],{"className":2189,"style":1232},[883],[581,2191,2193],{"className":2192},[888,889,890,891],[581,2194,2196,2199,2203],{"className":2195},[629,891],[581,2197,1341],{"className":2198},[629,891],[581,2200],{"className":2201,"style":2202},[722,891],"margin-right:0.1952em;",[581,2204,2206],{"className":2205},[629,727,891],[581,2207,1346],{"className":2208},[629,891],[581,2210,2211,2214],{"style":1241},[581,2212],{"className":2213,"style":1232},[883],[581,2215],{"className":2216,"style":1249},[1248],[581,2218,2220,2223],{"style":2219},"top:-3.4461em;",[581,2221],{"className":2222,"style":1232},[883],[581,2224,2226],{"className":2225},[888,889,890,891],[581,2227,2229,2232,2238,2241,2244],{"className":2228},[629,891],[581,2230,821],{"className":2231},[629,891],[581,2233,2235],{"className":2234},[629,891],[581,2236,829],{"className":2237},[828,891],[581,2239,1415],{"className":2240},[629,891],[581,2242],{"className":2243,"style":2202},[722,891],[581,2245,2247],{"className":2246},[629,727,891],[581,2248,1346],{"className":2249},[629,891],[581,2251,1275],{"className":2252},[1274],[581,2254,2256],{"className":2255},[872],[581,2257,2260],{"className":2258,"style":2259},[876],"height:0.345em;",[581,2261],{},[581,2263],{"className":2264},[1288,1211],[581,2266],{"className":2267,"style":991},[722],[581,2269,1043],{"className":2270},[995],[581,2272],{"className":2273,"style":991},[722],[581,2275,2277,2280,2283,2289,2293,2296,2299],{"className":2276},[620],[581,2278],{"className":2279,"style":817},[624],[581,2281,821],{"className":2282},[629],[581,2284,2286],{"className":2285},[629],[581,2287,829],{"className":2288},[828],[581,2290,2292],{"className":2291},[629],"015",[581,2294],{"className":2295,"style":991},[722],[581,2297,1043],{"className":2298},[995],[581,2300],{"className":2301,"style":991},[722],[581,2303,2305,2308,2311,2317,2320,2323],{"className":2304},[620],[581,2306],{"className":2307,"style":1304},[624],[581,2309,695],{"className":2310},[629],[581,2312,2314],{"className":2313},[629],[581,2315,829],{"className":2316},[828],[581,2318,833],{"className":2319},[629],[581,2321],{"className":2322,"style":723},[722],[581,2324,1083],{"className":2325},[629],", ohne Meter.",{"title":2328,"searchDepth":2329,"depth":2329,"links":2330},"",2,[2331,2332,2333],{"id":562,"depth":2329,"text":563},{"id":945,"depth":2329,"text":946},{"id":2096,"depth":2329,"text":2097},[2335,2338,2341,2344,2347,2350,2353,2355],{"lhs":2336,"rhs":2337},"abs(u - x)\u002Fabs(x)","abs(u\u002Fx - 1)",{"lhs":2339,"rhs":2340},"round(abs(3.14 - pi), 5)","0.00159",{"lhs":2342,"rhs":2343},"round(abs(3.14 - pi)\u002Fpi*100, 3)","0.051",{"lhs":2345,"rhs":2346},"round(abs(2.03 - 2), 10)","0.03",{"lhs":2348,"rhs":2349},"0.03\u002F2*100","1.5",{"lhs":2351,"rhs":2352},"round(abs(15.3 - 15), 10)","0.3",{"lhs":2354,"rhs":1341},"0.3\u002F15*100",{"lhs":2356,"rhs":2357},"0.5*10^(-2)","0.005","x \\neq 0 \\text{ (für den relativen Fehler)}","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>x\u003C\u002Fmi>\u003Cmo mathvariant=\"normal\">≠\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">x \\neq 0\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:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan> \u003Cspan class=\"katex\">(für den relativen Fehler)\u003C\u002Fspan>",null,"md","rounding-error","\\Delta x = |\\tilde{x} - x| \\qquad \\delta = \\frac{\\Delta x}{|x|}","\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 mathvariant=\"normal\">Δ\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmover accent=\"true\">\u003Cmi>x\u003C\u002Fmi>\u003Cmo>~\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>−\u003C\u002Fmo>\u003Cmi>x\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmspace width=\"2em\"\u002F>\u003Cmi>δ\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmrow>\u003Cmi mathvariant=\"normal\">Δ\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmrow>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003Cmi mathvariant=\"normal\">∣\u003C\u002Fmi>\u003C\u002Fmrow>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\Delta x = |\\tilde{x} - x| \\qquad \\delta = \\frac{\\Delta x}{|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:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">Δ\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\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 katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6679em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.35em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2222em;\">\u003Cspan class=\"mord\">~\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\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:1em;vertical-align:-0.25em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:2em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0379em;\">δ\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:2.2963em;vertical-align:-0.936em;\">\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:1.3603em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">∣\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003Cspan class=\"mord\">∣\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\">Δ\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\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:0.936em;\">\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\u002Fabsoluter-und-relativer-fehler",[],[2371,2372,2373],"absolute-value","percentage-rate","scientific-notation",{"title":548,"description":2328},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fabsoluter-und-relativer-fehler","Der absolute Fehler ist der Abstand zum wahren Wert, der relative Fehler setzt ihn ins Verhältnis zum wahren Wert.",[2378,2379,2380,2381,2382],"fehler","rundung","messfehler","genauigkeit","näherungswert",[2384,2387,2391,2394],{"symbol":606,"meaning":2385,"symbolHtml":2386},"exakter (wahrer) Wert","\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":2388,"meaning":2389,"symbolHtml":2390},"\\tilde{x}","Näherungswert, z.B. ein gerundeter oder gemessener Wert","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmi>x\u003C\u002Fmi>\u003Cmo>~\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\tilde{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:0.6679em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.6679em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.35em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2222em;\">\u003Cspan class=\"mord\">~\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":611,"meaning":2392,"symbolHtml":2393},"absoluter Fehler, in derselben Einheit wie x","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi mathvariant=\"normal\">Δ\u003C\u002Fmi>\u003Cmi>x\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\Delta 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:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">Δ\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">x\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":657,"meaning":2395,"symbolHtml":2396},"relativer Fehler, ohne Einheit, oft in Prozent angegeben","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>δ\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\delta\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:0.6944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0379em;\">δ\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","A0t1UzrDHO3uhwsRX5qzWrKSojyZ7kB-KZ4WvTDalgE",[2399,2402,2405],{"stem":2400,"title":2401,"category":5},"de\u002Fformulas\u002Fmath\u002Falgebra\u002Fbetrag-einer-zahl","Betrag einer Zahl",{"stem":2403,"title":2404,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fprozentsatz","Prozentsatz",{"stem":2406,"title":2407,"category":65},"de\u002Fformulas\u002Fmath\u002Farithmetic\u002Fwissenschaftliche-schreibweise","Wissenschaftliche Schreibweise",1793824258678]