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cout",[1042,1154,1155],{"class":1052},".",[1042,1157,1158],{"class":1087},"precision",[1042,1160,1161],{"class":1052},"(",[1042,1163,1164],{"class":1066},"19",[1042,1166,1167],{"class":1052},");",[1042,1169,1171],{"class":1170},"sHwdD","  \u002F\u002F 这句话可以调整输出精度为 19 位有效数字；否则默认只输出 6 位\n",[1042,1173,1175,1178,1181,1184,1186,1189],{"class":1044,"line":1174},8,[1042,1176,1177],{"class":1103},"    cout ",[1042,1179,1180],{"class":1052},"\u003C\u003C",[1042,1182,1183],{"class":1103}," a ",[1042,1185,1180],{"class":1052},[1042,1187,1188],{"class":1103}," endl",[1042,1190,1078],{"class":1052},[1042,1192,1194,1196,1198,1201,1203,1205],{"class":1044,"line":1193},9,[1042,1195,1177],{"class":1103},[1042,1197,1180],{"class":1052},[1042,1199,1200],{"class":1103}," b ",[1042,1202,1180],{"class":1052},[1042,1204,1188],{"class":1103},[1042,1206,1078],{"class":1052},[1042,1208,1210,1212,1214,1217,1219,1221],{"class":1044,"line":1209},10,[1042,1211,1177],{"class":1103},[1042,1213,1180],{"class":1052},[1042,1215,1216],{"class":1103}," c ",[1042,1218,1180],{"class":1052},[1042,1220,1188],{"class":1103},[1042,1222,1078],{"class":1052},[1042,1224,1226],{"class":1044,"line":1225},11,[1042,1227,1228],{"class":1052},"}\n",[1230,1231,1232],"blockquote",{},[918,1233,1234,1235,1239],{},"这里用到了关于输出的一些调整设置。更多的用法可以在",[1236,1237,1238],"a",{"href":336},"输入输出章节","找到。",[918,1241,1242,1243,1245,1246,1249,1250,1253],{},"我们令 ",[966,1244,1236],{}," 、 ",[966,1247,1248],{},"b"," 和 ",[966,1251,1252],{},"c"," 三个变量初始化为小数点后 20 位的圆周率值，并输出它们。最终得到的可能结果却是：",[1033,1255,1258],{"className":1256},[1257],"language-plain",[966,1259,1260,1261,1265,1266,1269,1270],{},"3.141592",[1262,1263,1264],"u",{},"741012573242","\n3.141592653589793",[1262,1267,1268],{},"116","\n3.14159265358979323",[1262,1271,1272],{},"9",[918,1274,1275,1276,1279],{},"注意下划线部分的数值已经与我们期望的数值不符。这就是浮点型精度的体现，",[922,1277,1278],{},"超过对应精度的部分将无法准确存储","。之所以会有这个结果，是由于浮点型的存储方式所造成的。",[926,1281,1282],{"id":1282},"存储细节",[918,1284,1285,1286,1288],{},"浮点数的存储方式由许多种。一般地，单精度浮点类型 ",[966,1287,968],{}," 按照 IEEE 754 标准进行存储。",[918,1290,1291],{},[1292,1293],"img",{"alt":1294,"src":1295},"IEEE 754","https:\u002F\u002Fs1.ax1x.com\u002F2020\u002F07\u002F06\u002FUCR8yj.png",[918,1297,1298,1299,1301,1302,1306,1307,1314],{},"在这个标准里，4 字节的 ",[966,1300,968],{}," 内存被分成了 3 个部分：",[1303,1304,1305],"em",{},"符号位（Sign）","、",[1303,1308,1309,1310,1313],{},"指数位（Exponent）",[1303,1311,1312],{},"和","小数位（Fraction）","。它表示了形如：",[918,1316,1317],{},"$$(-1)^S\\times 2^E\\times M$$",[918,1319,1320],{},"这一记数法的数，其中：",[1322,1323,1324,1332,1335],"ul",{},[1325,1326,1327,1328,1331],"li",{},"S(Sign)：可取 0 或 1，指示这个数是否为负数。用",[1303,1329,1330],{},"符号位","存储该值。",[1325,1333,1334],{},"E(Exponent)：取 -127~127 的任意值。用指数位存储该值 $+127$ 的原码。",[1325,1336,1337],{},"M(Mantissa)：取 1.xxx 。用小数位存储 xxx 的二进制值。",[918,1339,1340],{},"关于浮点数的存储是一个较为复杂的知识，我不希望一开始就陷入这样的细节。因此感兴趣的读者可以参考 IEEE 754 标准进行学习，网上也有更多相关的资料可供参考。",[926,1342,1343],{"id":1343},"注意事项",[918,1345,1346],{},"正因为浮点数特殊的存储方式，我们避免将较大的数与较小的数相加。因为这样得到的结果有效数字可能超过精度限制。例如：",[1033,1348,1350],{"className":1035,"code":1349,"language":1037,"meta":1038,"style":1038},"#include \u003Ciostream>\nusing namespace std;\nint main() {\n    float a{0.00042};\n    float b{42000};\n    float c{a + b};\n    cout \u003C\u003C c \u003C\u003C endl;\n}\n",[966,1351,1352,1362,1372,1382,1395,1408,1427,1441],{"__ignoreMap":1038},[1042,1353,1354,1356,1358,1360],{"class":1044,"line":1045},[1042,1355,1049],{"class":1048},[1042,1357,1053],{"class":1052},[1042,1359,1057],{"class":1056},[1042,1361,1060],{"class":1052},[1042,1363,1364,1366,1368,1370],{"class":1044,"line":1063},[1042,1365,1067],{"class":1066},[1042,1367,1071],{"class":1070},[1042,1369,1075],{"class":1074},[1042,1371,1078],{"class":1052},[1042,1373,1374,1376,1378,1380],{"class":1044,"line":1081},[1042,1375,1084],{"class":1070},[1042,1377,1088],{"class":1087},[1042,1379,1091],{"class":1052},[1042,1381,1094],{"class":1052},[1042,1383,1384,1386,1388,1390,1393],{"class":1044,"line":1097},[1042,1385,1100],{"class":1070},[1042,1387,1104],{"class":1103},[1042,1389,1107],{"class":1052},[1042,1391,1392],{"class":1066},"0.00042",[1042,1394,1113],{"class":1052},[1042,1396,1397,1399,1401,1403,1406],{"class":1044,"line":1116},[1042,1398,1100],{"class":1070},[1042,1400,1122],{"class":1103},[1042,1402,1107],{"class":1052},[1042,1404,1405],{"class":1066},"42000",[1042,1407,1113],{"class":1052},[1042,1409,1410,1412,1414,1416,1420,1423,1425],{"class":1044,"line":1131},[1042,1411,1100],{"class":1070},[1042,1413,1140],{"class":1103},[1042,1415,1107],{"class":1052},[1042,1417,1419],{"class":1418},"swJcz","a ",[1042,1421,1422],{"class":1052},"+",[1042,1424,1122],{"class":1418},[1042,1426,1113],{"class":1052},[1042,1428,1429,1431,1433,1435,1437,1439],{"class":1044,"line":1149},[1042,1430,1177],{"class":1103},[1042,1432,1180],{"class":1052},[1042,1434,1216],{"class":1103},[1042,1436,1180],{"class":1052},[1042,1438,1188],{"class":1103},[1042,1440,1078],{"class":1052},[1042,1442,1443],{"class":1044,"line":1174},[1042,1444,1228],{"class":1052},[918,1446,1447,1448,1450],{},"以上代码编译运行的结果为 ",[966,1449,1405],{}," 。正如之前所说，较小的精度被丢失掉了。",[926,1452,1453],{"id":1453},"练习",[1455,1456,1457,1460],"ol",{},[1325,1458,1459],{},"编写一段程序，输入圆的半径（可能是小数），计算圆的面积的近似值。",[1325,1461,1462],{},"编写一段程序：先输入正整数 n ，然后输入 n 个数；输出这 n 个数的平均值。",[926,1464,1465],{"id":1465},"练习参考答案",[1033,1467,1469],{"className":1035,"code":1468,"language":1037,"meta":1038,"style":1038},"#include \u003Ciostream>\nusing namespace std;\nint main() {\n    double r{0}, s{0}, pi{3.1415926};\n    cin >> r;\n    s = r * r * pi;\n    cout \u003C\u003C s \u003C\u003C endl;\n}\n",[966,1470,1471,1481,1491,1501,1535,1547,1569,1584],{"__ignoreMap":1038},[1042,1472,1473,1475,1477,1479],{"class":1044,"line":1045},[1042,1474,1049],{"class":1048},[1042,1476,1053],{"class":1052},[1042,1478,1057],{"class":1056},[1042,1480,1060],{"class":1052},[1042,1482,1483,1485,1487,1489],{"class":1044,"line":1063},[1042,1484,1067],{"class":1066},[1042,1486,1071],{"class":1070},[1042,1488,1075],{"class":1074},[1042,1490,1078],{"class":1052},[1042,1492,1493,1495,1497,1499],{"class":1044,"line":1081},[1042,1494,1084],{"class":1070},[1042,1496,1088],{"class":1087},[1042,1498,1091],{"class":1052},[1042,1500,1094],{"class":1052},[1042,1502,1503,1505,1508,1510,1513,1516,1519,1521,1523,1525,1528,1530,1533],{"class":1044,"line":1097},[1042,1504,1119],{"class":1070},[1042,1506,1507],{"class":1103}," r",[1042,1509,1107],{"class":1052},[1042,1511,1512],{"class":1066},"0",[1042,1514,1515],{"class":1052},"},",[1042,1517,1518],{"class":1103}," s",[1042,1520,1107],{"class":1052},[1042,1522,1512],{"class":1066},[1042,1524,1515],{"class":1052},[1042,1526,1527],{"class":1103}," pi",[1042,1529,1107],{"class":1052},[1042,1531,1532],{"class":1066},"3.1415926",[1042,1534,1113],{"class":1052},[1042,1536,1537,1540,1543,1545],{"class":1044,"line":1116},[1042,1538,1539],{"class":1103},"    cin ",[1042,1541,1542],{"class":1052},">>",[1042,1544,1507],{"class":1103},[1042,1546,1078],{"class":1052},[1042,1548,1549,1552,1555,1558,1561,1563,1565,1567],{"class":1044,"line":1131},[1042,1550,1551],{"class":1103},"    s ",[1042,1553,1554],{"class":1052},"=",[1042,1556,1557],{"class":1103}," r ",[1042,1559,1560],{"class":1052},"*",[1042,1562,1557],{"class":1103},[1042,1564,1560],{"class":1052},[1042,1566,1527],{"class":1103},[1042,1568,1078],{"class":1052},[1042,1570,1571,1573,1575,1578,1580,1582],{"class":1044,"line":1149},[1042,1572,1177],{"class":1103},[1042,1574,1180],{"class":1052},[1042,1576,1577],{"class":1103}," s ",[1042,1579,1180],{"class":1052},[1042,1581,1188],{"class":1103},[1042,1583,1078],{"class":1052},[1042,1585,1586],{"class":1044,"line":1174},[1042,1587,1228],{"class":1052},[1033,1589,1591],{"className":1035,"code":1590,"language":1037,"meta":1038,"style":1038},"#include \u003Ciostream>\nusing namespace std;\nint main() {\n    int n{0};\n    double average{0.0}, sum{0.0}, x{0.0};\n    cin >> n;\n    int i{1}; \u002F\u002F 计数用\n    while (i \u003C= n) {\n        cin >> x;\n        sum = sum + x;\n        i = i + 1;\n    }\n    average = sum \u002F n;\n    cout \u003C\u003C average \u003C\u003C endl;\n}\n",[966,1592,1593,1603,1613,1623,1637,1669,1679,1697,1718,1729,1745,1762,1768,1785,1801],{"__ignoreMap":1038},[1042,1594,1595,1597,1599,1601],{"class":1044,"line":1045},[1042,1596,1049],{"class":1048},[1042,1598,1053],{"class":1052},[1042,1600,1057],{"class":1056},[1042,1602,1060],{"class":1052},[1042,1604,1605,1607,1609,1611],{"class":1044,"line":1063},[1042,1606,1067],{"class":1066},[1042,1608,1071],{"class":1070},[1042,1610,1075],{"class":1074},[1042,1612,1078],{"class":1052},[1042,1614,1615,1617,1619,1621],{"class":1044,"line":1081},[1042,1616,1084],{"class":1070},[1042,1618,1088],{"class":1087},[1042,1620,1091],{"class":1052},[1042,1622,1094],{"class":1052},[1042,1624,1625,1628,1631,1633,1635],{"class":1044,"line":1097},[1042,1626,1627],{"class":1070},"    int",[1042,1629,1630],{"class":1103}," n",[1042,1632,1107],{"class":1052},[1042,1634,1512],{"class":1066},[1042,1636,1113],{"class":1052},[1042,1638,1639,1641,1644,1646,1649,1651,1654,1656,1658,1660,1663,1665,1667],{"class":1044,"line":1116},[1042,1640,1119],{"class":1070},[1042,1642,1643],{"class":1103}," average",[1042,1645,1107],{"class":1052},[1042,1647,1648],{"class":1066},"0.0",[1042,1650,1515],{"class":1052},[1042,1652,1653],{"class":1103}," sum",[1042,1655,1107],{"class":1052},[1042,1657,1648],{"class":1066},[1042,1659,1515],{"class":1052},[1042,1661,1662],{"class":1103}," x",[1042,1664,1107],{"class":1052},[1042,1666,1648],{"class":1066},[1042,1668,1113],{"class":1052},[1042,1670,1671,1673,1675,1677],{"class":1044,"line":1131},[1042,1672,1539],{"class":1103},[1042,1674,1542],{"class":1052},[1042,1676,1630],{"class":1103},[1042,1678,1078],{"class":1052},[1042,1680,1681,1683,1686,1688,1691,1694],{"class":1044,"line":1149},[1042,1682,1627],{"class":1070},[1042,1684,1685],{"class":1103}," i",[1042,1687,1107],{"class":1052},[1042,1689,1690],{"class":1066},"1",[1042,1692,1693],{"class":1052},"};",[1042,1695,1696],{"class":1170}," \u002F\u002F 计数用\n",[1042,1698,1699,1702,1705,1708,1711,1713,1716],{"class":1044,"line":1174},[1042,1700,1701],{"class":1048},"    while",[1042,1703,1704],{"class":1052}," (",[1042,1706,1707],{"class":1103},"i ",[1042,1709,1710],{"class":1052},"\u003C=",[1042,1712,1630],{"class":1103},[1042,1714,1715],{"class":1052},")",[1042,1717,1094],{"class":1052},[1042,1719,1720,1723,1725,1727],{"class":1044,"line":1193},[1042,1721,1722],{"class":1418},"        cin ",[1042,1724,1542],{"class":1052},[1042,1726,1662],{"class":1418},[1042,1728,1078],{"class":1052},[1042,1730,1731,1734,1736,1739,1741,1743],{"class":1044,"line":1209},[1042,1732,1733],{"class":1418},"        sum ",[1042,1735,1554],{"class":1052},[1042,1737,1738],{"class":1418}," sum ",[1042,1740,1422],{"class":1052},[1042,1742,1662],{"class":1418},[1042,1744,1078],{"class":1052},[1042,1746,1747,1750,1752,1755,1757,1760],{"class":1044,"line":1225},[1042,1748,1749],{"class":1418},"        i ",[1042,1751,1554],{"class":1052},[1042,1753,1754],{"class":1418}," i ",[1042,1756,1422],{"class":1052},[1042,1758,1759],{"class":1066}," 1",[1042,1761,1078],{"class":1052},[1042,1763,1765],{"class":1044,"line":1764},12,[1042,1766,1767],{"class":1052},"    }\n",[1042,1769,1771,1774,1776,1778,1781,1783],{"class":1044,"line":1770},13,[1042,1772,1773],{"class":1103},"    average ",[1042,1775,1554],{"class":1052},[1042,1777,1738],{"class":1103},[1042,1779,1780],{"class":1052},"\u002F",[1042,1782,1630],{"class":1103},[1042,1784,1078],{"class":1052},[1042,1786,1788,1790,1792,1795,1797,1799],{"class":1044,"line":1787},14,[1042,1789,1177],{"class":1103},[1042,1791,1180],{"class":1052},[1042,1793,1794],{"class":1103}," average 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