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关于二进制无法精确表示小数
在之前做过的一个项目中遇到了小数计算不精确的问题，如下图所示
我重现了一下，大致是1.05+1+1.05// 3.0999999999999996这种的，于是看了下二进制是如何表示小数的。
简单点讲的话，就是可以类比十进制的浮点数来理解二进制的浮点数十进制 1 2 3 . 5 8 9 理解方式 1*102 2*101 3*100 . 5*(1/101) 8*(1/102) 9*(1/10%3) 二进制 1 1 1 . 1 0 1 理解方式 1*22 1*21 1*20 . 1*(1/21) 1*(1/22) 1*(1/23) 因此二进制只能精确表示
0.5(1/2)、0.25(1/4)、0.125(1/8)、0.0625(1/16)、…这种的小数，当然了像1.0、2.0、3.0这种的小数部分全为0的也是可以精确表示的，其他的小数均无法精确表示，所以运算结果也就可能会出现长尾，之所以有一部分不会出现长尾，参考了其他资料后可以发现是语言本身做了部分优化，过分接近的数字会被语言直接优化成看似精确的值。十进制小数 二进制 0.1 0.0001100110011001100110011001100110011001100110011001101 0.2 0.001100110011001100110011001100110011001100110011001101 0.3 0.010011001100110011001100110011001100110011001100110011 0.4 0.01100110011001100110011001100110011001100110011001101 0.5 0.1 0.6 0.10011001100110011001100110011001100110011001100110011 0.7 0.1011001100110011001100110011001100110011001100110011 0.8 0.1100110011001100110011001100110011001100110011001101 0.9 0.11100110011001100110011001100110011001100110011001101 0.10 0.0001100110011001100110011001100110011001100110011001101 0.11 0.00011100001010001111010111000010100011110101110000101001 0.12 0.00011110101110000101000111101011100001010001111010111 0.13 0.00100001010001111010111000010100011110101110000101001 0.14 0.00100011110101110000101000111101011100001010001111011 0.15 0.0010011001100110011001100110011001100110011001100110011 0.16 0.0010100011110101110000101000111101011100001010001111011 0.17 0.0010101110000101000111101011100001010001111010111000011 0.18 0.001011100001010001111010111000010100011110101110000101 0.19 0.001100001010001111010111000010100011110101110000101001 0.20 0.001100110011001100110011001100110011001100110011001101 0.21 0.0011010111000010100011110101110000101000111101011100001 0.22 0.0011100001010001111010111000010100011110101110000101001 0.23 0.0011101011100001010001111010111000010100011110101110001 0.24 0.0011110101110000101000111101011100001010001111010111 0.25 0.01 0.26 0.0100001010001111010111000010100011110101110000101001 0.27 0.010001010001111010111000010100011110101110000101001 0.28 0.0100011110101110000101000111101011100001010001111011 0.29 0.010010100011110101110000101000111101011100001010001111 0.30 0.010011001100110011001100110011001100110011001100110011 0.31 0.010011110101110000101000111101011100001010001111010111 0.32 0.010100011110101110000101000111101011100001010001111011 0.33 0.010101000111101011100001010001111010111000010100011111 0.34 0.010101110000101000111101011100001010001111010111000011 0.35 0.01011001100110011001100110011001100110011001100110011 0.36 0.01011100001010001111010111000010100011110101110000101 0.37 0.01011110101110000101000111101011100001010001111010111 0.38 0.01100001010001111010111000010100011110101110000101001 0.39 0.01100011110101110000101000111101011100001010001111011 0.40 0.01100110011001100110011001100110011001100110011001101 0.41 0.011010001111010111000010100011110101110000101000111101 0.42 0.011010111000010100011110101110000101000111101011100001 0.43 0.011011100001010001111010111000010100011110101110000101 0.44 0.011100001010001111010111000010100011110101110000101001 0.45 0.011100110011001100110011001100110011001100110011001101 0.46 0.011101011100001010001111010111000010100011110101110001 0.47 0.0111100001010001111010111000010100011110101110000101 0.48 0.011110101110000101000111101011100001010001111010111 0.49 0.0111110101110000101000111101011100001010001111010111 0.50 0.1 0.51 0.1000001010001111010111000010100011110101110000101001 0.52 0.100001010001111010111000010100011110101110000101001 0.53 0.1000011110101110000101000111101011100001010001111011 0.54 0.10001010001111010111000010100011110101110000101001 0.55 0.1000110011001100110011001100110011001100110011001101 0.56 0.100011110101110000101000111101011100001010001111011 0.57 0.10010001111010111000010100011110101110000101000111101 0.58 0.10010100011110101110000101000111101011100001010001111 0.59 0.10010111000010100011110101110000101000111101011100001 0.60 0.10011001100110011001100110011001100110011001100110011 0.61 0.10011100001010001111010111000010100011110101110000101 0.62 0.10011110101110000101000111101011100001010001111010111 0.63 0.10100001010001111010111000010100011110101110000101001 0.64 0.10100011110101110000101000111101011100001010001111011 0.65 0.10100110011001100110011001100110011001100110011001101 0.66 0.10101000111101011100001010001111010111000010100011111 0.67 0.10101011100001010001111010111000010100011110101110001 0.68 0.10101110000101000111101011100001010001111010111000011 0.69 0.101100001010001111010111000010100011110101110000101 0.70 0.1011001100110011001100110011001100110011001100110011 0.71 0.10110101110000101000111101011100001010001111010111 0.72 0.1011100001010001111010111000010100011110101110000101 0.73 0.101110101110000101000111101011100001010001111010111 0.74 0.1011110101110000101000111101011100001010001111010111 0.75 0.11 0.76 0.1100001010001111010111000010100011110101110000101001 0.77 0.110001010001111010111000010100011110101110000101001 0.78 0.1100011110101110000101000111101011100001010001111011 0.79 0.11001010001111010111000010100011110101110000101001 0.80 0.1100110011001100110011001100110011001100110011001101 0.81 0.110011110101110000101000111101011100001010001111011 0.82 0.11010001111010111000010100011110101110000101000111101 0.83 0.11010100011110101110000101000111101011100001010001111 0.84 0.11010111000010100011110101110000101000111101011100001 0.85 0.11011001100110011001100110011001100110011001100110011 0.86 0.11011100001010001111010111000010100011110101110000101 0.87 0.11011110101110000101000111101011100001010001111010111 0.88 0.11100001010001111010111000010100011110101110000101001 0.89 0.11100011110101110000101000111101011100001010001111011 0.90 0.11100110011001100110011001100110011001100110011001101 0.91 0.11101000111101011100001010001111010111000010100011111 0.92 0.11101011100001010001111010111000010100011110101110001 0.93 0.11101110000101000111101011100001010001111010111000011 0.94 0.111100001010001111010111000010100011110101110000101 0.95 0.1111001100110011001100110011001100110011001100110011 0.96 0.11110101110000101000111101011100001010001111010111 0.97 0.1111100001010001111010111000010100011110101110000101 0.98 0.111110101110000101000111101011100001010001111010111 0.99 0.1111110101110000101000111101011100001010001111010111 -
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- 原文地址：https://blog.csdn.net/zidieq/article/details/125513241