About binary cannot express decimals accurately

In a previous project, I encountered the problem of inaccurate decimal calculation , As shown in the figure below

I reproduced it , Is roughly 1.05+1+1.05// 3.0999999999999996 Such , So I looked at how binary represents decimal .
To put it simply , That is, we can understand binary floating-point numbers by analogy with decimal floating-point numbers

Decimal system	1	2	3	.	5	8	9
Way of understanding	1*102	2*101	3*100	.	5*(1/101)	8*(1/102)	9*(1/10%3)
Binary system	1	1	1	.	1	0	1
Way of understanding	1*22	1*21	1*20	.	1*(1/21)	1*(1/22)	1*(1/23)

Therefore, binary can only accurately represent 0.5(1/2)、0.25(1/4)、0.125(1/8)、0.0625(1/16)、… This kind of decimal , Of course, like 1.0、2.0、3.0 This kind of decimal part is all 0 Of can also be accurately expressed , Other decimals cannot be expressed accurately , Therefore, the operation result may have a long tail , The reason why some of them will not have long tails , After referring to other materials, we can find that the language itself has been partially optimized , Too close numbers will be directly optimized into seemingly accurate values by language .

Decimal number	Binary system
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