Data structure-about PHP floating point accuracy problem

PHP manual says:

A rational number that can be accurately represented in decimal, such as 0.1 or 0.7, cannot be converted to a binary format without losing a little bit of precision, regardless of how many of the mantissa can be accurately represented by the binary used internally.

// example1$float = (0.1 + 0.7) * 10;echo (integer) $float;            // 7echo floor($float);               // 7// example2echo (integer) (1.5+1.5);         // 3echo floor(1.5+1.5);              // 3// example3echo (integer) (0.5*10);          // 5echo floor(0.5*10);               // 5

Why in Example 2 and Example 3, floating-point numbers 加 and 乘 operations can preserve precision?

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PHP manual says:

A rational number that can be accurately represented in decimal, such as 0.1 or 0.7, cannot be converted to a binary format without losing a little bit of precision, regardless of how many of the mantissa can be accurately represented by the binary used internally.

// example1$float = (0.1 + 0.7) * 10;echo (integer) $float;            // 7echo floor($float);               // 7// example2echo (integer) (1.5+1.5);         // 3echo floor(1.5+1.5);              // 3// example3echo (integer) (0.5*10);          // 5echo floor(0.5*10);               // 5

Why in Example 2 and Example 3, floating-point numbers 加 and 乘 operations can preserve precision?

It's time to present my blog again:

• Code Puzzle (iv)-floating point (from surprise to thinking)
• Code Puzzle (v)-floating point number (who stole your accuracy?) ）

0.1 + 0.7The result is0.7999999999999999

0.51.5you can use floating-point numbers for precise representations.

0.1The binary:

符号位 0 指数 01111011 （-4）位数 1.10011001100110011001101 （1.60000002384185791015625）

Put this number back in decimal:0.10000000149011612

0.7The binary:

符号位 0 指数 01111110  (-1)位数 1.01100110011001100110011 (1.39999997615814208984375)

Put this number back in decimal:0.699999988079071

