What is the accuracy of float?

float precision can reach 6 to 9 decimal places. According to the IEEE754 standard, the number of significant digits that the float type can represent is approximately 6 to 9 digits. It should be noted that this is only the theoretical maximum precision. In actual use, due to the rounding error of floating point numbers, the precision of the float type is often lower. When performing floating-point number operations in a computer, precision loss may occur due to the precision limitations of floating-point numbers. In order to improve the precision of floating point numbers, you can use higher precision data types, such as double or long double.

# Operating system for this tutorial: Windows 10 system, Dell G3 computer.

float is a data type used to represent numerical values ​​with decimal points. In computers, the float type usually uses 32 bits to store, of which 1 bit is used to represent the sign bit, 8 bits are used to represent the exponent, and 23 bits are used to represent the mantissa. This means that the precision of the float type is limited and cannot represent all real numbers.

According to the IEEE 754 standard, the number of significant digits that the float type can represent is approximately 6 to 9 digits. This means that in the float type, the maximum precision that can be represented is between 6 and 9 decimal places. However, it should be noted that this is only the theoretical maximum precision. In actual use, due to the rounding error of floating point numbers, the precision of the float type is often lower.

When performing floating-point number operations on a computer, precision loss may occur due to the precision limitations of floating-point numbers. For example, when two very large or very small numbers are added, rounding errors may occur in the result. This is because in the representation of floating point numbers, the precision of the mantissa is limited. When the number of mantissa digits of two numbers exceeds the number of mantissa digits of the float type, precision loss will occur.

In order to improve the precision of floating point numbers, you can use higher precision data types, such as double or long double. The double type usually uses 64 bits for storage, which can represent more significant digits, thereby improving precision. However, even using the double type cannot completely solve the problem of floating point precision.

In short, the accuracy of the float type can reach about 6 to 9 decimal places, but in actual use, it may be affected by the rounding error of floating point numbers, and the accuracy will be reduced. To increase accuracy, consider using higher-precision data types.

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