How Many Decimal Digits of Precision Do Java's `float` and `double` Data Types Offer?

Understanding the Binary Precision of Floating-Point Types in Java

The binary precision of floating-point data types, such as float and double, determines the number of significant digits that can be represented accurately.

float:

A float data type consists of 32 binary digits (bits) allocated as follows:

• 23 bits for the mantissa (significand), which represents the actual value
• 8 bits for the exponent, which controls the position of the decimal point
• 1 bit for the sign

Therefore, a float has approximately 7 decimal digits of precision.

double:

A double data type has 64 binary digits (bits) distributed as follows:

• 52 bits for the mantissa, providing up to 16 decimal digits of precision
• 11 bits for the exponent
• 1 bit for the sign

Decimal Equivalents and Precision

While the mantissa and exponent are stored in binary, the actual numbers represented by floating-point types are expressed in decimal. However, the conversion from binary to decimal is not always exact. Consequently, some decimal numbers cannot be stored precisely using floats or doubles.

Exceptions and Considerations:

Certain values, such as 0.5, 0.25, 0.75, and 0.125, can be stored exactly in binary and, therefore, have exact decimal equivalents. However, values like 0.1 cannot be represented exactly due to the limited precision of the mantissa.

In cases where precise decimal representation is essential, such as when dealing with monetary values, it is recommended to use data types like int, long, BigInteger, or BigDecimal instead of floats or doubles.

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