How Many Significant Digits Do Java's `float` and `double` Data Types Actually Offer?

How to Determine the Precision of Floating and Double Data Types in Java

Introduction

When working with floating-point numbers in computer programming, understanding how many significant digits they can represent is crucial. In Java, the float and double data types are commonly used for floating-point computations, but their precision can be misleading.

Number of Binary Digits

As mentioned in the question, a float has 32 binary digits (bits), and a double has 64 binary digits. However, it's important to note that not all of these bits contribute to the precision of the number.

Significant Digits

In floating-point representation, significant digits refer to the digits that determine the precision of the number. For a float, 23 bits are dedicated to the mantissa, which represents the number's significant digits. This equates to approximately 7 decimal digits.

For a double, 52 bits are used for the mantissa, providing about 16 decimal digits of precision.

Location of the Decimal Point

The decimal point in floating-point numbers is not explicitly stored. Instead, it is implicitly determined by the exponent. This means that the bits used to represent the exponent don't directly contribute to the precision of the number.

Implicit Bit

Both float and double use the trick of assuming one bit in the mantissa is implicitly 1 for non-zero numbers. This effectively increases the precision by one bit.

Non-Exact Conversions

Since floating-point numbers are represented in binary, conversions to decimal numbers are often not exact. Consequently, numbers like 0.1 may not be stored precisely.

Conclusion

When it comes to storing precise monetary values or numbers that require high precision, consider using int, long, BigInteger or BigDecimal data types instead of float or double.

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