What is the range of representation of floating point numbers?

The representation range of floating-point numbers: 1. For single-precision floating-point numbers, the representation range is approximately ±3.4 × 10^38, which can also be expressed as ±3.4E 38 in scientific notation; 2. For double-precision floating-point numbers Floating point numbers, which represent a wider range, are approximately ±1.8 × 10^308, or ±1.8E 308 in scientific notation.

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

The representation range of floating point numbers in the computer depends on the floating point number format used. The most common floating point number format is the IEEE 754 standard, which defines two floating point number representations: single precision (32 bits) and double precision (64 bits).

• For single-precision floating point numbers (32 bits), the representation range is approximately ±3.4 × 10^38, which can also be expressed in scientific notation as ±3.4E 38. Single-precision floating point numbers can represent numbers from a minimum value close to zero to a maximum value close to positive infinity.

• For double-precision floating point numbers (64 bits), the representation range is wider, approximately ±1.8 × 10^308, or ±1.8E 308 in scientific notation. Double-precision floating-point numbers have higher precision and a larger representation range than single-precision floating-point numbers, so they are widely used in many applications.

It should be noted that the representation range of floating point numbers is limited and there are representation errors. Rounding errors and loss of precision may occur when performing calculations over very large or small numerical ranges. To avoid these problems, consider using scientific notation or other numerical processing techniques for particularly large or small values.

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