Pick the correct statements on the 64-bit machine representation of numbers. The relative error in any elementary arithmetic operation is bounded above by machine precision.
Most of the decimal numbers are concentrated around zero.
Division by small numbers in an iterative process is a potential source of instability.
There are as many numbers between 1 and 2 as there are between 3 and 4.
Machine precision epsilon is the smallest decimal number that could be represented on the computer.

Floating-point arithmetic is considered an esoteric subject by many people. This is rather surprising because floating-point is ubiquitous in computer systems. Almost every language has a floating-point datatype; computers from PCs to supercomputers have floating-point accelerators; most compilers will be called upon to compile floating-point algorithms from time to time; and virtually every operating system must respond to floating-point exceptions such as overflow. This paper presents a tutorial on those aspects of floating-point that have a direct impact on designers of computer systems. It begins with background on floating-point representation and rounding error, continues with a discussion of the IEEE floating-point standard, and concludes with numerous examples of how computer builders can better support floating-point.

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