We live in a world of floating-point numbers, and we make frequent use of floating-point numbers when working with computers. In this chapter, we dive deeply into how floating-point numbers are represented in a computer. We briefly review the distinction between real numbers and floating-point numbers. Then comes a brief historical look at the development of floating-point numbers. After this, we compare two popular floating-point representations and then focus exclusively on the IEEE 754 standard. For IEEE 754, we consider representation, rounding, arithmetic, exception handling, and hardware implementations. We conclude the chapter with some comments about binary-coded decimal floating-point numbers.