Explore the precise definition and visualization of decimal numbers in this 44-minute mathematics lecture. Learn how decimal numbers are a special type of rational number, expressed as a/b where a and b are integers and b is a power of ten. Discover the extension of Hindu-Arabic notation for integers to include decimal forms with digits to the right of the decimal point. Understand the concept of successive magnifications on the number line to visualize decimal numbers. Delve into topics such as the relationship between rational and decimal numbers, creating decimal forms, arithmetic operations with decimals, and examples of decimal multiplication using rational numbers. This video is part of the MathFoundations series, which aims to establish solid mathematical foundations while addressing logical challenges in modern pure mathematics.