Explore the intricacies of decimal numbers in this comprehensive 28-minute lecture from the MathFoundations series. Delve into the extension of the Hindu-Arabic system to include negative powers of 10, such as tenths and hundredths. Examine the representation of fractions in the decimal system, learn new notation, and understand the various components of a decimal number. Practice identifying decimals as fractions through examples and discover a systematic approach to converting decimals to fractions. This lecture aims to clarify common misconceptions about decimal numbers at various educational levels, from primary school to university and research mathematics.