Repeating decimals

Learning Objectives Identify a repeating decimal. Distinguish between terminating and repeating decimals. Use bar notation to represent repeating decimals. Explain what makes a decimal a 'repeating decimal'. Convert simple fractions into their repeating decimal form using long division. Recognize that some fractions result in repeating decimals when divided. Have you ever tried to share 1 cookie among 3 friends perfectly, or divided numbers and the answer just keeps going and going? 🤯 In this lesson, you'll discover special decimals called 'repeating decimals' – numbers that never end but follow a pattern! We'll learn how to spot them, write them, and understand why they happen, helping you represent numbers more accurately. Real-World Applic...

TermDefinitionExample DecimalA number that uses a decimal point to show parts of a whole, like 0.5 or 3.25.0.75 (three-quarters), 1.2 (one and two-tenths) Terminating DecimalA decimal that ends or stops after a certain number of digits, like 0.5 or 0.25.1/2 = 0.5, 3/4 = 0.75 Repeating DecimalA decimal that has one or more digits that repeat infinitely (forever) in a pattern, like 0.333... or 0.141414...1/3 = 0.333..., 2/11 = 0.181818... RepetendThe digit or group of digits that repeat in a repeating decimal.In 0.333..., the repetend is '3'. In 0.181818..., the repetend is '18'. Bar Notation (Vinculum)A special way to write repeating decimals by placing a horizontal bar over the repetend to show which digits repeat.Instead of 0.333..., we write $0.\overline{3}$. Instead...

Identifying Repeating Decimals through Division When converting a fraction $\frac{a}{b}$ to a decimal using long division, if you encounter a remainder that you've had before, the decimal will begin to repeat. This rule helps you know when to stop dividing and recognize the repeating pattern. The digits between the first occurrence of that remainder and its repetition form the repetend. Using Bar Notation for Repeating Decimals To write a repeating decimal, identify the repetend (the repeating digit or group of digits) and place a bar (vinculum) over ONLY those repeating digits. For example, $0.121212... = 0.\overline{12}$. This notation is a shorthand to show that the pattern continues forever without having to write out many digits. It ensures accuracy and clarity....