Lesson objective: Understand that rational numbers have a decimal expansion that repeats either with 0s or a set of repeating digits. The decimal form of rational numbers has the same value and names the same point on the number line as the fraction form of the number.

Students bring prior knowledge of converting fractions to decimals from 7.NS.A.2b. This prior knowledge is extended to include repeating decimals as students place various fractions on a decimal number line. A conceptual challenge students may encounter is deciding how to locate a repeating decimal on a number line, or how to compare the value of finite and repeating decimals that use the same digits.

The concept is developed through work with a number line, which reinforces the idea that both fractions and their equivalent decimals live on the number line.

This work helps students deepen their understanding of numbers because they see that fractions, finite decimals, and repeating decimals are all representations of rational numbers, and can all be located on the number line.

Students engage in Mathematical Practice** **6** **(attend to precision) as they place each number (fractions that can be converted into both finite and repeating decimals) as accurately as possible on the number line.

**Key vocabulary:**

- repeating decimal
- finite decimal
- rational number