Students convert fractions to decimals using long division (Activity 1 and practice problems) and identify decimals as terminating or repeating (student pages and quiz). Students use prime-factorization of denominators to predict whether a fraction's decimal will terminate or repeat (Fun Tip and activity pages). Students set repeating decimals equal to x, multiply by powers of 10, subtract, and solve to convert repeating decimals into fractions (Day 3 activities, worked examples, and practice problems).

Students practice converting between fractions and decimals (e.g., converting 7/8 to 0.875 and 0.45 to 9/20) and identify decimal types (the quiz asks whether 0.8333... is terminating or repeating). Students work with problems that contrast terminating and repeating decimal behavior and pick which fractions produce terminating decimals. Several activities require students to recognize and write decimal expansions for rational numbers.

Students are given explicit definitions distinguishing rational and irrational numbers and shown examples (π and √2) that illustrate non-terminating, non-repeating decimals. Multiple activities have students approximate irrational square roots on number lines and refine decimal estimates, reinforcing that irrationals have endless non-repeating decimal expansions. The Review Quiz and activity items require students to convert 2/9 to a decimal (identifying repeating behavior) and to convert the repeating decimal 0.̅3 into the fraction 1/3, directly practicing conversion of repeating decimals to rational numbers.

Students are asked to classify √2 and 1.75 as irrational or rational and to justify their answers, and they are also asked to determine that √50 is irrational. Students convert decimals to fractions in Phase 4 (0.375 → 3/8 and 0.875 → 7/8). The parent/answer key language and tasks explicitly link the vocabulary "irrational" and "rational" to students' classification and justification work.

Students convert between fractions and decimals (e.g., 3/8 → 0.375; 0.75 → 3/4; 4.75 → 19/4; 0.6 → 3/5) and identify decimals as terminating or repeating (questions about 0.3 and 0.6). Students classify square roots as rational or irrational (√50, √45) and approximate irrational roots to given precisions (√10 to the nearest tenth, √45 to two decimals). The Parent Plan and problems explicitly have students approximate irrational numbers and use rational approximations to locate them on a number line (e.g., several root-approximation tasks).

Students are asked to convert repeating decimals to fractions (e.g., "Convert 0.444... into a fraction" with answer 4/9) and to perform long division to decide whether a decimal terminates or repeats (e.g., convert 13/16 to a decimal and identify it as terminating). Students classify numbers as rational or irrational in a table (√4, √9, √10, 3, 0.6) and explain why √2 is irrational by noting its non-repeating, non-terminating decimal expansion. Several skills-review items ask students to compare decimal approximations (√5 ≈ 2.236 vs 2.2) and to identify repeating decimals (7/9 = 0.777...).

The Parent Plan explicitly states that students should "Know that numbers that are not rational are called irrational" and that rational decimal forms "terminate in 0s or eventually repeat," matching the language of the standard. Activity 4 has students classify a list of numbers as rational or irrational, approximate square roots (placing irrational roots between integers), and identify √2 as irrational, giving practice with irrational number recognition and approximation. Activity 2 and its linked video focus on fractions and decimals (including a "Repeating Decimals to Fractions" video) and include matching tasks that pair fractions with terminating or repeating decimal representations (for example pairing 2/9 with 0.6̅2), offering practice recognizing repeating decimal expansions and equivalences between fractions and decimals.

Students are asked to convert a fraction to a decimal (Problem 5: convert 7/16 to a decimal) and to convert a decimal to a fraction (Problem 6: convert 0.375 into a fraction). Students are asked to identify whether a decimal is terminating or repeating (Problem 7: Is 0.42 terminating or repeating?) and to classify a number as rational or irrational (Problem 13: Is 15/18 rational or irrational?). Students also estimate a nonperfect square root (Problem 12: estimate √30), which involves working with nonterminating square-root values.