Decimal Expansions of Numbers

Description

In Topic B, students learn that to get the decimal expansion of a number, they must develop a deeper understanding of the long division algorithm learned in Grades 6 and 7. Students learn a procedure to get the approximate decimal expansion of. At this point, students learn that the definition of an irrational number is a number that is not equal to a rational number.

Defining irrational numbers as those that are not equal to rational numbers provides an important guidepost for students’ knowledge of numbers. Students learn that an irrational number is something quite different than other numbers they have studied before. They are infinite decimals that can only be expressed by a decimal approximation. Now that students know that irrational numbers can be approximated, they extend their knowledge of the number line gained in Grade 6 to include being able to position irrational numbers on a line diagram in their approximate locations.