# Understanding Rational Numbers

Student View (Opens in new window) # Lesson Overview

Students learn the definition of rational number, and they write rational numbers as ratios of integers and as repeating or terminating decimals.

# Key Concepts

Students have been working with rational numbers throughout this unit, but the term rational number is formally defined in this lesson. A rational number is a number that can be written in the form $\frac{p}{q},$ where p and q are integers. All the integers, fractions, decimals, and percents students have worked with so far in their math classes are rational numbers. Following are some rational numbers written as ratios of integers:

$36=\frac{36}{1}$

$-1.2=\frac{-12}{10}$

$5%=\frac{5}{100}$ $-\frac{1}{2}=\frac{-1}{2}$

Any rational number can also be written as a decimal that terminates or that repeats forever in a regular pattern. For example, $\frac{3}{5}$ = 0.6 and $\frac{7}{11}$ = 0.63636363… Repeating decimals are often written with a bar over the digits that repeat. For example, 0.63636363… can be written as $0.\overline{63}$.

There are numbers that are irrational. These numbers include π and the square root of any whole number that is not a perfect square, such as $\sqrt{2}$. The decimal form of an irrational number does not terminate, and the digits do not follow a repeating pattern. Students will study irrational numbers in Grade 8.

# Goals and Learning Objectives

• Understand the definition of rational number.
• Write rational numbers as ratios of integers.
• Write rational numbers as terminating or repeating decimals.

SWD: Students with disabilities may have difficulty working with decimals and fractions, especially moving between the two. If students demonstrate difficulty to the point of frustration, provide direct instruction on the basics for finding equivalent fractions and decimals.

ELL: Target and model key language and vocabulary. Specifically, focus on the term rational, as well as terms such as terminate. As you’re discussing the key points, write the words on the board or on large sheets of paper and explain/demonstrate what the words mean. Since these are important points that students will be using throughout the module, write them on large poster board so that students can use them as a reference. Have students record new terms, definitions, and examples in their Notebook.