book icon
Lesson plan

Convert rational number to repeating decimal expansion


In this lesson, we’ll introduce the concept of converting a fraction to a repeating decimal for `8`th graders. We’ll start with a review of long division as well as a review of how to use the recurring bar to represent a repeating digit or repeating digits. Then students will get the chance to practice on their own.

Grade 8
Number System
Step-by-step help

ByteLearn gives students targeted feedback and hints based on their specific mistakes

Preview step-by-step-help

arrow icon


Students will be able to convert a fraction into a repeating decimal.


  • Teacher Slideshow
  • Online Practice

How to Teach Converting a Fraction to a Repeating Decimal

Bell Ringer

Start students off with a review of long division. They’ll likely need some support, as it’s possible they haven’t thought about long division in a few years! I usually let my students work with a partner, and consult other groups if they’re stuck. Display slide `1` for students to start with.

edit icon

Copy these Google Slides for free

Notice how I started students off with the division sentence, but also set up the long division for them! We want to give them a little bit of a hint as this is a much older topic we’re reviewing. 

Review as a class

When students are finished with the problem, ask for volunteers to see if someone wants to show their work on the board and explain their thinking. You can answer any questions students may have throughout. You can then rewrite the division sentence as `258/3` to show students the division could have been written as a fraction. This will help us eventually tie the fractions into the lesson.

Introduce repeating decimals

Remind the class that we can use long division to convert fractions into decimals. Specifically, we’ll focus on repeating decimals. Ask students how we represent repeating decimals. For example, if we write the decimal equivalent of `1/3`, how would we show that as a decimal? Bringing up a common fraction like this will allow students to start thinking about how they would write the decimal expansion.

Writing a decimal expansion

Then, display slide `3` on the board. 

Have students work together or work on these as a class! You’ll want to talk specifically about the recurring bar and how that shows us which digits are repeated. Introducing writing a fraction as a repeating decimal this way allows us to review the prerequisite skills rather than jumping right into new content. 

Converting a fraction to a repeating decimal with long division

The slideshow contains `6` sample problems to do with the class. Start the long division for the first problem with the class. Once you see the remainder repeating, you can point it out to the class. It’s likely one of the students will point it out as well! 

You can note that we are starting to see the digits in the quotient repeating. Because of these reasons, we can now write the fraction as a repeating decimal! Write the answer with a recurring bar.

More examples as a class

You can go through the rest of the examples with the whole class. Depending on your group of students, you may want to have them try some problems on their own, then you can go over them as a class. 

Converting Fractions to Repeating Decimals Practice

Now that you’ve practiced strategies for writing a fraction as a repeating decimal as a class, it’s time for students to practice on their own! Try assigning the ByteLearn practice below to your classes! As students work on their online practice, they receive immediate feedback on their answers and step-by-step help if they need it!

notepad icon
Converting Fractions to Repeating Decimals Practice
Problem 1 of 4
<p>Write a decimal equivalent to `5/6`.</br><highlight data-color="#666" data-style="italic">Use a recurring bar if needed.</highlight></p>

View this practice

arrow icon