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Terminating or Repeating Decimals

Seventh graders divide to turn fractions into decimals and discover that some stop cleanly while others repeat a digit pattern forever, then sort each fraction as terminating or repeating.

Grade 7Terminating or Repeating Decimals30 minutes1 class periodPlay-BasedExplicit teaching4 StandardsCommon Core
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Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Turn a fraction into a decimal.
  • ✓Tell terminating from repeating.
  • ✓Use bar notation.
  • ✓Sort each fraction.
Essential Question

Divide 1 by 4 and the decimal ends; divide 1 by 3 and it repeats forever. What makes a fraction's decimal terminate or repeat?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Sort the Fractions · Interactive

Sort the Fractions

Project this and sort each fraction into terminating or repeating — tap a fraction, then tap which kind of decimal it makes.

🔢 Sort each fraction: terminating or repeating decimal?Try it
⏹️ Terminating
🔁 Repeating
Tap a fraction, then tap whether its decimal terminates (ends) or repeats forever.
The Lesson · Play-Based Learning (Gather · Explore · Play · Reflect)

30 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Hook — Does It Ever Stop?

5 min

Divide 1 by 4 and you get 0.25, which ends. Divide 1 by 3 and you get 0.333..., which never stops. Why do some fractions end as decimals and others repeat forever?

👩‍🏫 Teacher Moves

  • Show 1/4 and 1/3 as decimals.
  • Ask what is different.
  • Set the goal.

🎒 Student Actions

  • Think.
  • Share.
  • Get ready.
2

Use — Sort the Fractions

12 min

Students sort fractions into terminating and repeating.

👩‍🏫 Teacher Moves

  • Send students to Sort the Fractions.
  • Drop each fraction.
  • Explain each choice.

🎒 Student Actions

  • Sort.
  • Say.
  • Explain.
3

Modify — Divide to Check

13 min

Students convert a fraction to decide.

👩‍🏫 Teacher Moves

  • Pick a fraction.
  • Divide to get the decimal.
  • Say terminating or repeating.

🎒 Student Actions

  • Pick.
  • Divide.
  • Say.
4

Create — My Decimal Chart

15 min

Students record conversions.

👩‍🏫 Teacher Moves

  • List four fractions.
  • Write each as a decimal.
  • Label each terminating or repeating.

🎒 Student Actions

  • List.
  • Write.
  • Label.
5

Reflect — Ending or Forever

5 min

Students reflect on decimal forms.

👩‍🏫 Teacher Moves

  • What makes a decimal terminating?
  • How do you write a repeating decimal?
  • Complete the exit ticket.

🎒 Student Actions

  • Say it.
  • Say it.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics (Grade 7).

CCSS
7.NS.A.2.D

Convert a rational number to a decimal using long division; know the decimal form terminates or eventually repeats.

CCSS
7.NS.A.2

Apply and extend previous understandings of multiplication and division to rational numbers.

CCSS
8.NS.A.1

Understand that rational numbers have decimal expansions that terminate or repeat.

CCSS
MP.8

Look for and express regularity in repeated reasoning.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Fraction = decimal cards.
  • Sentence frame: “___ is ___ because its decimal ___ .”
  • Sort two fractions at a time.

Support & Access

IEP / 504
  • Start with 1/2 and 1/3.
  • Divide one fraction together.
  • Sort all terminating ones first.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Predict from the denominator before dividing.
  • Add fractions with longer repeating blocks.
  • Explain why denominators of 2s and 5s terminate.
Materials

What to gather

  • 📽️Projector / board
  • 🔢Fraction = decimal cards
  • 💻Sort the Fractions
  • 🧮A calculator to check
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

rational numbera number that can be written as a fraction of two integersdecimala number written with a decimal point, like 0.75terminating decimala decimal that ends after a set number of digitsrepeating decimala decimal with a digit or group that repeats foreverlong divisiondividing the numerator by the denominator to get a decimalbar notationa bar drawn over the digits that repeat, like 0.3 with a barnumeratorthe top number of a fractiondenominatorthe bottom number of a fraction
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
What makes a decimal terminating?
It ends after a set number of digits, like 0.25 or 0.875, with nothing repeating.
QUESTION 2
How do you write a repeating decimal like 0.333...?
Write the repeating digit with a bar over it (0.3 with a bar), or show the pattern with an ellipsis.
QUESTION 3
Is 2/3 terminating or repeating?
Repeating: 2 divided by 3 is 0.666..., which goes on forever.

Create: my decimal chart.

Have students list four fractions, write each as a decimal, and label it terminating or repeating, so the two kinds become easy to tell apart. A printable terminating-and-repeating-decimals worksheet is in the Mathematics library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Terminating or Repeating DecimalsFlip
Card 1
Term
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Meaning
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Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Terminating or Repeating DecimalsQuiz
Score: 0
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Question 1
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Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Terminating or Repeating DecimalsPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: bar notation, decimal, denominator, long division, numerator, rational number, repeating decimal, terminating decimal
  1. a decimal with a digit or group that repeats forever
  2. dividing the numerator by the denominator to get a decimal
  3. the top number of a fraction
  4. the bottom number of a fraction
  5. a decimal that ends after a set number of digits
  6. a bar drawn over the digits that repeat, like 0.3 with a bar
  7. a number that can be written as a fraction of two integers
  8. a number written with a decimal point, like 0.75

Part B · Show what you learned

  1. What makes a decimal terminating?
  2. How do you write a repeating decimal like 0.333...?
  3. Is 2/3 terminating or repeating?
Answer key — Part A: 1) repeating decimal · 2) long division · 3) numerator · 4) denominator · 5) terminating decimal · 6) bar notation · 7) rational number · 8) decimal
Part B: 1) It ends after a set number of digits, like 0.25 or 0.875, with nothing repeating. 2) Write the repeating digit with a bar over it (0.3 with a bar), or show the pattern with an ellipsis. 3) Repeating: 2 divided by 3 is 0.666..., which goes on forever.