Repeating decimals – Grade 7 math lesson
Lesson 5 of 21 in the Grade 7 math course
US version. US grades, US spelling and dollars ($). · UK Maths Department
A complete 45-minute lesson for grade 7 (ages 12–13) that runs on this page – at school or at home. Every answer is graded right away, with a worked explanation.
- Time
- 45 minutes + 20 min homework
- Grade
- Grade 7 (ages 12–13)
- You need
- Paper, a pencil and this page
- Graded
- Instantly, with explanations
For parents: how to use this lesson
You don't need to know this topic yourself. The lesson explains each step on screen, one tidy step at a time. Every answer is graded straight away with a worked explanation, so you never have to grade anything.
- Read what your child will learn and the big ideas together.
- Press Start the lesson below and sit with your child for the teaching and the worked examples (about 19 minutes).
- Let them do the practice on their own. They choose Getting started, On track or Challenge – start on On track and move up after a few right in a row.
- Finish with the exit ticket and the talk question: “Which fractions give decimals that stop? Look at the denominators.”
- Later that day or the next day: the homework (20 minutes), then a practice test.
Watch out for
- Writing 1/3 as 0.3. Divide: 1 ÷ 3 = 0.333… – it keeps going.
- Multiplying by the wrong power of 10 for a two-digit repeat. Two repeating digits: multiply by 100.
Tip for home: Try dividing by 3, 7, 9 and 11 on a calculator and look for patterns.
What your child will learn
Learning goal: convert between fractions and decimals, including repeating decimals.
Success looks like
- I can change fractions to decimals.
- I can recognize recurring decimals.
- I can change a recurring decimal to a fraction.
Key words
- terminating decimal
- a decimal that stops
- repeating decimal
- a decimal that repeats forever
- numerator
- the top of a fraction
- denominator
- the bottom of a fraction
What to have ready
- Paper and a pencil
- This page on a computer, tablet or phone
- For the hands-on part: Use long division to change 1/7 to a decimal and spot the repeating pattern.
The big ideas (for the adult)
To change a fraction to a decimal, divide the numerator by the denominator. Some decimals stop; others repeat for ever.
A repeating decimal has a digit or block of digits that repeats: 1/3 = 0.333…, written with a bar over the 3.
To turn a recurring decimal into a fraction, let x be the decimal, multiply by 10 or 100 so the repeating parts line up, and subtract.
The lesson, step by step
| Part | Time | How it is checked |
|---|---|---|
| Starter: quick recall | 5 min | Graded by Classfern |
| Teaching input | 10 min | Not assessed, self-checked |
| Worked examples and guided practice | 9 min | Not assessed, graded by Classfern |
| Independent practice | 15 min | Graded by Classfern |
| Closure and exit ticket | 6 min | Graded by Classfern, self-checked |
Starter, "your turn", practice and exit ticket are graded by Classfern. Worked examples and teaching are not assessed. The hands-on task and the reflection are self-assessed. Explanations in talk are judged by the parent and not recorded.
The lesson
It runs here on the page. No sign-up and no names – progress is kept only in this browser.
Homework and practice at home
20 minutes: 10 practice questions, 3 multiple-choice questions and 2 to remember from earlier work, then a short reflection. New questions every time, all graded instantly.
More practice
More Grade 7 math lessons
- Ratios
- Percent
- Proportional relationships
- Operations with integers
- Evaluating expressions
- Simplifying expressions
- Expanding expressions
- Solving equations
- Inequalities
- Scale drawings and maps
- Angle relationships
- Area of triangles, parallelograms and trapezoids
- Circles: circumference and area
- Volume and surface area
- Cross sections of 3-D figures
- Probability
- Experimental probability
- Compound events
- Box plots and interquartile range
- Sampling and making inferences
Curriculum
Common Core State Standards 7.NS.A.2.d: “Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.”
Common Core State Standards 8.NS.A.1: “Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.”
Our lessons and questions are our own. They are not written or endorsed by any government department, testing agency or exam board.