Back To Course

6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will be able to convert any repeating decimal that you come across into a fraction. Learn how to write the two equations that are needed for the conversion.

If you go shopping at all, then you are very familiar with decimal numbers. **Decimal numbers** are our numbers with a decimal point. When you are shopping, you see decimal numbers all around you. Your favorite game might have a price tag of $24.99. That's a decimal number!

If you do cooking or baking, then you are familiar with fractions such as 1/3 and 1/4. As you know, fractions and decimal numbers are related to each other. To convert a fraction into a decimal, all we need to do is divide the fraction's numerator by its denominator. 1/4 turns into 0.25. That's a nice decimal that we can easily write out.

But what about 1/3? What kind of a decimal number does that turn into? Going ahead with our division, we get 0.3333â€¦. We get a decimal that keeps on repeating a series of numbers. We call this type of decimal number a **repeating decimal**.

In this case, the repeating series of numbers is 3. You recall that to convert a decimal into a fraction, you write the number after the decimal point in the numerator and you put a 1 in the denominator followed by zeroes. The number of zeroes you put in the denominator will equal the number of digits you have in the numerator. So, for the decimal 0.25, you would write it as 25/100. You can then simplify this fraction down to 1/4.

While you know how to convert a decimal number that ends into a fraction, you are unsure about repeating decimals. How do you go about converting these into fractions? The process is actually very different than what you are familiar with. But we will see that it's not all that difficult as long as you follow the same process each time. So, put your thinking cap on, for the rest of this lesson requires just a bit of brain muscle.

Let's try and convert the repeating decimal 0.3333â€¦ to see what we get. The process of converting repeating decimals requires writing two equations and then subtracting them to find the fraction. First, we will say that *x* equals 0.333â€¦ We will call this equation our defining equation.

*x* = 0.333â€¦

To find our first equation, we first note which numbers are being repeated. It is the number 3. So, we now need to figure out what to multiply our defining equation, *x* = 0.333â€¦, by so that our repeating numbers are on the left side of the decimal point. If we multiply the 0.333â€¦ by 10, then we will have moved the decimal point one space to the right and we will have our repeating number to the left of the decimal point. Because we are using our defining equation, we also need to multiply the left side of our equation by 10. We get 10*x* = 3.333... for our first equation.

To find our second equation, we again use our defining equation. This time, we need to manipulate it so that the repeating numbers are to the right of the decimal point. Looking at our defining equation, we see that our repeating numbers are already to the right of the decimal point, so we don't need to change anything. Our second equation is *x* = 0.333â€¦.

Now that we have our two equations, we now subtract them from each other. We get 10*x* - *x* = 3.333â€¦ - 0.333â€¦. See how we simply subtracted the two sides from each other on both sides of the equation? We can now go ahead and solve this equation for *x*. This will give us our fraction.

10*x* - *x* = 3.333â€¦ - 0.333â€¦

9*x* = 3

*x* = 3/9

*x* = 1/3

We solved our equation for *x* by first combining like terms and then performing operations that gave us our *x* by itself. We then simplified our answer to find that our converted decimal is a fraction of 1/3. And we are done!

Let's look at another example.

1.0242424â€¦

Looking at this decimal number, we see that it begins with a 1, the decimal point, a 0, and then it keeps repeating the 24. So our repeating number is 24. We first write a defining equation of *x* = 1.0242424â€¦.

To find our first equation, we manipulate our defining equation so that our repeating number is to the left of the decimal point. We want to move the decimal three spaces to the right so that the 24 is left of the decimal point. To do this, we need to multiply by 1,000. So our first equation is 1,000*x* = 1024.2424â€¦.

To find our second equation, we need to manipulate the defining equation so that the 24 is directly to the right of the decimal point. Looking at our decimal, we see that we have a 0 before the first 24. So, we need to move the decimal point one space to the right. We need to multiply by 10. Our second equation then is 10*x* = 10.2424â€¦.

Now, we can go ahead and subtract our two equations. We get 1000*x* - 10*x* = 1024.2424â€¦ - 10.2424â€¦. Solving for *x*, we get the following:

1000*x* - 10*x* = 1024.2424â€¦ - 10.2424â€¦

990*x* = 1014

*x* = 1014/990

*x* = 169/165

Our repeating decimal 1.02424â€¦ converts to the fraction 169/165. We are done!

Let's review what we've learned. **Decimal numbers** are our numbers with a decimal point. A **repeating decimal** is a decimal that keeps on repeating a series of numbers. To convert a repeating decimal to a fraction, we first write a defining equation where *x* equals the repeating decimal. We then manipulate this equation to get two equations that we subtract from each other to find our fraction.

The first equation results in our repeating numbers being on the left side of the decimal point. The second equation results in our repeating numbers being directly to the right of the decimal point. We multiply our defining equation by a corresponding amount, be it 10, 100, 1,000, etc. so that we get our desired result. We then subtract the second equation from the first and then solve for *x* to find our fraction.

Make sure that you can complete these goals once you've watched the lesson:

- Identify a repeating decimal
- Convert a repeating decimal into a fraction

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Login here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
3 in chapter 15 of the course:

Back To Course

6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

- Inequalities with Decimals 5:36
- Converting Decimals to Mixed Numbers 5:44
- Converting Repeating Decimals into Fractions 7:06
- Multiplying and Dividing Decimals: Examples & Word Problems 5:29
- How to Estimate with Decimals to Solve Math Problems 8:51
- Estimating Sums, Differences & Products of Decimals 5:53
- Solving Problems Using Decimal Numbers 6:57
- Estimation: One & Two Operation Problems with Positive Decimals 5:31
- Guess and Check: One & Two Operation Problems with Positive Decimals 6:47
- Look for a Pattern: One & Two Operation Problems with Positive Decimals 7:10
- Solving Multi-Step Inequalities with Decimals 8:01
- Maps with Decimal Distances 4:17
- How to Simplify Expressions Involving Decimals 5:04
- Go to 6th-8th Grade Math: Operations with Decimals

- Computer Science 109: Introduction to Programming
- Introduction to HTML & CSS
- Introduction to JavaScript
- Computer Science 332: Cybersecurity Policies and Management
- Introduction to SQL
- Early Civilizations & The Ancient Near East
- Fundamental Overview of World War I
- The Virginia Dynasty & Jacksonian America
- 1920's America and the Great Depression
- Building the United States After the American Revolution
- CEOE Test Cost
- PHR Exam Registration Information
- Claiming a Tax Deduction for Your Study.com Teacher Edition
- What is the PHR Exam?
- Anti-Bullying Survey Finds Teachers Lack the Support They Need
- What is the ASCP Exam?
- ASCPI vs ASCP

- Subtraction in Java: Method, Code & Examples
- Hydrogen Chloride vs. Hydrochloric Acid
- Extraction of Aluminum, Copper, Zinc & Iron
- Iroquois Culture, Traditions & Facts
- Noun Clauses Lesson Plan
- Adverb of Manner Lesson Plan
- Timeline Project Ideas for High School
- Quiz & Worksheet - Multi-Dimensional Arrays in C
- Quiz & Worksheet - What is a Diastereoisomer?
- Quiz & Worksheet - Mauryan Empire Art & Culture
- Quiz & Worksheet - What is a Convergent Sequence?
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- Algebra 2 Worksheets
- Cyberbullying Facts & Resources for Teachers

- Physics 101: Help and Review
- Principles of Microeconomics Syllabus Resource & Lesson Plans
- Criminal Justice 102: Introduction to Law Enforcement
- Remedial Earth Science
- Calculus Syllabus Resource & Lesson Plans
- Michigan Merit Exam - Math: Triangles & Trigonometry
- OAE Reading: Vocabulary Development
- Quiz & Worksheet - The Things They Carried Synopsis & Themes
- Quiz & Worksheet - Steps of Preliminary Investigation
- Quiz & Worksheet - Rise of the Abbasid Caliphate
- Quiz & Worksheet - Warren Court Cases & Decisions
- Quiz & Worksheet - Communicating Therapeutically in Nursing

- Implied Metaphor: Definition & Examples
- Newport-Mesa Unified School District v. State of California Department of Education
- 4th Grade Writing Prompts
- Using Reading Level Correlation Charts
- Dr. Seuss Bulletin Board Ideas
- Corporate Team Building Activity Ideas
- 7th Grade Summer Reading List
- Persuasive Writing Prompts: 4th Grade
- Math Word Walls: Ideas & Vocabulary
- How to Find Financial Aid for Teachers
- 9th Grade Reading List
- Using an Online Tutor

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject