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Copyright © Swun Math Grade 8 Unit 1 Lesson 4 C TE

Convert Repeating Decimals

to Fractions

Conceptual Lesson

Grade 8 · Unit 1 · Lesson 4
MC: 8 .NS. 1

Problem of the Day

Objective: I will convert a repeating decimal into a fraction.

Vocabulary Teacher Resources

Rational Numbers: whole numbers, fractions,

and decimals represented as a ratio; can be

represented in fractional form:

where 푥푥푦푦 are integers and y ≠ zero.

1.5 =

3

2 =^ ratio^

Irrational Numbers: the set of all numbers that

cannot be written as a ratio of two integers; it

cannot be written as a simple fraction because

the decimal is non-terminating and non-

repeating

0.101101110... , �^23 ,π,√ 10 ,√1.6,−√ 123

Repeating Decimal: a decimal number that has

digits that repeat indefinitely; the repeating digit

is marked with a bar notation

1

3

= 0. 3333 = 0. 3�

Coefficient: a number used to multiply a variable

7 m; 7 is the coefficient

Considerations:

Consider having students recall how multiplying a

decimal by multiples of ten affects the decimal. Use a

calculator to demonstrate the equivalency between

the fraction and the repeating decimal. Have students

work in pairs or groups to discuss/compare the

example problems and find the patterns.

Have students practice the steps with smaller

numbers if they are struggling with large patterns.

Steps:

1. Determine the repeating digit(s).


2. Write an equation where x = the repeating
   decimal.


3. Label this Equation #1.


4. Multiply both sides of the equation by the
   power of 10 equal to the number of repeating
   digits.


5. Label this Equation #2. Keep a set of the
   repeating digits to the right of the decimal.


6. Subtract Equation #1 from Equation #2.


7. Solve for x by dividing each side of the
   equation by the coefficient.


8. Simplify.

Application of MPs:

MP5: What tool can help you convert a repeating

decimal into a fraction?

A tool I can use to help convert a repeating

decimal into a fraction is ________________.

MP7: What pattern was used when converting a

repeating decimal into a fraction?

A pattern I used when converting a repeating

decimal into a fraction is _________________.

MPs

Applied MP

* Embedded MP

1 2 3 4 5 6 7 8

* ^ ^ *

Student Journal Pages

16 - 19