G8

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

Homework

Unit 1 · Lesson 4: Convert Repeating Decimals to

Fractions

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

Vocabulary Steps:

Rational Numbers: whole numbers, fractions,

and decimals represented as a ratio of two

integers; can be represented in fractional form:

where 푥푥푦푦 are integers and y ≠ zero.

1.5 =^32 = 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

1. Determine the repeating digits.


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.

Name: ___

Date: ___