G8

Copyright © Swun Math Grade 8 Unit 1 Lesson 5 P TE

Homework

Unit 1 · Lesson 5: Convert Repeating Decimals to

Fractions

Objective: I will convert repeating decimals into fractions.

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 =

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

1. Find the repeating digits.


2. Write an equation where x = the
   repeating decimal. Label this
   Equation #1.


3. Multiply both sides of the equation
   by the power of 10 equal to the
   number of repeating digits. Label
   this Equation #2. Keep a set of the
   repeating digits to the right of the
   decimal.


4. Subtract Equation #1 from Equation
   #2.


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


6. Simplify.

Name: ___

Date: ___