G8

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

Homework

Unit 1 · Lesson 4: Convert Repeating Decimals to

Fractions

Examples

Directions: Convert the decimal into a fraction.

0. 4 � 0. 2 �

Solution:

Create two equations:

• Equation #1
  o x=0.4 (single digit pattern).


• Determine the number of repeating digits (1) and
  multiply by that power of 10.


• Equations #2
  o 10 x=4.4(multiply by 10 it is a single digit
  pattern).


• Subtract the first equation from the second.


• 10 xx−= −4.4 0.4
  94 x=


• Answer: x=^49

Solution:

x = 0. 2 �

Create two equations:

• Equation #1
  o x = 2. 2 �


• Equation #2
  o 10x = 2.2...

Solve:

10x – x = 2.2... – 0.2...

92

99

x=

2

x= 9

Answer: x=^2

9