G8

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

Homework

Unit 1 · Lesson 5: Convert Repeating Decimals to

Fractions

Example # 1

Directions: Convert the decimals into fractions.

Based on your experience with conversions, what can you predict about the answer?

0.222...

Solution:

• Using horizontal subtraction, create two equations:


• x = 0.222...


• 10x = 2.22...

Solve:

10x – x = 2.22... – 0.222...

92

99

x=

2

x= 9

Answer:^29

Possible answer: I can predict that the denominator will be 9 since the decimal has a one digit-repeating pattern.

Example # 2

The following decimal has a triple-digit repeating pattern. How does this affect the outcome of its fraction

form?

0.1243243...

Solution:

• Use vertical subtraction.


• x = 0.1243243...

Create two equations:

• 10x = 1.243243...


• 10000x – 10x = 1243.243243...

Solve:

• 10000x – 10x = 1243.243... – 1.243243...
  9990x = 1242
  x =^1242621
  9990 = 4995

Answer:

69

553

Possible answer: Since the decimal contains one digit plus a repeating pattern containing 3 digits, the unsimplified fraction

has a 4-digit denominator.