G8

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

Input/Model

(Teacher Presents)

Directions: Convert the decimals into fractions.

1.222...

Solution:

• Determine the repeating pattern: 2


• x = 1. 2 �

Create two equations:

• Equation 1: x = 1. 2 �


• Equation 2: 10x = 12. 2 �

Solve:

• 10x ─ x = 12.2 ─ 1.2


• 9x = 11


• x =^119

0.1243243...

Solution:

Determine the repeating pattern: 243

x = 0.1 243 �����

Create two equations: * Remember the goal is to get the repeating numbers to the right of the decimal in both

equations, so choose powers of ten that will help you to do so.

• 10x = 1. 243 ����� (keep the repeating pattern right after the decimal)


• 10 000x = 1243. 243 �����

Solve:

• 10 000x – 10x = 1243.243... – 1.243243...
  999 0x = 1242
  x =^12429990 = 4995621 = 55369

Answer: 55369