G8

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

Challenge Problems

Directions: Solve.

1. Convert 0.999... into a fraction. Consider
   rounding. Also, remember the fractions
   with a base nine--how is this example
   different?

Solution:

Create two equations:

● 1x = 0.999...

● 10x = 9.99...

Solve:

10x – 1x = 9.99... - 0.999...

9x = 9

x =^99 = 1

Answer: x=1

2. What is the previous problem telling you?
   Can you think of another way of showing
   that this is true?

Solution:

(^1111)
333 ++=and 0.333... + 0.333... + 0.333... = 0.999...^
Since^1111
333 ++=
and 0.333... + 0.333... + 0.333... = 0.999
then, 1 = 0.999...
Answer: x = 0.999
Extension Activity

• MP1: Make sense of the problem and persevere in solving it.


• MP4: Apply mathematics in everyday life.
  Imagine you are a scientist working on a project in a lab, and you need to make a calculation
  using a repeating decimal. Provide a pro and a con for estimating the value of the repeating
  decimal to a specific place value versus converting to an equivalent fraction.