1. Writing Decimals as Fractions

2. What is the fraction representation of each decimal?
0.3
= 3/10
0.27
= 27/100
= 493/1000
0.493

3. REMINDER!! ALWAYS WRITE FRACTIONS IN SIMPLEST FORM. Example:
0.45 = 45/100 = 9/20
2.6 = 2 6/10 = 2 3/5

4. 0.3333….
What is the fraction representation of this decimal?

5. …..
How could you write this decimal as a fraction?

6. 45/100 = 0.45 Make the denominator a bit greater. 45/101 = 0.44554455…
45/100 = 0.45
Making the denominator greater does what to a fraction?
It makes the fraction smaller.
Make the denominator a bit greater.
45/101 = …
You will discover that the fraction is even less.

7. Complete “Follow Up” problems 5.3
Today’s problems will involve looking for
patterns to help write repeating decimals
as fractions.
Assignment:
Complete handout 5.3
Class discussion
Complete “Follow Up” problems 5.3

8. SUMMARY
What is the decimal representation for these fractions?
19/9
20/9
= …
= …

9. What is the decimal representation for these fractions?
50/99
100/99 … = = …

10. What fraction is equivalent to 4.111111……
Answers: /9 or 37/9
35/99

11. Can you predict the decimal representations for fractions with denominators of 999 and 9999?
If there are 3 digits repeating the denominator will be 3 nines.
If there are 4 digits repeating the denominator will be 4 nines.

12. Exploration Another method to change repeating decimals to fractions.
Change … to a fraction
Call the unknown fraction N.
N = …..
Multiply both sides of the equation by 100.
100N = …
Subtract the first equation from the second:
- N = …
99N = 45
Therefore: N = 45/99 or 5/11