How do you know which fractions are
terminating decimals and which are
repeating decimals?
5
?
6
10
0.?
In this lesson you will learn how
to determine whether fractions
convert to terminating or
repeating decimals by using
proportional reasoning and
double tape diagrams.
Let’s Review
A terminating decimal has a finite or countable
number of digits after the decimal point.
= 0.2
= 0.25
= 0.125
A repeating decimal has a pattern of digits which repeats
forever. The pattern that repeats is called
the repetend and is shown with a bar.
= 0.
= 0.1
= 0.
A Common Misunderstanding
Thinking that the repetend bar goes over
every digit of a repeating decimal.
1
6
=0.16
This is the
repetend
bar.
1
≠0.16
6
Core Lesson
A team has won 5 out of the last 8 games.
What is the team’s winning percentage?
Core Lesson
5
Games won
0
1.25
1.25
1.25
1.25
2.5
2.5
0.625
0.625
0.625
0.625 0.625
0.625
0.625
0.625
1
1
0
1
1
1
1
1
1
Games played
5 ÷ 8 = 0.625 =
625
625
1000
=
8
62.5
100
= 62.5%
=1000 because 8 is a factor of 1000.
Core Lesson
A recipe calls for 5 cups of chicken broth for
6 servings. What decimal part of each
serving is chicken broth?
Core Lesson
So our picture shows that the recipe has
cups of
broth per serving.
1
1
0
5
Broth
0
1
1
1
1
1
1
Servings
1
1
1
1
6
Core Lesson
So how is
written as a decimal? Remember that
decimals are fractions with denominators that are
powers of ten.
5
?
6
10
0.?
Core Lesson
5
6
6x
10
1
X
X
10 = 10
6
10 = 8
5x
6
6
10
6
8
10
0.8
Core Lesson
5
6
6x
X
100 = 100
6
100 = 83
5x
6
100
1
X
6
100
6
83
100
0.83
Core Lesson
5
6
6x
1000
1
X
X
1000 = 100
6
1000 = 833
5x
6
6
1000
6
833
1000
0.833
Core Lesson
Any fraction in lowest terms with a denominator that is
not a power of ten is a repeating decimal.
A bar is placed over only the pattern of digits that
repeat (the repetend).
5
833
6
1000
0.83
In this lesson you learned how to
determine whether fractions
convert to terminating or
repeating decimals by using
proportional reasoning and
double tape diagrams.