Goal: I will be able to
to fractions.
Tool Bag
convert fractions to decimals, and decimals
Here’s How…Notes & Examples
Formulas, equations,
Vocabulary, etc.
With your partner, discuss…
Decimals
What are some examples from real world where
decimals are used?
Fractions
What are some examples from the real world where
fractions are used?
Have you ever seen a recipe call for 2.7 cups of flour?
Why or why not?
How would people react if a gas station posted gas
3
prices as $2 per gallon? Why?
7
Because fractions and decimals are used in a variety of ways
in life, it is important to be able to change back and forth
based upon the usage.
Review
Decimal
Say
(Word Form)
0.1
One tenth
1
10
0.01
One hundredth
1
100
0.001
One thousandth
1
1000
Fraction
Fraction with
Powers of 10
1
10
1
10
1
10
1
2
3
Looking at the powers, what do you notice about the number
of decimal places and the power in the denominator?
We Try
Express 3.25 as a fraction or mixed number.
𝟐𝟓
Three and twenty-five hundredths, or 𝟑 𝟏𝟎𝟎
Example #1
Three Methods
Converting Decimals to Fractions
Express 0.8 as a fraction in simplest form.
Greatest Common
Base 10 Model
Prime Factors
Factor
8
0.8 =
8
10
0.8 =
GCF = 2
2•2•2
10
=
2•5
2
8
=
4
10 ÷ 2
=
5
4
=
5
8
10
We Try
=
4
5
Express 3.25 as a fraction or mixed number in simplest
form.
𝟐𝟓
Three and twenty-five hundredths, or 𝟑 𝟏𝟎𝟎
𝟏
𝟐𝟓
𝟐𝟓 ∙ 𝟏
=
=
𝟒
𝟏𝟎𝟎
𝟐𝟓 ∙ 𝟒
𝟏
𝟑
𝟒
Example #2
Express 0.08 as a fraction in simplest form.
Greatest Common
Base 10 Model
Prime Factors
Factor
8
0.08 =
8
100
0.08 =
GCF = 4
2•2•2
100
=
2•2•5•5
4
8
=
100 ÷ 4
2
=
25
2
=
25
8
2
=
100
25
Looking back
at the 0.8 bar
model.
You Try
What do you notice
about the two
different bar
models for 0.8 and
0.08?
Express 0.36 as a fraction in simplest form.
Converting Fractions to Decimals
Memorize
When the denominator is 10, 100,
or 1000
1
= 0.5
2
1
= 0.16
6
4
10
1
= 0.3
3
1
= 0.25
4
1
= 0.125
8
1
= 0.1
9
276
= 0.276
1000
25
= 0.25
100
= 0.4
1
= 0.2
5
The denominator tells us how many decimal places.
Making Equivalent Change the denominator to 10, 100, or 1000.
Fractions
Examples
1)
2
5
=
=
2
5
4
10
•
2
2
2)
=
= 0.4
You Try
1)
5
4
3
=
25
3
25
12
100
= 0.12
2)
7
250
•
4
4
Using Division
5
Examples
1)
=5÷8
8
= 0.625
3)
15
3•5
=
9
3•3
=5÷3
You Try
1)
7
8
0. 6 2 5
8 5 .000
48
20
16
40
40
0
1. 6 6
3 5 .00
3
20
18
20
18
2
2)
27
72
2)
5
8
4
8
1
=
2
=
+
+
1
8
1
8
= 0.5 + 0.125
= 0.625