Download Lesson 3.1: Fractions to Decimals

November 14, 2014
Lesson 3.1: Fractions to Decimals
Focus: Use patterns to convert between decimals and fractions
Numbers can be written in both fraction and decimal form.
For example:
3 can be written as 3 and 3.0
1
A __________ illustrates division; that is, 1 means 1 10
10
Here are some examples of fractions and decimals from earlier grades:
Get Started: p. 86
We can write a fraction as a division question:
What division does 1/2 represent?
What is the quotient?
What other fractions can you write in decimal form?
Ex1)
Ex2)
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This chart represents one whole.
What does each row in the chart
represent?
Each small square?
How can you use the chart to show
3/4?
How much of the chart would be shaded?
How do you know?
How can you check your answer?
Explore: p. 86
>Use a calculator.
A)
1) Write each fraction as a decimal:
Fraction: 1/11
2/11
3/11
4/11
Decimal:
2) What patterns do you see?
3) Use your patterns to predict the decimal forms of these
fractions:
5/11,
6/11,
7/11,
8/11,
9/11,
10/11
4) Use a calculator to check your predictions.
November 14, 2014
B) Use a calculator.
1) Write each fraction as a decimal:
Fraction:
Decimal:
1/9
2/9
3/9
2) What patterns do you see?
3) Were you able to use your patterns to write 0.888 888 888 as a
fraction? Explain.
4) Which patterns were easier to use to make predictions?
5) Do you think patterns like these could be found in other lists of
fractions?
Connect: p. 87
Decimals such as 0.1 and 0.25 are terminating decimals. Each
decimal has a definite number of decimal places.
What did you notice about the last digit display in the fractions
with denominator 9?
When the repeating digit was greater than 4, the calculator ____________________
______________________________________________________
Ex)
Decimals such as 0.333 333 333...; 0.454 545 454...; 0.8111 111 111
are repeating decimals. Some digits in each repeating decimal
repeat forever.
We can write repeating decimals using "bar notation".The bar is
written over the digit that repeats.
examples:
a) 1/3
b) 1/18
November 14, 2014
Lesson 3.1:Fractions to Decimals
-Lets practice!
A/ Terminating Decimals
Terminating Decimals can be written as fractions where their place
value is the denominator of the fraction.
Example: 0.21 = 21/100
0.7
= 7/10
0.287 = 287/1000
B/ Converting Fractions to Terminating Decimals
Remember: The denominator represents the place value of the fraction.
Example: 3/10
69/100
389/1000
=
=
=
But, what happens when the denominator is not a place value number or
a power of 10?????
Example:
2/5
=
16/200
=
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Rule: You must change the denominator into another denominator that
is a place value number.
You are creating EQUIVALENT FRACTIONS
Examples:
1. 11/20
2. 1/5
3. 13/200
4. 14/25
More Examples:
5. 19/50
6. 33/500
7. 17/25
4. 1/8
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C/ Converting Fractions to Repeating Decimals
Remember: The denominators are always made of nines.
Example: 3/9
=
69/99
=
389/999
=
Write each fraction as a repeating decimal:
1. 4/999
2. 28/999
3. 2/99
4. 8/9
D/ Converting Repeating Decimals to Fractions
Write each repeating decimal as a fraction:
1. 0.2222222...
2. 0.026 026 026...
__
3. 0.54
___
4. 0.002
November 14, 2014
Practice: (Do together as a class) p. 88 #1-3
Homework: p. 89 #4, 5,
6, 8, 9, 10 & 11