In Lesson 2.1.1, you worked with different fractions and found ways to rewrite
those fractions as repeating and terminating decimals. In this lesson, you will
reverse your thinking and will instead represent decimals as fractions.
As you work with your team today, ask each other these questions to focus your
discussion:
How else can I describe the portion?
How many pieces are in the whole?
2-18. Complete the Representations of a Portion Web for each number below. An
example for
is shown at right.
a.
b. 0.75
c. Three-fifths
d.
e. With your team, explain how you rewrote 0.75 as a fraction in part (b).
Is there more than one way? Be as specific as possible.
2-19. Since 0.7 is described in words as “seven-tenths,” it is not a surprise that the
equivalent fraction is . Obtain a set of decimal cards from your teacher or use
the list below to complete the following tasks:

Use the names of fractions (like “twenty-three hundredths”) to
rewrite each terminating decimal as a fraction. First try to use what you
know about place value to write the fraction.

With your calculator, check to be sure the fraction is equal to the
decimal.
a.
0.19
b. 0.391
c. 0.001
d. 0.019
e. 0.3
f. 0.524
2-20. Jerome works at the Fraction Factory in the department that changes
decimals into fractions. He has just received an order to rewrite
as a
fraction. He started to rewrite it as
Is
equal to
, but he is not sure that he is correct.
? Be ready to justify your answer.
2-21. Katrina is now responsible for finding the decimal equivalent for each of the
numbers below. She thinks these fractions have something to do with the decimals
and fractions in problem 2-19, but she is not sure.

Get a set of the fractions in parts (a) through (f) below on cards from
your teacher, and use your calculator to change each fraction into a decimal.
Add the decimal information to the card. Can you find a pattern?
a.
b.
c.
d.
e.
f.
g. What connections do these fractions have with those you found in
problem 2-19? Be ready to share your observations with the class.
h. Use your pattern to predict the fraction equivalent for
your guess with a calculator.
. Then test
i. Use your pattern to predict the decimal equivalent for
answer with your calculator.
. Check your
2-22. REWRITING REPEATING DECIMALS AS FRACTIONS
j.
Jerome wants to figure out why his pattern from problem 2-21 works. He
noticed that he could eliminate the repeating digits by subtracting, as he did in
the work at right. This gave him an idea. “What if I multiply by something
before I subtract, so that I’m left with more than zero?” he wondered. He
wrote:
“The repeating decimals do not make zero in this problem. But if I multiply by
100 instead, I think it will work!” He tried again:
a.
Discuss Jerome’s work with your team. Why did he multiply by
100? How did he get 99 sets of
? What happened to the repeating
decimals when he subtracted?
b.
“I know that 99 sets of
are equal to 73 from my
equation,”Jerome said. “So to find what just one set of
is equal to,
I will need to divide 73 into 99 equal parts.” Represent Jerome’s idea as
a fraction.
c.
Use Jerome’s strategy to rewrite
to explain your reasoning.
as a fraction. Be prepared
2-23. DESIGN A DECIMAL DEPARTMENT
Congratulations! Because of your new skills with rewriting fractions and
decimals, you have been put in charge of the Designer Decimals Department of
the Fraction Factory. People write to your department and order their favorite
fractions rewritten as beautiful decimals.
Recently, your department has received some strange orders. Review each order below
and decide if you can complete it. If possible, find the new fraction or decimal. If it is
not possible to complete the order, write to the customer and explain why the order
cannot be completed.
o
o
Order 1: “I’d like a terminating decimal to represent
.”
Order 2: “Could you send me 0.208 as two different fractions,
one with 3000 in the denominator and one with 125 in the
denominator?”
o
Order 3: “Please send me
written as a fraction.”
2-24. Additional Challenge: A strange order has arrived in the Designer Decimals
Department. The order requests a new kind of decimal to be written as a fraction.
The order is reprinted at right. With your team, rewrite the decimal as an
equivalent fraction or explain why you cannot rewrite it.
2-25. LEARNING LOG


Make an entry in your Learning Log that summarizes what you have
learned in the past two lessons. For example, how can you tell if a decimal is
repeating or terminating? How can you change a decimal to a fraction,
especially if it is repeating? Can every fraction be represented as a decimal,
and can every decimal be represented as a fraction?
Title your entry “Repeating and Terminating Decimals” and include
today’s date.
Fraction ⇔Decimal ⇔Percent
The Representations of a
Portion web diagram at right
illustrates that fractions,
decimals, and percents are
different ways to represent a
portion of a number. Portions
can also be represented in
words, such as “four-fifths”
or “twelve-fifteenths,” or with
diagrams.
The examples below show
how to convert from one form
to another.
Decimal to percent: Multiply Percent to decimal: Divide
the decimal by 100.
the percent by 100.
Fraction to percent: Set up an
equivalent fraction using 100
as the denominator. The
numerator is the percent.
Percent to fraction: Use 100
as the denominator. Use
the digits in the percent as
the numerator. Simplify as
needed.
Terminating decimal to
fraction: Make the digits the
numerator. Use the decimal
place value as the
denominator. Simplify as
needed.
Fraction to decimal: Divide
the numerator by the
denominator. If sets of
digits repeat, then write just
one of the repeating sets
and place a “bar” over it.
Repeating decimal to fraction:
Count the number of decimal
places in the repeating block.
Write the repeating block as
the numerator. Then, write
the power of 10 for the