Lesson 2.1.2
HW: 2-26 to 2-30
Learning Target: Scholars will develop strategies for rewriting terminating and repeating decimals as
fractions.
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
shown at below.
is
1.
2. 0.75
3. Three fifths
4.
5. 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.
1.
2.
3.
4.
5.
6.
0.19
0.391
0.001
0.019
0.3
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
sure that he is correct. Is
equal to
as a fraction. He started to rewrite it as
, but he is not
? 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?
1.
2.
3.
4.
5.
6.
7.  What connections do these fractions have with those you found in problem 2-19? Be ready to
share your observations with the class.
8.  Use your pattern to predict the fraction equivalent for
calculator.
Use your pattern to predict the decimal equivalent for
. Then test your guess with a
. Check your answer with
2-22. REWRITING REPEATING DECIMALS AS FRACTIONS
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:
1. 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?
2. “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.
3. Use Jerome’s strategy to rewrite
as a fraction. Be prepared to explain your reasoning.
9. your calculator.
2-26. Which of the following fractions are repeating decimals and which are terminating? Show how you
made your decisions.
1.
2.
3.
4.
2-27. Copy the portions webs below and fill in the missing parts.
5.
6.
2-28. Lila is making a spinner game for her cousins
to play. She has divided it into 8 equal sections and has labeled each section with a
symbol. When the spinner lands on a flower (
), her cousins will win a prize. Create a
spinner to explore your ideas! 2-28 HW eTool (CPM).
7. What is P(
)? Express your answer as a fraction, as a decimal, and as a percent.
8. What is the probability of not getting
and as a percent.
? Write your answer as a fraction, as a decimal,
9. What is P(
)? Write your answer as a fraction, as a decimal, and as a percent.
10. If Lila's cousins spin 100 times, about how many times would you expect them to spin a
heart (
)?
2-29. Copy the graphs below onto your paper. Then complete the scale by labeling the remaining tick
marks.
2-30. Approximately 3 out of every 25 Americans live in California. About 3 out of every 50
Americans live in New York, and about 2 out of every 25 Americans live in Texas.
11. Which state has the largest population?
12. Which state has the smallest population?
13. About what percentage of Americans do not live in California, New York, or Texas?
Lesson 2.1.2

2-18. See below:
1. seven-tenths, 0.7, 70%
2. seventy-five hundredths,
=
, 75%
3.
= 0.6, 60%
4. five-eighths, 0.625, 62.5%
5. See the “Suggested Lesson Activity” for possible responses.

2-19. See below:
1.
2.
3.
4.
5.
6.

2-20. Sample response: 0.73 is equal to

2-21. See below:
, but because
repeats, it is not.
1.
2.
3.
4.
5.
6.
7. Each fraction in this list matches with a fraction from problem 2-19 that has the
same numerator and a denominator that is greater by one; in each pair, the
fraction with the denominator that is a power of 10 terminates, and the fraction
that has a denominator that is one less than a power of 10 has the same digits but
repeats.
8.
or
9.

2-22. See below:
1. The decimal repeats in multiples of 100, so multiplying by 100 keeps the
repeating blocks aligned. He had 100 sets of
and he subtracted one set of
, leaving 99. When he subtracted, the repeating decimals became zero.
2.
3.

2-26.
1.
2.
3.
4.

2-27. See below:
1. five-eighths
See below:
repeating
terminating
terminating
repeating
2. 3

or
2-28. See below:
1.
, 0.375, 37.5%
2. 1 −
=
3.
, 0.25, 25%
=
, 0.875, 87.5%
4. 25. Sample reasoning:
of the spaces are hearts, and 25 times would be
of
100; or, there are hearts, and 8 goes into 100 just more than 12 times; so, since
2 · 12 = 24, about 25 times.

2-29. See diagrams below:
1.
2.
3.

2-30. See below:
1. California
2. New York
3. About 74 %