Untitled Lesson

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Lesson 6.1

Fractions, Decimals, and

Percents

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WARM-UP

Write the fraction represented by the model.

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Learning Target:
Rewrite fractions, decimals, and percents using different
representations.

Success Criteria:

• I can write percents as decimals and decimals as percents.
• I can write fractions as decimals and percents.
• I can compare and order fractions, decimals, and percents.

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Work with a partner. Determine which number is greater. Explain your method.

a. 7% sales tax or
1
20sales tax

b. 0.37 cup of flour or 1

3cup of flour

c.5

8−inch wrench or 0.375−inch wrench

d. 12 3

5dollars or 12.56 dollars

e. 5 5

6fluid ounces

or 5.6 fluid ounces

EXPLORATION 1

Comparing Numbers in Different Forms

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Work with a partner and follow the steps below.

• Write five different numbers on individual slips of paper. Include at least

one decimal, one fraction, and one percent.

• On a separate sheet of paper, create an answer key that shows your

numbers written from least to greatest.

• Exchange slips of paper with another group and race to order the

numbers from least to greatest. Then exchange answer keys to check
your orders.

EXPLORATION 2

Ordering Fractions, Decimals, and Percents

Math Practice

Make a Plan
Make a plan to order
the numbers. How
might having a plan
help you to order
numbers quickly?

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Key Ideas

Bar notation
indicates one or more
repeating digits.

Writing Percents as Decimals

Words Remove the percent symbol. Then divide by 100, which moves

the decimal point two places to the left.

Numbers82% = 82.% = 0.82

2.45% = 02.45% = 0.0245

Writing Decimals as Percents

Words Multiply by 100, which moves the decimal point two places to

the right. Then add a percent symbol.

Numbers0.47 = 0.47 = 47%

0.ത2 = 0.222 . . . = 22.ത2%

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EXAMPLE 1

Write each percent as a decimal or each decimal as a percent. Use a model to
represent each number.

c. 0.27

a. 61%

d. 0.3

b. 8%

= 61 %.
= 0.61
=
8 %.0
= 0.08

= 0333 . . . .
= 33.3 %
= 027 = 27%

.

Converting Between Percents and Decimals

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Try It

Write the percent as a decimal or the decimal as a percent. Use a model to represent
the number.

1. 39%

2. 12.ത6%

4. 1.25

3. 0.05

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So, 15

11can be written as 1.36 or 136.36%.

= 13636 . . .

4
5= 4 × 20

5 × 20= 80

100= 80% = 0.8

EXAMPLE 2

a.4

5

Write each fraction as a decimal and a percent.

For a fraction
with a denominator

of 100,
n

100= n%.

Writing Fractions as Decimals and Percents

1.36

b. 15

11
Use long division to divide 15 by 11.

Write 1.36 as a percent.

15
11= 1.36

The remainder
repeats. So, it
is a repeating
decimal.

11 15.0000
− 11

4

7

4

1.3636

− 3 3

− 66

0

0

4

− 33

0

7

− 66

0

.
= 136.36%

.

So, 4

5can be written as 0.8 or 80%.

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Try It

Write the fraction as a decimal and a percent.

5.5

8
6.1

6

8.
3

1000
7.11

3

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Self-Assessment for Concepts & Skills

Write the percent as a decimal or the decimal as a percent. Use a model to represent
the number.

9. 46%

10. 66.ത6%

11. 0.18

12. 2.ത3

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Self-Assessment for Concepts & Skills

Write the fraction as a decimal and a percent.

13.7

10
14.5

9

16.17

15
15.
7

2000

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February: 16% = 16 % = 0.16

Write 3

25and 16% as decimals.

January:3

25 = 12

100= 0.12

EXAMPLE 3

Month

December

January

February

Portion of Guests

0.72
3
25

16%

An ice rink is open December through February. The table shows the attendance
each month as a portion of the total attendance. How many times more guests
visit the ice rink in the busiest month than in the least busy month?

The busiest month was December, the second busiest month was February,
and the least busy month was January. So, divide 0.72 by 0.12.

Modeling Real Life

.

So, 6 times more guests
visit the ice rink in the
busiest month than in the
least busy month.

6.

12 72.

− 72

0

0 12 0 72

.

.

Multiply each number by 100.

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Self-Assessment for Problem Solving

17. An astronaut spends 53% of the day working, 0.1 of the day

eating, 3

10 of the day sleeping, and the rest of the day

exercising. Order the events by duration from least to
greatest. Justify your answer.

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Self-Assessment for Problem Solving

18. A band plays one concert in Arizona, one concert in California, and one concert in

Georgia. In California, the band earned 3

2the profit that they earned in Arizona. Of the

total profit earned by the band, 32% is earned in Arizona. How many times more money
did the band earn at the most profitable concert than at the least profitable concert?
Justify your answer.

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Mini-Assessment

1. Write 12% as a decimal.

2. Write 2.25 as a percent.

3. Write5

11as a decimal and a percent.

4. Order the numbers from least to greatest.

0.334, 1

3 , 33.3%, 0.33

5. You, your friend, and your cousin have a soccer competition where

each person attempts the same number of shots. You make 84% of
your shots, your friend makes 0.72 of his shots, and your cousin

makes 9

11 of her shots. How many times more shots are made by the

first place finisher than the third place finisher?