Relating Decimals, Fractions, and Percents 6-1 Learn to compare and order decimals, fractions, and percents.

$Page 1: Relating Decimals, Fractions, and Percents 6-1 Learn to compare and order decimals, fractions, and percents.$
Relating Decimals, Fractions, and Percents6-1

Learn to compare and order decimals, fractions, and percents.


Percents are ratios that compare a number to 100.


Think of the % symbol as meaning per 100 or /100. 75% = 75/100 = 0.75

Reading Math


To convert a fraction to a decimal, divide the numerator by the denominator.

18 = 1 ÷ 8 = 0.125

To convert a decimal to a percent, multiply by 100 and insert the percent symbol.

0.125 100 12.5%


Find the missing ratio or percent equivalent for each letter a–g on the number line.

Example 1: Finding Equivalent Ratios and Percents

1

10a: 10% =

10100

=



Example 1 Continued

b: 0.25 =14

= 25%



Example 1 Continued

c: 40% =40100

=2

5

4

10=



Example 1 Continued

d: 0.60 =35

= 60%



Example 1 Continued

e: 23

% =66 0.666 = 23



Example 1 Continued

f: 12

% =87 0.875 = 78

8751000

=



Example 1 Continued

g: 125% =125 100

=5

4=

1

41


Example 2


a: 12

% =12 0.125 = 18

1251000

=

c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1


Example 2 Continued

b: 25% =25100

=1

4


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1


Example 2 Continued

c: 0.375 =38

= 37 %1

2


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1


Example 2 Continued

d: 50% =50100

=1

2


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1


Example 2 Continued

e: 0.625 =58

= 62 %1

2


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1


Example 2 Continued

f: 75% =75100

=3

4


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1


Example 2 Continued

g: 1 =100 100

= 100%


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1


Example 3: Comparing Fractions, Decimals, and Percents

Compare. Write <, >, or =.

40%14

14

= 0.25

0.25 < 0.40

Write as a decimal.

Compare.

14

< 40%

When multiplying a decimal by 100, simply move the decimal point two spaces to the right.

Remember!


Example 4: Comparing Fractions, Decimals, and Percents


0.893 50%

50% = 0.50

0.893 > 0.50

Write as a decimal.

Compare.

0.893 > 50%


Example 5


65%34

34

= 0.75

0.75 > 0.65

Write as a decimal.

Compare.

34

> 65%


Example 6


0.136 20%

20% = 0.20

0.136 < 0.20

Write as a decimal.

Compare.

0.136 < 20%


Example 7: Ordering Fractions, Decimals, and Percents

Write 0.075%, , 0.41, and 100% in order

from least to greatest.

34

34

= 0.75

100% = 1.000.075% = 0.00075

Write as decimals.

Compare.

34

0.075% < 41% < 75% < 100%

0.075%, 0.41, , 100%


Example 8

Write 35%, 0.25, , and 200% in order


12

12

= 0.50

35% = 0.35200% = 2.00

Write as decimals.

Compare.

12

25% < 35% < 50% < 200%

0.25, 35%, , 200%


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz: Part I

Find each equivalent value.

1. as a percent

2. 20% as a fraction

3. as a decimal


4. 30%

5. 0.650 97% <

37.5%

0.625

>

38

711

15

58


Lesson Quiz: Part II

6. Write 245%, , 0.133, and 66.6% in order


5. About 342,000 km2 of Greenland’s total area (2,175,000 km2) is not covered with ice. To the nearest percent, what percent of Greenland’s total area is not covered with ice?

16%

0.133, , 66.6%, 245%

15

15


1. Identify the equivalent value of as a percent.

A. 45.3%

B. 55.5%

C. 78.3%

D. 86.5%


59


2. Identify the equivalent value of 45% as a fraction.

A.

B.

C.

D.



3. Identify the equivalent value of as a decimal.

A. 0.252

B. 0.375

C. 0.456

D. 0.698


38


4. Identify the correct symbol to compare.0.430___50%

A. >

B. <

C. =

D. >


Relating Decimals, Fractions, and Percents 6-1 Learn to compare and order decimals, fractions, and percents.

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