Relating Decimals, Fractions, and Percents6-1
Learn to compare and order decimals, fractions, and percents.
Relating Decimals, Fractions, and Percents6-1
Think of the % symbol as meaning per 100 or /100. 75% = 75/100 = 0.75
Reading Math
Relating Decimals, Fractions, and Percents6-1
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%
Relating Decimals, Fractions, and Percents6-1
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
=
Relating Decimals, Fractions, and Percents6-1
Find the missing ratio or percent equivalent for each letter a–g on the number line.
Example 1 Continued
b: 0.25 =14
= 25%
Relating Decimals, Fractions, and Percents6-1
Find the missing ratio or percent equivalent for each letter a–g on the number line.
Example 1 Continued
c: 40% =40100
=2
5
4
10=
Relating Decimals, Fractions, and Percents6-1
Find the missing ratio or percent equivalent for each letter a–g on the number line.
Example 1 Continued
d: 0.60 =35
= 60%
Relating Decimals, Fractions, and Percents6-1
Find the missing ratio or percent equivalent for each letter a–g on the number line.
Example 1 Continued
e: 23
% =66 0.666 = 23
Relating Decimals, Fractions, and Percents6-1
Find the missing ratio or percent equivalent for each letter a–g on the number line.
Example 1 Continued
f: 12
% =87 0.875 = 78
8751000
=
Relating Decimals, Fractions, and Percents6-1
Find the missing ratio or percent equivalent for each letter a–g on the number line.
Example 1 Continued
g: 125% =125 100
=5
4=
1
41
Relating Decimals, Fractions, and Percents6-1
Example 2
Find the missing ratio or percent equivalent for each letter a–g on the number line.
a: 12
% =12 0.125 = 18
1251000
=
c
a b
e
d
50%12 %
f
g
38
25%12
58
75%
1
Relating Decimals, Fractions, and Percents6-1
Example 2 Continued
b: 25% =25100
=1
4
Find the missing ratio or percent equivalent for each letter a–g on the number line.
c
a b
e
d
50%12 %
f
g
38
25%12
58
75%
1
Relating Decimals, Fractions, and Percents6-1
Example 2 Continued
c: 0.375 =38
= 37 %1
2
Find the missing ratio or percent equivalent for each letter a–g on the number line.
c
a b
e
d
50%12 %
f
g
38
25%12
58
75%
1
Relating Decimals, Fractions, and Percents6-1
Example 2 Continued
d: 50% =50100
=1
2
Find the missing ratio or percent equivalent for each letter a–g on the number line.
c
a b
e
d
50%12 %
f
g
38
25%12
58
75%
1
Relating Decimals, Fractions, and Percents6-1
Example 2 Continued
e: 0.625 =58
= 62 %1
2
Find the missing ratio or percent equivalent for each letter a–g on the number line.
c
a b
e
d
50%12 %
f
g
38
25%12
58
75%
1
Relating Decimals, Fractions, and Percents6-1
Example 2 Continued
f: 75% =75100
=3
4
Find the missing ratio or percent equivalent for each letter a–g on the number line.
c
a b
e
d
50%12 %
f
g
38
25%12
58
75%
1
Relating Decimals, Fractions, and Percents6-1
Example 2 Continued
g: 1 =100 100
= 100%
Find the missing ratio or percent equivalent for each letter a–g on the number line.
c
a b
e
d
50%12 %
f
g
38
25%12
58
75%
1
Relating Decimals, Fractions, and Percents6-1
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!
Relating Decimals, Fractions, and Percents6-1
Example 4: Comparing Fractions, Decimals, and Percents
Compare. Write <, >, or =.
0.893 50%
50% = 0.50
0.893 > 0.50
Write as a decimal.
Compare.
0.893 > 50%
Relating Decimals, Fractions, and Percents6-1
Example 5
Compare. Write <, >, or =.
65%34
34
= 0.75
0.75 > 0.65
Write as a decimal.
Compare.
34
> 65%
Relating Decimals, Fractions, and Percents6-1
Example 6
Compare. Write <, >, or =.
0.136 20%
20% = 0.20
0.136 < 0.20
Write as a decimal.
Compare.
0.136 < 20%
Relating Decimals, Fractions, and Percents6-1
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%
Relating Decimals, Fractions, and Percents6-1
Example 8
Write 35%, 0.25, , and 200% in order
from least to greatest.
12
12
= 0.50
35% = 0.35200% = 2.00
Write as decimals.
Compare.
12
25% < 35% < 50% < 200%
0.25, 35%, , 200%
Relating Decimals, Fractions, and Percents6-1
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
Relating Decimals, Fractions, and Percents6-1
Lesson Quiz: Part I
Find each equivalent value.
1. as a percent
2. 20% as a fraction
3. as a decimal
Compare. Write <, >, or =.
4. 30%
5. 0.650 97% <
37.5%
0.625
>
38
711
15
58
Relating Decimals, Fractions, and Percents6-1
Lesson Quiz: Part II
6. Write 245%, , 0.133, and 66.6% in order
from least to greatest.
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
Relating Decimals, Fractions, and Percents6-1
1. Identify the equivalent value of as a percent.
A. 45.3%
B. 55.5%
C. 78.3%
D. 86.5%
Lesson Quiz for Student Response Systems
59
Relating Decimals, Fractions, and Percents6-1
2. Identify the equivalent value of 45% as a fraction.
A.
B.
C.
D.
Lesson Quiz for Student Response Systems
Relating Decimals, Fractions, and Percents6-1
3. Identify the equivalent value of as a decimal.
A. 0.252
B. 0.375
C. 0.456
D. 0.698
Lesson Quiz for Student Response Systems
38