6-1 Fractions, Decimals, and Percents
Learn to write decimals and fractions as
percents.
6-1 Fractions, Decimals, and Percents
The students at Westview Middle School
are collecting cans of food for the local
food bank. Their goal is to collect 2,000
cans in one month. After 10 days, they
have 800 cans of food. What percent of
their goal have they reached?
6-1 Fractions, Decimals, and Percents
0
200
1
5
0
0
0
400
0
600
800
2
5
1,000
1,200
1,400
1,600
3
5
4
5
1,800
2,000
5
5
0.2
0.4
0.6
0.8
1.0
20%
40%
60%
80%
100%
800 2
The model shows that 800 out of 2,000 can be written as
, ,
2000 5
0.4, or 40%. The students have reached 40% of their goal.
6-1 Fractions, Decimals, and Percents
Additional Example 1: Writing Decimals as Percents
Write 0.7 as a percent.
Method 1: Use pencil and paper.
0.7 =
7
70
=
10 100
= 70%
Write the decimal as a fraction
with a denominator of 100.
Write the numerator with a
percent sign.
6-1 Fractions, Decimals, and Percents
Additional Example 1 Continued
Write 0.7 as a percent.
Method 2: Use mental math.
0.70 = 70%
= 70%
Move the decimal point two
places to the right and add a
percent sign.
6-1 Fractions, Decimals, and Percents
Check It Out: Example 1
Write 0.3 as a percent.
Method 1: Use pencil and paper.
0.3 =
3
30
=
10 100
= 30%
Write the decimal as a fraction
with a denominator of 100.
Write the numerator with a
percent sign.
6-1 Fractions, Decimals, and Percents
Check It Out: Example 1 Continued
Write 0.93 as a percent.
Method 2: Use mental math.
0.30 = 30%
= 30%
Move the decimal point two
places to the right and add a
percent sign.
6-1 Fractions, Decimals, and Percents
Additional Example 2: Writing Fractions as Decimals
Write 5 as a percent.
8
Method 1: Use pencil and paper.
5 =5÷8
8
= .625
= 62.5%
Use division to write the
fraction as a decimal.
Write the decimal as a percent.
Remember!
To divide 5 by 8, use long division and place a decimal point
followed by a zero after the 5.
.625
8 5.00
6-1 Fractions, Decimals, and Percents
Additional Example 2 Continued
Write 5 as a percent.
8
Method 2: Use mental math.
5
8
●
●
12.5 = 62.5
12.5
100
= 62.5%
Write an equivalent fraction
with a denominator of 100.
Write the numerator with a
percent sign.
6-1 Fractions, Decimals, and Percents
Check It Out: Example 2
Write 3 as a percent.
5
Method 1: Use pencil and paper.
3 =3÷5
5
= 0.60
= 60%
Use division to write the
fraction as a decimal.
Write the decimal as a percent.
6-1 Fractions, Decimals, and Percents
Check It Out: Example 2 Continued
Write 3 as a percent.
5
Method 2: Use mental math.
3
5
•
•
20
20
= 60
100
Write an equivalent fraction
with a denominator of 100.
= 60%
Write the numerator with a
percent sign.
6-1 Fractions, Decimals, and Percents
Additional Example 3: Ordering Rational Numbers
4
3
Order 17%, 0.25,
, 0.1, 5 , and 20% from
4
least to greatest.
Step 1: Write the numbers as decimals with the
same number of decimal places.
17% = 0.17
0.25 = 0.25
3 = 0.75
4
0.1 = 0.10
4 = 0.80
5
20% = 0.20
6-1 Fractions, Decimals, and Percents
Additional Example 3 Continued
4
Order 17%, 0.25, 3 , 0.1,
, and 20% from
5
least to greatest. 4
Step 2: Graph the numbers on the number line.
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
Step 3: Compare the decimals.
0.10 < 0.17 < 0.20 < 0.25 < 0.75 < 0.80
From least to greatest, the numbers are: 0.1, 17%,
20%, 0.25, 3 , 4 .
4 5
6-1 Fractions, Decimals, and Percents
Check It Out: Example 3
3
1
Order 12%, 0.20,
, 0.8, 4 , and 40% from
2
least to greatest.
Step 1: Write the numbers as decimals with the
same number of decimal places.
12% = 0.20
0.20 = 0.20
1 = 0.50
2
0.8 = 0.80
3 = 0.75
4
40% = 0.40
6-1 Fractions, Decimals, and Percents
Check It Out: Example 3 Continued
3
Order 12%, 0.20, 1 , 0.8,
, and 40% from
4
least to greatest. 2
Step 2: Graph the numbers on the number line.
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
Step 3: Compare the decimals.
0.12 < 0.20 < 0.40 < 0.50 < 0.75 < 0.80
From least to greatest, the numbers are: 12%,
0.20, 40%, 1 , 3 , 0.8.
2 4
6-1 Fractions, Decimals, and Percents
Additional Example 4: Choosing a Method of
Computation
Decide whether using pencil and paper, mental math, or a
calculator is most useful when solving the following
problem. Then solve.
If 27 out of 50 people have the newspaper delivered to their
home, what percent of these people have the newspaper
delivered to their home?
27
Think: 27 ÷ 50 divides evenly.
50
Using pencil and paper is the best method.
= 0.54
27 out of 50 =
Write the decimal as a percent.
= 54%
54% of the people have the newspaper delivered to their
home.
6-1 Fractions, Decimals, and Percents
Check It Out: Example 4
Decide whether using pencil and paper, mental math, or a
calculator is most useful when solving the following
problem. Then solve.
If 10 out of 50 students have blue backpacks, what
percent of the students have blue backpacks?
10 out of 50 =
20
10
=
50 100
Think: The denominator is a
multiple of 100.
Mental math or pencil and paper is the best method.
= 0.20
= 20%
Write the decimal as a percent.
20% of the students have blue backpacks.
6-1 Fractions, Decimals, and Percents
Lesson Quiz
1. Write 0.65 as a percent.
65%
2. Write 6 as a percent.
10
60%
Choose the most useful method of computation.
Then solve.
3. If 36 out of 80 people surveyed have been
on a boat, what percent of these people have
been on a boat?
Calculator; 45%