6-1 fractions, decimals, and percents learn to write decimals and fractions as percents
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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
0 200 400 600 800 1,000 1,200 1,400 1,600 1,800 2,000
0 15
25
35
45
55
00 0.2 0.4 0.6 0.8 1.0
0 20% 40% 60% 80% 100%
The model shows that 800 out of 2,000 can be written as , ,
0.4, or 40%. The students have reached 40% of their goal.
8002000
25
6-1 Fractions, Decimals, and Percents
Write 0.7 as a percent.
Additional Example 1: Writing Decimals as Percents
Method 1: Use pencil and paper.
0.7 = 70100
= 70%
Write the decimal as a fraction with a denominator of 100.
Write the numerator with a percent sign.
710
=
6-1 Fractions, Decimals, and Percents
Write 0.7 as a percent.
Additional Example 1 Continued
Method 2: Use mental math.
0.70 =
= 70%
Move the decimal point two places to the right and add a percent sign.
70%
6-1 Fractions, Decimals, and Percents
Write 0.3 as a percent.
Check It Out: Example 1
Method 1: Use pencil and paper.
0.3 = 30100
= 30%
Write the decimal as a fraction with a denominator of 100.
Write the numerator with a percent sign.
310
=
6-1 Fractions, Decimals, and Percents
Write 0.93 as a percent.
Check It Out: Example 1 Continued
Method 2: Use mental math.
0.30 =
= 30%
Move the decimal point two places to the right and add a percent sign.
30%
6-1 Fractions, Decimals, and Percents
Write as a percent.58
58
= 5 ÷ 8
= .625
= 62.5%
Use division to write the fraction as a decimal.
Write the decimal as a percent.
Additional Example 2: Writing Fractions as Decimals
Method 1: Use pencil and paper.
To divide 5 by 8, use long division and place a decimal point followed by a zero after the 5.
8 5.00
Remember!
.625
6-1 Fractions, Decimals, and Percents
5 ● 12.5 8 ● 12.5
Write an equivalent fraction with a denominator of 100.
=
Write as a percent.58
Additional Example 2 Continued
Method 2: Use mental math.
62.5 100
Write the numerator with a percent sign.= 62.5%
6-1 Fractions, Decimals, and Percents
Write as a percent.35
35
= 3 ÷ 5
= 0.60
= 60%
Use division to write the fraction as a decimal.
Write the decimal as a percent.
Check It Out: Example 2
Method 1: Use pencil and paper.
6-1 Fractions, Decimals, and Percents
3 • 20 5 • 20
Write an equivalent fraction with a denominator of 100.
=
Write as a percent.35
Check It Out: Example 2 Continued
Method 2: Use mental math.
60 100
Write the numerator with a percent sign.= 60%
6-1 Fractions, Decimals, and Percents
Order 17%, 0.25, , 0.1, , and 20% from least to greatest.
Additional Example 3: Ordering Rational Numbers
Step 1: Write the numbers as decimals with the same number of decimal places.
17% = 0.17
45
34
0.25 = 0.25 34 = 0.75
0.1 = 0.10 45 = 0.80 20% = 0.20
6-1 Fractions, Decimals, and Percents
Order 17%, 0.25, , 0.1, , and 20% from least to greatest.
Additional Example 3 Continued
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
0.10 < 0.17 < 0.20 < 0.25 < 0.75 < 0.80
45
34
Step 3: Compare the decimals.
From least to greatest, the numbers are: 0.1, 17%,
20%, 0.25, , .34
45
6-1 Fractions, Decimals, and Percents
Order 12%, 0.20, , 0.8, , and 40% from least to greatest.
Check It Out: Example 3
Step 1: Write the numbers as decimals with the same number of decimal places.
12% = 0.20
34
12
0.20 = 0.20 12 = 0.50
0.8 = 0.80 34 = 0.75 40% = 0.40
6-1 Fractions, Decimals, and Percents
Order 12%, 0.20, , 0.8, , and 40% from least to greatest.
Check It Out: Example 3 Continued
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
0.12 < 0.20 < 0.40 < 0.50 < 0.75 < 0.80
34
12
Step 3: Compare the decimals.
From least to greatest, the numbers are: 12%, 0.20, 40%, , , 0.8.1
234
6-1 Fractions, Decimals, and Percents
Decide whether using pencil and paper, mental math, or a calculator is most useful when solving the following problem. Then solve.
27 out of 50 =
Using pencil and paper is the best method.
Think: 27 ÷ 50 divides evenly.
Write the decimal as a percent.
Additional Example 4: Choosing a Method of Computation
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?
2750
= 0.54
= 54%54% of the people have the newspaper delivered to their home.
6-1 Fractions, Decimals, and Percents
10 out of 50 =
Mental math or pencil and paper is the best method.
Think: The denominator is a multiple of 100.
Write the decimal as a percent.
Check It Out: Example 4
If 10 out of 50 students have blue backpacks, what percent of the students have blue backpacks?
1050
= 0.20
= 20%
20% of the students have blue backpacks.
20100
=
Decide whether using pencil and paper, mental math, or a calculator is most useful when solving the following problem. Then solve.
6-1 Fractions, Decimals, and Percents
Lesson Quiz
60%
1. Write 0.65 as a percent.
2. Write as a percent. 610
Choose the most useful method of computation. Then solve.
65%
Calculator; 45%
3. If 36 out of 80 people surveyed have been on a boat, what percent of these people have been on a boat?