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6.1 Basics of Percent Objectives 1. Learn the meaning of percent. 2. Write percents as decimals. 3. Write decimals as percents. 4. Understand 100%, 200%, and 300%. 5. Use 50%, 10%, and 1%. Copyright © 2010 Pearson Education, Inc. All rights reserved.

The figure has one hundred squares of equal size. Eleven of the square are shaded. The shaded portion is or 0.11 of the total figure. The shaded portion is also 11% of the total or “eleven parts out of 100 parts.” Read 11% as “eleven percent.” Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 1 Understanding Percent If 52 out of 100 chickens are hens, then 52 per 100 or , or 52% of the chickens are hens. b. If a person pays a tax of \$9 on every \$100 of purchases, then the tax rate is \$9 per \$100. The ratio is and the percent of tax is 9%. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 2 Writing Percents as Decimals Write each percent as a decimal. 32% p% = p ÷ 100 32% = 32 ÷ 100 = 0.32 78% 78% = 78 ÷ 100 = 0.78 93.4% 93.4% = 93.4 ÷ 100 = 0.934 200% 200% = 200 ÷ 100 = 2.00 Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 3 Writing Percents as Decimals by Moving the Decimal Point Write each percent as a decimal by moving the decimal point two places to the left. 23% 23.% 0.23 23% = 0.23 180% 180.% = Decimal point starts at far right side Percent sign is dropped (Step 1) Decimal point is moved two places to the left. (Step 2) 180.% = 1.80 or 1.8 Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 3 Writing Percents as Decimals by Moving the Decimal Point Write each percent as a decimal by moving the decimal point two places to the left. c % is attached so the decimal point can be moved two places to the left. 0.7% 0.7% = 0.007 Two zeros are attached so the decimal point can be moved two places to the left. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 4 Writing Decimals as Percents by Moving the Decimal Point Write each decimal as a percent by moving the decimal point two places to the right. 0.26 Decimal point is moved two places to the right. 0.26 = 26% b Percent sign is attached and decimal point is not written with whole number percents. = 37.6% Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 4 Writing Decimals as Percents by Moving the Decimal Point Write each decimal as a percent by moving the decimal point two places to the right. 1.83 d. 3.4 3.4 = 340% 5 5. = 5.00 so 5 = 500% = 183% = 3.40 0 is attached so the decimal point can be moved two places to the right. Attach % sign. Two zeros are attached so the decimal point can be moved two places to the right. Attach % sign. Copyright © 2010 Pearson Education, Inc. All rights reserved.

When working with percents, it is helpful to have several reference points. 100%, 200% and 300% are three such reference points. 100% means 100 parts out of 100 parts. That’s all of the parts. If 100% of the 18 people attending last week’s meeting attended this week’s meeting, then 18 people (all of them) attended this week. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 5 Finding 100%, 200%, and 300% of a Number Fill in the blanks. 100% of 24 people is _____. 100% is all of the people. 100% of 24 people is 24 people. 200% of \$25 is _____. 200% is twice (2 times) as much money. 200% of \$25 is 2  \$25 = \$50. Copyright © 2010 Pearson Education, Inc. All rights reserved.

Parallel Example 5 Finding 100%, 200%, and 300% of a Number Fill in the blanks. c. 300% of 12 animals is _____. 300% is 3 times as many animals. 300% of 12 animals is 3  12 = 36 animals. Copyright © 2010 Pearson Education, Inc. All rights reserved.

50% means 50 parts out of 100 parts, which is half of the parts. So, 50% of \$24 is \$12 (half of the money). 10% means 10 parts out of 100. To find 10% of a number we move the decimal point one place to the left. To find 1% of a number, we move the decimal point two places to the left. Copyright © 2010 Pearson Education, Inc. All rights reserved.