Section 8.1 D1 Percents Math in Our World

Learning Objectives  Convert between percent, decimal, and fraction form.  Perform calculations involving percents.  Solve real-world problems involving percents.

Percent Percent means hundredths, or per hundred. That is, 1% = Converting Percents to Decimals In order to change a percent to a decimal, drop the % sign and move the decimal point two places to the left.

EXAMPLE 1 Changing Percents to Decimals Change each percent to a decimal. (a) 84%(b) 5%(c) 37.5%(d) 172%

Percent to Fractions Converting Percents to Fractions A percent can be converted to a fraction by dropping the percent sign and using the percent number as the numerator of a fraction whose denominator is 100.

EXAMPLE 2 Changing Percents to Fractions Change each percent to a fraction. (a) 42% (b) 6% (c) (d) 15.8%

Decimals to Percents Converting a Decimal to a Percent To change a decimal to a percent, move the decimal point two places to the right and add a percent sign.

EXAMPLE 3 Changing Decimals to Percents Change each decimal to a percent. (a) 0.74 (b) 0.05 (c) (d) 5.463

Fractions to Percents Converting a Fraction to a Percent To change a fraction to a percent, first change the fraction to a decimal, and then change the decimal to a percent.

EXAMPLE 4 Changing Fractions to Percents Change each fraction to a percent. (a) (b) (c) (d)

Problems Involving Percents The most common calculations involving percents involve finding a percentage of some quantity. When writing a percentage statement in symbols, the word “of” becomes multiplication, and the word “is” becomes an equal sign. Also, we must change the percent into decimal or fractional form. 50% of 10 is x 10 = 5

EXAMPLE 5 Finding a Certain Percentage of a Whole In a class of 66 students, 32% got a B on the first exam. How many students got a B?

EXAMPLE 6 Finding a Certain Percentage of a Portion Of 60 runners who started a 5k race, 45 finished the race in under 40 minutes. What percent is that?

EXAMPLE 7 Finding a Whole Amount Based on a Percentage A medium-sized company reported that it had to cut its work force back to 70% of what it was last year. If it has 63 workers now, how many did it have a year ago?

EXAMPLE 8 Calculating Sales Tax The sales tax in Allegheny County, Pennsylvania, is 7%. What is the tax on a calculator that costs $89.95? What is the total amount paid?

EXAMPLE 9 Calculating Cost of Sale from Commission A real estate agent receives a 7% commission on all home sales. How expensive was the home if she received a commission of $5,775.00?

Classwork p. 428: 11, 13, 21, 23, 27, 35, 37, 45, 49, 51