Percents

MATH 102Contemporary Math

S. Rook

Overview

• Section 9.1 in the textbook:– Percents– Percent of change– Percent equation

Percents

Percents

• Percents are used in many applications:– e.g. Interest rate, credit card rate, scores

• Percent means per 100– e.g. 23% means 23 per 100 or 23⁄100

• To convert a percent to a decimal:– Drop the percent sign and move the decimal point two

places to the left• To convert a decimal to a percent:– Move the decimal point two places to the right and

append a percent sign

Percents (Continued)

• To convert a fraction to a percent:– Recall that the fraction bar indicates division– Either use long division or a calculator to convert the

fraction into a decimal– Convert the decimal to a percent

• You MUST understand how to convert to percents and from percents!

Percents (Example)

Ex 1: Convert:

a) 0.35% to a decimalb) 0.423 to a percentc) 4⁄250 to a percent

Percent of Change

Percent Change

• Percents can be used to indicate change from a past observation to a new observation– If the new observation is greater than the past

observation, there has been a percent increase– If the past observation is greater than the new

observation, there has been a percent decrease

• The percent change is always relative to the past observation

past

new -past change %

Percent Change (Example)

Ex 2: Find the percent change and indicate whether it is an increase or decrease:

a) The HCC student population was approximately 3000 in 2000 and is approximately 8000 in 2010.

b) A cake originally priced at $11.00 is marked down to $5.00.

Percent Equation

Percent Equation

• Most percent problems can be solved using the following equation:

percent x base = amount– The percent is usually converted to a decimal

when used in calculations– The base can sometimes be considered the whole• Usually preceded by the word “of”

– The amount can sometimes be considered the part

Percent Equation (Example)

Ex 3: Solve:

a) 12 is what percent of 80?

b) 77 is 22% of what number?

c) What is 12.25% of 160?

Percent Equation (Example)

Ex 4: In a recent year, the top-selling cookie in America was Nabisco’s Chips Ahoy with sales of $294.6 million. The total cookie sales for that year were $3,124 million. What percent of the total cookie sales were due to Chips Ahoy?

Percent Equation (Example)

Ex 5: According to the U.S. Bureau of the Census, from 2005 to 2006, the average price of a new home in the Northeast increased by 7.88% to $428,000. What was the average price of a new home in the Northeast in 2005 – round the answer to the nearest thousand.

Percent Equation (Example)

Ex 6: Jed works for Metal Fabricators Inc. which just lost a large contract and has asked employees to take a pay cut. If Jed now makes $34,500 per year before the pay cut and $30,360 afterwards, what percent was his pay cut?

Summary

• After studying these slides, you should know how to do the following:– Convert to and from percents– Calculate percent change– Solve application problems involving percent

• Additional Practice:– See problems in Section 9.1

• Next Lesson:– Interest (Section 9.2)