Percents MATH 102 Contemporary Math S. Rook

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

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 decimal b) to a percent c) 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

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

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)