Section 3A: Uses and Abuses of Percentages

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1 Section 3A: Uses and Abuses of Percentages Percentages A percent means out of 100 or divided by 100. So P % = P 100. Percentages can be converted to decimals or fractions: Example: 75% = 0.75 = = 3 4. Example. A recent Gallup poll shows that President Obama has a 43% approval rating. The poll had 1,500 participants. How many participants approve of President Obama? After surveying 30,000 adults in July 2011, another Gallup poll shows an unemployment rate of 8.8%. How many of those polled stated they were unemployed? Of those 30,000 adults polled, 5,552 of them stated they were underemployed. What percentage of those polled are underemployed? After reviewing last quarters fiscal report, it was observed that 115% of the pension fund was being allocated to paying pensions. If the pension fund has 1.2 million dollars, what was the payout, and what was the overage? 1

2 Absolute and Relative Change The absolute change describes the actual increase or decrease from a reference value to a new value: absolute change = new value reference value The relative change if a fraction that describes the size of the absolute change in comparison with the reference value: new value reference value relative change = reference value The relative change can be converted from a fraction to a percentage by multiplying by 100%. Example. Answer the following questions involving percentages. You buy a stock valued at $45. After some time, the price jumps to $55. What is the absolute change in price? The relative change? A certain baseball card was valued at $30. After some time (and some wear), the value dropped to $24. What is the absolute change and relative change in value? A 2006 Toyota Prius originally retailed for $21,725, while the 2006 Toyota Corolla retailed for $14,105. Their current true market values are $12,614 and $8,308 respectively. What is the absolute and relative change in the values of the cars? 2

3 Example. Evaluate the following using percentages. The population of Mali in 2009 was 13,010,209. The population of Burkina Faso at that time was approximately 21.11% more than Mali. What was the population of Burkina Faso? In 2009, the population of Rwanda was 76.84% of the population of Mali. What was the population of Rwanda? The population of Guinea 22.61% less than that of Mali. What is the population of Guinea? Suppose the population of Mali grows by 250% in the next 60 years. What will the population be then? 3

4 Example. Tom makes a $25,000 salary. Dick s salary is 10% more than Tom s salary. Harry s salary is 9% less than Dick s salary. How much does Harry earn? What percentage of Tom s salary does Harry make? Example. In a particular promotion scheme, a meritorious employee receives a 2% pay increase of your current pay every 3 years. What will be the percent change in salary after working for 15 years as a meritorious employee? 4

5 Percentage Points Versus % When you see a change or difference expressed in percentage points, you can assume it is an absolute change or difference. If it is expressed with the % sign or the word percent, it should be a relative change or difference. Example. Answer the following questions involving percentages or percentage points. In July 2009, President Obama s job approval rating was 58% as determined by a Gallup poll. A recent Gallup poll sees his approval rating at 42%. What is the percent change in his approval rating? What is the change in percentage points? In 2005, Apple s market share was 4.4%. In 2006, Apple saw its market share increase by 16%. What was Apple s percentage of market share in 2006? By how many percentage points did it increase? Apple s market share in 2011 is 10.7%. What was the percent change from 2006? What was the change in percentage points? 5

6 Example. Suppose a department store allows coupon and sale stacking. A pair of shoes have a regular price of $69.99, but are currently 40% off. You have a coupon for 60% off the current price of one item. If you buy this pair of shoes while on sale and use your coupon, how much will you pay? Assume 6% sales tax. Example. Staples has a 3-terabyte hard drive for sale at $ Best Buy has the same hard drive on sale for $ Staples has a price-matching policy which reduces the price by 110% of the difference in the price. If you buy the hard drive from Staples and have them price match, then use a 20%-off coupon, and tax is 6%, what will be your final price to pay? 6

7 Example. A 14-watt light bulb uses what percentage of energy less than a 60-watt light bulb? Example. An advertisement claimed that their new light bulb uses 200% less energy than a common 60-watt light bulb. What wattage does the new light bulb use? Example. In a poll of 3,500 likely voters, 47% said they would vote for a generic Republican in the upcoming presidential race. In a parallel poll of 1,500 people, 53% said they would vote for a generic Republican. What percentage of all those polled would vote Republican? 7

8 Example. You purchased a new laptop from Best Buy for $ after taxes. You can be reimbursed by your employer for the pre-tax total of the laptop. Suppose tax in your area is 7%. What was the base price for the laptop? Example. The population of Mongolia was million people in 2009, which followed a 6.118% increase from What was the population in 2006? Example. Nokia s handset market share in 2011 is 25%, down 18.03% from last year. What was its market share in 2010? 8