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Unformatted text preview: Uses and Abuses of Percentages Wednesday January 5, 2011 Review per cent means divided by 100, so for example, 50% = 50 / 100 = . 5 and 125% = 125 / 100 = 1 . 25. To convert a percent to a fraction, replace the percent sign with division by 100 (then reduce the fraction). For example, 25% = 25 100 = 1 4 . To convert a percent to a decimal, drop the % symbol and move the decimal two places to the left (i.e. divide by 100). For example, 25% = . 25 and 1% = . 01 To convert a decimal to a percentage, move the decimal two places to the right (i.e. multiply by 100) and attach the % symbol. For example, . 12 = 12% and . 0013 = 1 . 3% To convert a fraction to a percentage, first convert the fraction to a decimal (using a calculator if necessary) then convert the decimal to a percentage as above. For example 1 5 = . 2 = 20% Three Ways of Using Percentages 1. As Fractions Example 1. Express the following as a percent: Of 305 million Americans, 40.4 million are under the age of 15. 1 Solution Write as a fraction then convert to percentage: 40 . 4 305 = . 13245902 = 13 . 245902% So approximately 13 . 25% of Americans are under the age of 15. 2. To Describe Change Absolute change refers to the increase or decrease from a reference value to a new value. Relative change is a fraction that describes the relative change in comparison to the reference value. Example 2. During a 6-month period, Nokias stock doubled from $10 a share to $20 a share. What were the absolute and relative changes in the stock price? Solution The reference value is $10, the starting price of the stock. The new value of the stock price is $20. Therefore, absolute change = new value- reference value = $20- $10 = $10 and relative change = absolute change reference value = $10 $10 = 1 Remarks: (a) Although the stock price doubled, the relative increase is only %100 (as opposed to %200). (b) The relative change is unitless. (c) The relative change can be converted to a percent by multiplying by 100 Example 3. The population of the United States increased form 249 million in 1990 to 308 million in 2010. Find the absolute and percentage change in the the U.S. pop- ulation from 1990 to 2010. Solution reference value = 249 million new value = 308 million absolute change (in millions) = 308- 249 = 59 relative change = 59 249 = . 237 So the percent change is 23 . 7%....
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