Percent and the calculation of percent is essential in daily life. Our percent body fat each of us has determines whether or not we are just plump or obese. click here to access a page to estimate your percent body fat.
Annual inflation in food prices, etc cuts our buying power by about 3% in an average year. click here to access a page on inflation rates.
Every time you use your credit card, borrow money or buy on a time payment contract money is added to the cost based on the percent interest. Bank interest paid on savings accounts tells how much the bank pays for using your money to make loans.
Percent is part of figuring grades in course. click here to check access class grades and point percentages.
Percent is important in chemistry because it ties into the composition of compounds. Every compound has a characteristic percent composition by weight. For example water has the formula H2O with a composition by weight that is 89% oxygen and 11% hydrogen. This helps us identify materials. The percent composition of a compound is an intensive property. It is the same for all size amounts of the compound.
Percent is a code word for analyzing things by comparison using ratios. The mathematical definition is
Percent = 100 x [part of a total] / [sum total of all parts] in other words
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Percent = 100 [ part / total] |
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This chapter stresses unit labels and conversions from one unit to another. The irony is that percent calculations are ratios and they have no units because of this. In percent calculations the units HAVE to be the same in both the top and bottom of the calculation. The unit labels cancel out. Percent really comes down to describing things in terms of parts per hundred. This is true whether you have 100 parts or not. For example one penny is 10 percent of a dime.
Percent = % = 100 x [ 1 penny ] / [1 dime ]
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Percent = % = 100 [ 1 penny ]/[10 pennies] = 10 % |
EXAMPLE |
| The population of the United States was about 300,000,000 people |
| people in 2009. click here to access the US population clock |
| The US population was 285,230,516 people in 2000. What is the percent increase from 2000 to 2009? click here to access 2000 population data |
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| SOLUTION |
| 1. figure the increase in the population 300,000,0000 - 285,000,000 |
| 300,000,0000 people - 285,000,000 people = 15,000,000 people |
| 2. Set up the percent calculation |
| percent increase = 100 [ increase people ] / [total people] |
| 3. % increase = 100 [ 15,000,000 people ] / [300,000,000 people] |
| 4. % increase = 100 [0.05] = 5% |
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EXAMPLE |
| Mark McGwuire, Big Mac, played baseball for the St Louis Cardinals. In 1998 he hit a total of 70 homeruns and set a new homerun record. (it has been broken by Barry Bonds). If McGwuire had 509 at bats, on average what percentage of his at bats produced a homerun? |
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| SOLUTION |
| 1. figure the at bats that resulted in a homerun 70 homeruns at bats |
| 2. figure the total of at bats 509 at bats |
| 3. Set up the percent calculation |
| percent homerun at bats = 100 [ 70 homerun at bats] / [ 509 total at bats] |
| 4. % homerun at bats = 100 [ 70 ] / [ 509 ] |
| 5. % homerun at bats = 100 [0.139] = 13.9 % |
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EXAMPLE |
| An adult patient has a body weight of 185 pounds. A percent body fat measurement was done using the total underwater immersion method. |
| The test indicated the patient has 26% body fat. How many pounds of fat does this patient have in his/her body? It is estimated that a US typical adult has 18% body fat. |
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| SOLUTION |
| 1. percent body fat = 100 [ pounds body fat ] / [ pounds body weight ] |
| 2. The unknown is the pounds of body fat |
| 3. The 26% body fat means the person has 26 lb body fat / 100 lb body weight |
| 26 lb fat / 100 lb body weight = x lb body fat / 185 lb body weight |
| 4. x lb body fat = (185 lb body weight )(26 lb body fat / 100 lb body weight) |
| 5. x pounds body fat = 185 [ 0.26 ] = 48.1 pounds body fat |
6. We need to round off the answer to two significant figures 48 lb
Click here for more about normal % body fat |
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