1 PERCENTS Practice Problems We all know, intuitively, what “100%” means. However, a percent is actually a ratio, parts per hundred parts. It is a commonly used to express the concentration of a solution. For example, a solution may be 35% ethanol. Because percents are ratios, we can solve proportions involving percents when calculating how to prepare a laboratory solution. For now, let us consider how to convert using percents: 35% is what as a fraction? 35% means 35 parts per hundred, or 35 /100 0.25% is what as a fraction? 0.25% means 0.25 parts per hundred, or 0.25 /100 Express the following as percents: 1. 15/45 2. 2/2 3. 10/100 4. .003/89 5. 0.0078 6. 0.50 Express the following percents as fractions: 1. 0.5% 2. 75% 3. 28.3% 4. 0.005% Express the following percents as decimals: 1. 63% 2. 0.28% 3. 100% 4. 0.05% 2 PERCENT ERROR Percent error is one of the most commonly used applications of percents in the biotechnology laboratory to express the correctness of experimental results. How does this work? Imagine that you are given a small object that weighs exactly 5.00 grams. In order to test your ability to use a balance in the lab, you weigh the 5.00 gram object five times and get the following values: 5.00 grams 4.99 grams 5.01 grams 4.99 grams 4.98 grams Clearly there is some error in your measurements because you did not get 5.00 grams each time you weighed the 5.00 gram object. So, what do we do next? First, we can determine an experimental weight for the object by averaging the values: (5.00 g) + (4.99 g) + (5.01 g) + (4.99 g) + (4.98 g) = 4.99 grams 5 Now we can determine the percent error, which will reflect how accurate our weighing procedure was: % error = experimental value – true value X 100% true value So here, % error = 4.99 grams – 5.00 grams X 100 % = -0.2% 5.00 grams 3 EXAMPLE PROBLEM: Meg is weighed at the doctor’s office on a very expensive, well-maintained scale. This scale tells us that Meg weighs 132 lbs. Let us assume that this represents Meg’s true weight. Meg now goes home and weighs herself 6 times on her bathroom scale. She gets the following results: 130 lb 131 lb 129 lb 129 lb 131 lb 128 lb What is the percent error in Meg’s bathroom scale measurements?