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?