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General Studies Science: Help & Review24 chapters | 338 lessons | 1 flashcard set

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Lesson Transcript

Instructor:
*Sarah Friedl*

Sarah has two Master's, one in Zoology and one in GIS, a Bachelor's in Biology, and has taught college level Physical Science and Biology.

Calculating a missing value in an equation is something you may come across in your scientific analyses. As long as you know the relationship between the variables in the equation, as well as the rest of the measured values, this is a relatively straightforward process for you to master.

As a scientist, a very useful skill to have is to be able to determine unknown values from known ones. In fact, this happens quite frequently as you work through data collection and analysis. For example, you may wish to know the density of an object, but you only know its mass and its volume. Or, maybe you want to know how fast something is travelling (its speed), but only know the distance that object travelled and the time it took to do so.

What's great is that as long as you know the other values, you can easily calculate the missing one by using simple mathematic relationships. Sometimes you may need to reorganize your formulas to get the known values together. But after you've done this, you're free to calculate away!

Let's take a look at some examples of how we go about determining a **missing value** in an equation, which is any value in the equation that has not been measured or collected by other means. First and foremost, you have to know the formula! You may need to simply memorize some of the more basic ones, while others you can often look up online or in texts.

Next, you need to get all of the known values on the same side of the equation. For example, if you have the equation 2 + *x* = 5, you would subtract 2 from each side to get the unknown value, the *x*, by itself. You end up with 5 - 2 = *x*, and when you solve this you get *x* = 3. Pretty easy, right?

Let's try something a little more relevant. Let's say you have a chunk of copper and you know its density is 8.96 g/cm^3. You also know that the mass of the copper chunk is 25 g. It's not going to be easy to get the volume of your copper piece because there are no 'clean' straight edges to measure along. You could go find a beaker, fill it with water, dunk in the copper chunk, and then measure the volume of water that's displaced. This will certainly get you the volume of your mineral.

But what's easier is to simply calculate the volume from the other known values. You may recall that density = mass / volume. Since we know the density and the mass, we'll need to get the volume alone in the equation. So, we multiply both sides by volume and divide both sides by density, leaving us with volume = mass / density. Plug in our known values and we get volume = 25 g / 8.96 g/cm^3. The grams cancel out, so our volume is calculated to be 2.79 cm^3.

Let's try another one. This time, you know that a racecar was going 125 mph and it took 15 minutes to completely go around the track. What you want to know now is the distance of that track. The same principle applies here. In this case, speed = distance / time, so we rearrange our equation to get distance by itself: distance = speed * time. Now, we plug in our values and solve: distance = 125 m/h * 0.25 h. The hours cancel out, giving us 31.25 miles.

Want to do one more? Okay, this time you have a book sitting on a table. That book exerts 2 pounds of pressure over 1 ft^2, but you want to know the force of the book on the table. This one is really straightforward because force = pressure / area, so you can just plug in your values and calculate without any shuffling of the equation! For the book, then, we have force = 2 pounds/1 ft^2, which comes to 2 pounds/ft^2.

In scientific analysis, we often calculate values based on other data that we've collected. Sometimes we do this because obtaining the unknown value is difficult or time consuming. Regardless of why you're doing it, if you are only missing one value from an equation you can easily determine it through the other known values. It may take a bit of formula rearrangement, but once you've got all the pieces in place you're free to calculate to your heart's content!

After you have reviewed this lesson, you should be able to calculate the missing value in a scientific equation by rearranging a relevant formula.

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General Studies Science: Help & Review24 chapters | 338 lessons | 1 flashcard set

- Identifying Sources of Unavoidable Experimental Error 6:44
- Identifying Potential Reasons for Inconsistent Experiment Results 5:03
- Evaluating Data: Precision, Accuracy & Error 7:02
- Using Appropriate Tools for Scientific Tests & Data Collection 5:37
- Understanding Statistical Variability 7:01
- Importance of Controlled Tests in Scientific Research 4:17
- Understanding Risks & Taking Safety Precautions in Science Experiments 5:47
- Print & Electronic Sources for Scientific Research 8:22
- Scientific Sources: Accuracy, Reliability & Validity 5:45
- Solve for Unknowns in Scientific Equations 4:24
- Go to Using Data for Investigation & Experimentation

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