Video: Learning to Love Laboratory Math

Slide 1: Title

• Welcome to “Learning to Love Laboratory Math”. In this short Skill Blitz, we’ll be reviewing some basic mathematical concepts that you might encounter in the scientific research laboratory. We won’t be able to review every topic comprehensively, so check out the “Resources” document at the end of this presentation for more detailed information if needed. Alright, let’s get started.

Slide 2: Data and numerical fluency is a crucial skill in science

• First, let’s talk about why researchers need to feel comfortable with numbers. It’s not enough to just know about biology, chemistry, physics and other “science” topics in the lab. As scientists, we use calculations to plan and perform experiments. We collect quantitative data and we need to convert those raw numbers into something we can understand and share with others. Of course, not all experiments will work, and when we need to understand what went wrong, it’s useful to know whether the range of tests we’re doing or range of data we’re collecting from the experiment are appropriate.
• For example, imagine you want to test the effectiveness of a drug on cells you’re growing in the lab. You prepare a mixture of the drug and it kills all your cells. So now, you’ll need to play around with the conditions to make sure you’re using the right dose of the drug and you’ll use mathematical calculations to do that.

Slide 3: Topics covered in this skill blitz

• Today, we’ll briefly go over the following topics, which should be familiar to most of you.
• We’ll start with scientific notation and exponents, then units of measurement followed by molecular weight and molarity.
• Then we’ll see how these are all used in some basic lab business like preparing solutions and serial dilutions.

Slide 4: Topics not covered in this skill blitz

• There are some additional topics that you should be familiar with but we won’t be able to go over for the sake of time here.

Slide 5: Exponents explained!

• Exponents are just a simple way to write how many times a number is multiplied by itself. (Give example)
• Exponents can be positive or negative. A negative exponent is just a way to write the inverse of the positive exponent. (Give example)
• Remember, that a negative exponent does NOT indicate a negative number.
• Then there are some special rules; any number raised to the 1^st power equals itself and any number to the 0^th power equals 1.

Slide 6: Research often uses powers of ten

• Exponents are used in research because they are fast to write and any number can be written as a power of ten.
• “Scientific notation” specifically means writing numbers as SOMETHING times ten to the SOMETHING power.

Slide 7: Measuring with the metric system

• In our daily lives in the United States, we are used to the US customary system of measurements. We measure weights in pounds and volumes in gallons. However, in the lab, we use the metric system which is based on the powers of ten. The metric units for length, mass, volume and amounts or “counts” are shown in the table.
• One unit of measurement we don’t always think about in our daily lives is a standard unit to count things.
• In the metric system the number of particles are counted in units of “moles”. These particles can be atoms, ions, or molecules.
• 1 mole is a very specific number- 6.02 x 10^23 particles, which you may be familiar with as “Avogadro’s number”.
• If we had a mole of jelly beans, well, that would be a LOT of jelly beans. Way more than could fit in this jar. But molecules are very very small, so a mole of something like a sugar molecule is actually something you could measure in the lab.

Slide 8: Measuring with the metric system

• The metric system is useful because common prefixes are related to each other by powers of ten. This makes it easy to convert between them and to refer to large and small numbers using the scientific notation system we just talked about.
• Everything starts relative to the “base unit” which would be “liter”, “gram”, “meter” or “mole”. Quantities that are larger than this base unit are referred to with the prefixes “Kilo”, “Mega”, “Giga”, and “Terra” and quantities that are smaller begin with “Milli”, “Micro”, “Nano” and “Pico”. Notice that all of these prefixes also have shorter abbreviations.

Slide 9: Calculating conversions between units

• Here’s an example of converting between different units of measurement. Let’s go through this step-by-step.
• First, determine how you want to express the number. Do you want to report something in MILLImeters or MICROmeters.
• Then, figure out how those two quantities are related-”the conversion factor”
• Next, write out the expression and multiply out.
• Double check by making sure you have the right unit.

Slide 10: Calculating conversions between units

• Here’s another example of converting between different units of measurement. Let’s go through this step-by-step.

Slide 11: Solutions are homogenous mixtures

• When you walk into most “wet bench” laboratories, one of the first things you’ll see are bottles of different solutions. Making solutions is a routine part of many research labs. Remember that solutions are mixtures of two or more substances. The most common types of solutions you may encounter in the lab are mixtures of two or more liquids, a solid and a liquid or mixtures of gases. We encounter solutions in everyday life as well. Lemonade for example, is a mixture of water (a liquid), lemon juice (another liquid) and sugar (a solid).
• An important characteristic of solutions is the concentrations of the different solutes and the different ways of describing a concentration are shown in the table.

Slide 12: Making a simple solution

• Let’s make a simple solution.

1. Determine the final desired volume of the solution
2. Determine the total amount of solute needed for desired concentration
3. Use molecular weight to convert to molarity, if needed

Slide 13: Simple solution for making dilutions

• Sometimes in the lab, you don’t need to make a solution from scratch. Instead there is already a concentrated solution that you need to dilute in order to use for your experiment. This is useful because diluting a stock solution is easier than making a solution that would require weighing out very tiny amounts of a substance. But how do you know how much to dilute to get to your desired “working concentration”? There is a simple equation to help with that called “C1V1” = “C2V2”.
• C1 represents the concentration of your stock solution.
• V1 is the VOLUME of the stock solution you will need.
• C2 represents the concentration of your working solution, this is the solution you need for your experiment.
• V2 represents the VOLUME of the working solution. You’ll want to make enough of your working stock for however much your experiment needs. Plus a little extra.
• We can easily solve this equation because 3 out of the 4 variables are known.

Slide 14: Simple solution for making dilutions

• Let’s walk through an example. How would you make 100 mL of a 250 mM solution of glucose? We already have a stock of 1M on our shelf.
• In order for this equation to work, the units of all the variables have to be the same.
• Therefore, we’ll convert 250mM to molar. There are 1000 milimoles in 1 mole so we have 0.25 Molar.
• Next, we’ll write out the equation, filling it what we know.
• We know the stock concentration.
• We know the working concentration.
• We know the final working volume.
• We rearrange the equation to solve for our unknown which is the volume of the stock solution we will need.
• We solve the equation to find that the volume is 25 mL.
• Now don’t forget we’re making a dilution, so we’ll take the 25 mL of the stock and DILUTE it with 75 mL water to make a final volume of 100 mL

Slide 15: Solving problems with serial dilutions

• One useful application is serial dilutions. These are repeated dilutions of a solution and usually the dilution factor, or the amount the solution is diluted from one tube to another is constant. Some examples of using serial dilutions in the lab include when you have to make a highly diluted solution from a concentrated stock and it’s not practical to do it in a single step. Another time is when you need to test a range of concentrations.
• Recall the experiment where we treated something with a drug and it killed everything. We could prepare a serial dilution of the drug and THEN treat with all the dilutions to find the right dose.
• Another example is when you need to prepare a standard curve where the concentration of the standard is known and you use that to figure out the concentration on an unknown sample.
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Slide 16: Setting up a serial dilution

• Here is an example of how you would set up a ten-fold serial dilution. “Ten-fold” here means that the dilution factor is a factor of 10. Each tube is 10 times more dilute than the one before it. Microliters are fairly small volumes and you use a pipette to measure these volumes.
• You can see that by the end of the serial dilution you went from a 1M stock solution to a 0.0001 M or 100 micromolar.
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Slide 17: Topics covered in this skill blitz

• Just to review; these are the topics we covered today
  • Scientific notation and exponents
  • Units of measurement
  • Molecular weight and molarity
  • Preparing solutions and serial dilutions.
• Check out the National Institutes of Health Office of Intramural Training and Education’s Youtube Channel for their “Resources for Young Scientists” series for more examples laboratory math.