1. Module 1 Biotechnology Basics
Module 1. Biotechnology Basics. Biotechnology programs prepare students to work in the bioscience industry in the areas of research and development, quality systems, production, clinical testing, and diagnostic work. To succeed in biotechnology, it is crucial to be comfortable with the math calculations that are part of everyday lab work.
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2. Lessons for Module 1
1.1 Overview of Biotechnology 1.2 Cell Structure and Function 1.3 DNA Structure and Function 1.4 Protein Synthesis 1.5 Protein Structure and Function 1.6 Math Skills 1.7 Lab Overview
Now that you have a good understanding of molecular biology, there’s just one more thing you need to know before we can begin talking about biotechnology applications. You need a quick math review! The sixth lesson of module 1 will provide a brief overview of the math skills needed by a biotechnician.
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3. Goals for Lesson 1.5 Identify significant figures
Calculate in scientific notation
Convert numbers in the metric system
Describe units of concentration
Perform calculations necessary for preparing stock solutions
Calculate parallel dilution formulas
This lesson is going to teach you how to identify significant figures, calculate in scientific notation, and convert numbers in the metric system. This lesson will also teach you about units of concentration, and how to make and dilute solutions.
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4. Significant Figures
All the numbers for which actual measurements are made plus one estimated number 1 2
You would estimate this measurement as 1.5
First of all, let’s talk about how we take measurements. It is important to make accurate measurements and to record them correctly. No physical measurement is exact, there is always some degree of uncertainty. The number of significant figures in a quantity is an indication of this uncertainty. When recording data, the number of significant figures is the number of known digits plus one estimated digit. For example, look at the top ruler. Let’s say this is a meter stick. What number would you record for this measurement? You know for sure it is between 1 and 2, so the 1 is the accurate digit. But you will have to estimate where it is between the one and the two. I think it looks half-way, so I will record 1.5 m. The 0.5 is estimated. See? Now you try on the second ruler. This time you know for sure it is between 1.4 and 1.5, but you will have to guess how far between. My guess is 1.48, but you may have guessed Do you see how that last number is an estimate? Good! 1 2
You would estimate this measurement as 1.48
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5. Significant Figures
Tells the person interpreting your data about the accuracy of the measuring instrument used to obtain the data
It is important to record your data with the correct number of significant figures because it tells the person interpreting your data about the accuracy of the measuring instrument. For example, on the electronic balance in this picture you would record your data with 2 decimal places, even if the last number is a zero. This brings up an important question. How do you know when zeroes are significant? I’m so glad you asked! Let’s talk about rules for counting significant figures.
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6. Significant Figures Rules for counting sig figs
1. Digits other than zero are always significant.
96 = 2 sig figs
61.4 = 3 sig figs
2. Zeroes between 2 other sig figs are always
significant.
5.029 = 4 sig figs
306 = 3 sig figs
If a number is not zero, it is significant. Period. So in example one, 96 has 2 significant figures and 61.1 has three significant figures. That’s easy, but what about zeroes? Well, if zeroes are sandwiched between 2 non-zero numbers they are significant. So in example 2, has 4 signifcant figures and 306 has three significant figures.
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7. Significant Figures Rules for counting sig figs
Leading zeroes are never significant when they are to the left of non-zero numbers.
= 2 sig figs
= 3 sig figs
Trailing zeroes are only significant if there is a decimal present and they are to the right of nonzero numbers.
100 = 1 sig fig
100.0 = 4 sig figs
= 3 sig figs
It gets a little trickier when zeroes are in front or at the end of a number. Leading zeroes are never significant when they are to the left of non-zero numbers because they are only place holders. So in example 3, only the non-zero numbers are significant. That means that has only two significant figures (the 2 and the 5) and will have three significant figures. The trailing zeroes are a little trickier. The trailing zeroes are only significant if there is a decimal present AND they are to the right of non-zero numbers. So, in example 4a, there is no decimal so those zeroes are not significant. The number 100 has only one significant figure. However, in example 4b the addition of the decimal causes all of the zeroes to be significant. So will have 4 significant figures. In example 4c, the leading zeroes are only place holders and are not considered significant. The zeroes trailing after the decimal point are significant because they tell you that the measurement was taken on an instrument, such as a balance, that goes to 4 decimal places. So has three significant figures. Click on the link to drill yourself on identifying the correct number of significant figures in a given number.
Sig Fig Practice
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8. Significant Figures Rules for calculating with sig figs
In addition and subtraction, the answer should be rounded off so that it has the same number of decimal places as the quantity having the least number of decimal places.
= = 226 (rounded to no decimal places)
2.65 – 1.4 = 1.25 = 1.3 (rounded to 1 decimal place)
In multiplication and division, the answer should have the same number of significant figures as the given data value with the least number of significant figures.
4.60  45 = 207 = 210 (rounded to 2 sig figs)
1.956  3.3 = = 0.59 (rounded to 2 sig figs)
Sometimes you will need to perform calculations on your data. The number of significant figures in your calculation are going to be determined by the data you recorded. When you are adding and subtracting, the answer will be based on the data with the least number of decimal places. Therefore, in example 1a, when you add those two numbers together the sum will have to be rounded to 0 decimal places because the data point 225 does not have any decimal places. So will have to be rounded to In example 1b, the data point 1.4 has only one decimal place, which is the least. That means the answer 1.25 will be rounded to 1.3 so that there is only one decimal place. When you are multiplying and dividing numbers with significant figures, the answer will be based on the data with the least number of significant figures. Therefore, in example 2a, you need to determine the number of significant figures for each data point has three because the zero follows a decimal, it is significant. 45 only has two significant figures. Two is less than three, so the answer 207 will have to be rounded to two significant figures. The answer will be Wait a minute. 210….doesn’t that have 3 significant figures? No! There is no decimal, so the zero is a placeholder, but not significant. The number 210 only has 2 significant figures. In example 2b, the answer will also have to rounded to 2 significant figures because the data point 3.3 has only 2 significant figures, which is the least number of significant figures. So we round to 0.59.
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9. Scientific Notation A way to write very large and very small numbers
A number in scientific notation is written in two parts, the coefficient and an exponent of 10
5 x 1022
coefficient exponent of 10
In biotechnology we often work with numbers that are very small. Our hand gets tired from writing out so many zeroes, plus it’s hard to read, so we write numbers in scientific notation. Scientific notation is a way to write very large and very small numbers. In scientific notation, all numbers are expressed by a coefficient (number between one and 9) multiplied by a power of 10. The exponent tells how many times 10s are multiplied together.
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10. Scientific Notation Changing standard numbers to scientific notation
Numbers greater than 10
Move decimal until only ONE number is to the left of the decimal.
The exponent is the number of places the decimal has moved and it is POSITIVE.
Ex. 125 =
15,000,000,000 =
Numbers greater than 10 are written with a positive exponent. To convert a large number written in standard notation as a number in scientific notation you will need to move the decimal until there is only one number to the left of the decimal. The exponent is the number of places the decimal has moved, and it is positive. So for the number 125, you will have to move the decimal two places to the left. That means the exponent will be 2. To write 125 in correct scientific notation, you will write 1.25 times ten to the second power. To write 15 billion in scientific notation, you need to move the decimal 10 places to the left, so you will write 1.5 times ten to the 10th power.
1.25  102
1.5  1010
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11. Scientific Notation Changing standard numbers to scientific notation
Numbers less than 1
Move decimal until only one number is to the left of the decimal.
The exponent is the number of places the decimal has moved and it is NEGATIVE.
Ex = =
Numbers less than 10 are written with a negative exponent. To convert a small number in standard notation to scientific notation, you will again move the decimal until there is only one number to the left of the decimal. The exponent is still the number of places the decimal has moved, but this time it is negative. So for you will move the decimal 4 places to the right and the number written correctly in scientific notation will be 1.89 times 10 to the negative 4. The example only requires the decimal to move one place to the right, so this number written in correct scientific notation will be times ten to the negative one.
1.89  10-4
5.476  10-1
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12. Scientific Notation Changing standard numbers to scientific notation
To change a number written in incorrect scientific notation:
Move the decimal until only one number is to the left of the decimal.
Correct the exponent. (remember: take away, add back)
Ex  106 =
 10-2 =
If a number is written in incorrect scientific notation, meaning there is more than one number to the left of the decimal, you will move the decimal until there is only number one number to the left of it. You have to change the exponent to reflect the movement of the decimal. So in the first example the decimal moved two places to the left and caused the number to be smaller (from 504 to 5). Therefore, the exponent will need to increase by 2 to reflect this change and the 6 becomes an 8. So times ten to the sixth should be written as times ten to the eighth. In the second example, the decimal has moved 3 places to the right and has caused the number to become larger (from 0 to 8). Therefore, the exponent will need to decrease by 3 to reflect this change and the -2 becomes a -5. So this number written correctly is 8.9 times ten to the negative five.
5.042  108
The coefficient decreased by 2, so the exponent must increase by 2
8.9  10-5
The coefficient increased by 3, so the exponent must decrease by 3
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13. Scientific Notation
Changing numbers in scientific notation to standard notation
If the exponent is (+) move the decimal to the right the same number of places as the exponent.
1.65  101 = 16.5
1.65  103 = 1650
If the exponent is (-) move the decimal to the left the same number of places as the exponent.
4.6  10-2 = 0.046
1.23  10-3 =
Sometimes a number will be written in scientific notation and you will want to convert it to standard notation. If the exponent is positive, you will move the decimal to the right the same number of places as the exponent. In example 1a, 1.65 times ten to the one tells you to move the decimal one place to the right and the number in standard notation is In example 1b, the exponent is 3 so you will need to move the decimal 3 places to the right, so the number in standard notation is If the exponent is negative, you will move the decimal to the left the same number of places as the exponent. So in example 2a, 4.6 times ten to the negative two tells you to move the decimal two places to the left. This number in standard notation is In example 2b, the exponent -3 tells you to move the decimal three places to the left and the number written in standard notation will be Click on the link to practice writing numbers in scientific notation.
Scientific Notation Drill
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14. Scientific Notation Multiplication and division in scientific notation
To multiply numbers in scientific notation
Multiply the coefficients.
Add the exponents.
Convert the answer to correct scientific notation.
Ex: (2  109) x (4  103) = 8 x 1012
A major advantage of scientific notation is that it simplifies the process of multiplication and division. To multiply numbers in scientific notation you just multiply the coefficients and add the exponents. So in the example, 4 x 2 is 8 and the exponent is which is 12. The final answer to this problem is eight times ten to the twelfth.
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15. Scientific Notation Multiplication and division in scientific notation
To divide numbers in scientific notation
Divide the coefficients.
Subtract the exponents.
Convert the answer to correct scientific notation.
Ex: (8.4  106)  (2.1  102) = 4 x 104
To divide numbers in scientific notation you will divide the coefficients and subtract the exponents. So in the example, 8.4 divided by 2.1 is 4 and the exponent will be 6 – 2 which is 4. The final answer is four times ten to the fourth. Click on the link to drill yourself on multiplying and dividing numbers in scientific notation.
Multiplying and Dividing in Scientific Notation
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16. Scientific Notation Addition and Subtraction in Scientific Notation
Before numbers can be added or subtracted, the exponents must be equal.
Ex. (5.4  103) + (6.0  102)
= (5.4  103) + (0.6  103)
= 6.0  103
Adding and subtracting numbers in scientific notation is a little different. The exponents have to be the same before you can add or subtract the coefficients. So in the example, let’s change the exponent of 2 to be a 3 so that it matches the exponent in the first number. Remember the take away/add back rule. If we change the exponent to be one more, we must move the decimal so that the coefficient is one less. Therefore the 6 becomes So now, to add 5.4 times ten to the third with 0.6 times ten to the third, we can just add the coefficients together and keep the exponent the same is 6 and the exponent remains 3. The final answer is 6 times ten to the third.
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17. Metric System Unit of length…..meter (m) Unit of mass ……gram (g)
Unit of volume …liter (L)
Unit of time …….second (s)
Unit of temperature…degrees Celsius (°C)
Whew! That’s a lot of math! Now that you understand about significant figures and scientific notation, let’s move on to talk about the international system of measurement. Did you know that prior to the 1800’s the system of measurements varied from country to country and depended on the body parts of the ruling monarch. For example, a foot was the length of the ruling monarch’s foot. In 1793 a consortium of French scientists gathered to come up with an international system of measurements. This is what we call the SI system of measuring, or the metric system. The SI unit of length is the meter, the SI unit of mass is the gram, the SI unit of volume is the liter, the SI unit of temperature is degrees celsius and the SI unit of time is the second.
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18. Metric System The metric system is based on units of 10. Prefix symbol
Prefix name
Prefix value
Fraction or Multiple
Power G
giga
one billion
1,000,000,000
109 M
mega
one million
1,000,000
106 k
kilo
one thousand
1000
103
BASIC UNIT: m, g, L, 1 10 d
deci
1/10
0.1
10-1 c
centi
1/100
0.01
10-2 m
milli
1/1000
0.001
10-3
micro
1/1,000,000
10-6 n
nano
1/1,000,000,000
10-9
The metric system is very useful because it is based on units of 10. In the chart above you can see that units larger than the base include the kilo, which is 1000 times bigger than the base unit, Mega which is a million times larger and giga which is one billion times larger. Conversely, the units smaller than the base include the deci, which is 10 times smaller, or one tenth the size of a base unit. Centi is 100 times smaller, milli is 1000 times smaller and micro is a million times smaller. We most frequently work on the micro scale in the biotechnology lab. You will get very comfortable converting between milli and micro units. So, how do you do this conversion?
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19. Metric System
Converting measurements within the metric system is a simple matter of multiplying or dividing by 10, 100, 1000, etc.
Even simpler, it is a matter of moving the decimal point to the left or right.
Well, because the metric system is based on units of 10 it is mathematically as simple as multiplying and dividing by factors of 10. Practically it’s as simple as just moving the decimal the correct number of places to the left or the right.
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20. Metric System Ex. 3 mg = 3000 µg Ex. 3 L = 0.003 kL
One way to know where to place the decimal is to draw a "metric line" with the basic unit in the center, marking off six units to the left and six units to the right.
To convert from one unit to another simply count the number of places to the left or right, and move the decimal in that direction that many places.
One way to know how far to move the decimal is to draw a metric line as the one shown here with the base unit in the center and marking off 6 units to the left and right of the base unit. To convert between units, you simply count the number of lines between units and move the decimal that number of places. For example, to convert 3 milligrams to micrograms you will have to move three lines to the right, that means you move the decimal over three places to the right and 3 mg becomes 3000 ug. The example on the left shows how to convert 3 liters to kiloliters. You will need to move 3 lines to the left which means you need to move your decimal 3 places to the left and 3 L becomes kL.
Ex. 3 mg = 3000 µg
Ex. 3 L = kL
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21. Units of Concentration
A solution is a homogeneous mixture of one substance (the solute) dissolved in another substance (the solvent).
Concentration is a ratio of the amount of solute to the amount of solvent.
A common task in a biotechnology lab is preparing solutions. What exactly is a solution? A solution is a mixture of what is dissolved (the solute) and the dissolving medium (the solvent). For example, if you are making koolaid the colored sugar is the solute and the water in the pitcher is the solvent. The concentration of a solution is the ratio of the amount of solute to solvent. It is necessary to prepare solutions with the correct concentration or you can destroy months of hard work in a biotechnology lab.
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22. Units of Concentration
Molarity (M) is the most common unit of concentration
Molarity is an expression of moles/Liter of the solute.
Molarity is the most common unit of concentration. You will often be asked to prepare a given molarity of solution. What does molarity mean? Well, it tells you the number of moles of solute in a liter of solvent.
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23. Units of Concentration
A mole is the SI unit of number of particles and can be used as an expression of the molecular weight of a substance.
So your next question is probably “what is a mole”? Well, it’s not the furry animal wearing sunglasses in the previous slide, it is actually the SI unit of number of particles in one gram of substance. It is a chemistry term that can be used to calculate the formula weight of a substance. In fact formula weight is often called molar mass. The formula weight of an element is recorded on the periodic table. For example, the formula weight of sodium is grams/mole.
The formula weight of an element is expressed as grams/mole
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24. Units of Concentration
The molar mass of a compound can be calculated by adding the molar mass of the individual elements.
To calculate the molar mass of a compound, you simply add the formula weights of the individual elements. So in this example you add the formula weight of sodium (22.990) with the formula weight of chlorine (35.453) to tell you that the molar mass of salt (NaCl) is grams/mole.
= g/mol
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25. Making Solutions g = M x L x molar mass
You just calculated the molar mass of sodium chloride to be g/mol.
To determine how to make a stock solution of sodium chloride, use the formula:
You have to know the formula weight of a compound if you are going to prepare the correct concentration of a solution with that compound. The formula (grams = molarity x liters x molar mass) is used to tell you how much of a compound to use to make a solution with a specific concentration.
g = M x L x molar mass
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26. Making Solutions g = M x L x molar mass
How many grams of NaCl would you need to prepare 500 mL of a 1 M solution?
g = M x L x molar mass
g = (1mol/L) (0.5L) (58.44g/mol)
g = g
For example, if I wanted to make a 500 milliliters of sodium chloride with a concentration of 1 M, how much of the compound would I use? Remember that Molarity actually stands for moles per Liter. That means I’m going to have to convert 500 milliliters to liters. On our metric line, there were three places between milli and the base unit, so we will have to move our decimal three places to the left. That means 500 milliters is 0.5 L. Now we can plug our numbers into our formula. According to my formula, the number of grams I need will be 1M x 0.5L x g/mol. After canceling units and multiplying these three numbers together, I get the answer 29.22g. My balance goes to 2 decimal places, that means that I will weigh out grams of NaCl and add 0.5 L or 500 millilters of water. When making a stock solution, we usually dissolve the solid in about two-thirds volume of water. So that means we would dissolve our g of NaCl in only about 300 mls of water and stir. When it is completely dissolved, we would transfer the solution to a graduated cylinder and bring it to the final volume of 500 milliliters. Click on the link in the bottom right corner for additional practice preparing a sodium chloride solution.
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Making a Solution

27. Diluting Solutions
Once you have made a stock solution, you often will need to dilute it to a working concentration.
To determine how to dilute the stock solution, use the formula:
Great! Now that you’ve made your one molar stock solution of sodium chloride, you may need to dilute it to a different concentration as a working solution. The formula C1V1 = C2V2 is used to figure out this dilution. C2 is the concentration of the new solution you want to make and V2 is the volume of that solution you want to make. C1 is the concentration of your stock solution. The question is “how much of that stock do you need to make your dilution”? That’s why you will usually be solving for V1.
C1 – concentration of stock
C2 - concentration of diluted solution
V1 – volume needed of stock
V2 – final volume of dilution
C1V1 = C2V2
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28. Diluting Solutions
How many milliliters of a 1 M stock solution of NaCl are needed to prepare 100 ml of a 0.05 M solution?
C1 V1 = C2 V2
V1 = (0.05)(100)
V1= 5 ml
If you want to make 100 milliliters (that’s your V2) of a 0.05 M sodium chloride solution (that’s your C2). The concentration of the stock solution is 1M (that’s your C1) How much of that stock solution will you need (that’s your V1)? So to solve for V1, let’s plug our numbers in to the formula and see. Solving for V1 means we have to multiply 0.05 by 100 and divide by 1. That gives us an answer of 5 milliliters. That means we will use 5 milliliters of our stock solution. Can you guess how much water we add to that 5 mls to dilute it? That’s right! We wanted a final volume of 100 mls, so means we will add 95 mls of water to produce our final product of a 0.05 M solution of sodium chloride. Click on the Dilutions tutorial for more practicing diluting solutions.
Dilutions Tutorial
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29. Resources
You are now ready to take the test for Module 1 Lesson 6. If you would like extra practice before you take your exam, click on the review link for an interactive math review. Click on the link for classroom lesson plans related to this lesson. These lesson plans are also available in the resource folder on the Project Share course home page.
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