Do Now: Convert using dimensional analysis. Show work! 1. Diovan is used to treat patients who have high blood pressure and who are at risk for heart failure. According to the drug label, the dosage strength per tablet is 80 mg. How many grams (g) are in each tablet? 2. Xanax is used to treat anxiety and panic disorders. The dosage strength for each tablet is 0.5 mg. How many micrograms (µg) are there in each tablet? 3. Wellbutrin is a common pharmaceutical used to treat depression. According to the drug label, the dosage strength per tablet is 75 mg. If a patient needs to take 1 tablet, 3 times a day (t.i.d.), then how many total grams (g) of Wellbutrin is the patient taking each day? 4. Zyvox is an antibiotic which treats bacterial infections which can become resistant to other antibiotics, such as pneumonia, urinary tract infection (UTI), and skin infection. If the dosage strength is 100 mg/5 ml, then what is the equivalent in g/l (grams per liter)? Hint: This will require 2 conversions. 5. 0.14 dl = μl 468 dm = km
Scientific Notation: used to express or numbers more easily It is written as a (decimal between 1 & 10) x 10 raised to an exponent ex: 3.2 x 10 3, 7.2 x 10 4 decimal between 1 & 10 10 raised to an exponent How to express a number in terms of scientific notation: 1. Move the decimal point of your number so that you have a decimal between 1 and 10 360,000: 0.00037 360,000. 3.60000 0.00037 3.7 *Note: if no decimal point is written, the decimal point is at the end of the number! 2. Count the number of spaces (n) and which direction you moved the decimal point 360,000 3.60000: 5 decimal places to the left 5 4 3 2 1 0.00037 3.7: 4 decimal places to the right 1 2 3 4 3. If you moved the decimal point to the left multiply (x) your decimal by 10 n: 360,000 3.6 x 10 5 If you moved the decimal point to the right, multiply (x) your decimal by 10 n: 0.00037 3.7 x 10 4 Practice: Write the following numbers in terms of scientific notation 1) 198,000,000 3) 7200 2) 0.000023 4) 0.0000047 How to express a value given in scientific notation as a normal number: 1. Identify the exponent 3.6 x 10 5 : exponent 5 3.7 x 10 4 : exponent 4 2. If the exponent is a positive number, move the decimal point the same number of places to the right 3.6 x 10 5 : move decimal 5 places to the right: 3.6_._._._. 360,000 1 2 3 4 5 If the exponent is a negative number, move the decimal point the same number of places to the left. 3.7 x 10 4 : move decimal 4 places to the left:._._._.3.7 0.00037 4 3 2 1 Practice: Write the following scientific notation expressions as a normal number 1) 9.3 x 10 7 2) 1.7 x 10 4 3) 1.03 x 10 3 4) 3.937 x 10 5
Dimensional Analysis Continued: Non SI-SI conversions: MULTIPLE STEPS! Ex 1: Let s revisit the problem: How many breaths do you think you take in a lifetime? Let s start with how many breaths you take in 1 minute Ex 2: Measure the number of beats your heart makes in 30 seconds. Determine your cardiac output in ml of blood per minute. Assume your heart pumps 70 ml of blood per beat (this is known as the stroke volume). Assume your body contains 5 L of blood. How long does it take in minutes to pump all of your blood around your body once? Ex 3: You re traveling from the US to Europe to China. You have $1000 (US currency) left over in the form of Euros. You take these Euros to exchange them for RMB when you land in China. How much money in RMB should you expect to receive? Assume $1 US = 0.76 Euros and 1 Euro = 8.12 RMB.
Unit Conversion Activity Use dimensional analysis to answer each of the following questions. Show your work for each calculation. Express your final answer as both normal and scientific notation. Station 1: Length of Pencil Find the length of a pencil in miles. There are 1.6 kilometers in a mile. Station 2: Mass of a paper clip Find the mass of a paper clip in tons. There are 2.2 pounds in a kilogram and 2000 pounds in a ton. Station 3: Volume of water in a graduated cylinder Find the volume of the water in the graduated cylinder in gallons. There are 3.78 liters in a gallon.
Station 4: Area of a block (the largest side) Find the area of a block in square meters. *Note: For this problem you must convert cm 2 into m 2, so you need to cancel out the unit cm twice (since cm 2 =cm x cm)! Station 5: Speed to WALK from this room to the bathroom. Measure the distance from the front door of this room to the front door of the bathroom. (Assume 1 tile = exactly one foot). Using a stopwatch, time how long it takes you to WALK from this classroom to the bathroom. a. Calculate your speed in feet per second. b. Convert your speed (from a) into miles per hour. There are 5280 feet in a mile. c. Convert your speed (from a) into meters per second. There are 2.54 centimeters in an inch.
*Accuracy= (Bull s eye!) To determine accuracy, we look at the of our results. *Precision= To determine precision, we look at the of our results. When you do an experiment and analyze your results, there are 4 possibilities: Accurate=Bull s Eye Precise=Again and again and again Determining Accuracy and Precision of Results from Scientific Experiments Example: Measuring 1. Look at the Vitamin C in Orange and ask yourself, are the results Juice (Actual (close to the right Answer=100 mg)-- answer)? Tropicana claims that each cup of orange juice has Cup # Amount of Vitamin C 100 mg of Vitamin 1 30 mg C. Julia did an 2 50 mg experiment to see 3 70 mg whether this was Average 50 mg true. Her results are shown in the table. Are Julia s results accurate? 2. Look at and ask yourself, are the results (did the experimenter get about the same answer each time)? Cup # Amount of Vitamin C 1 30 mg 2 50 mg 3 70 mg Average 50 mg Are Julia s results precise? Practice: 1. Measuring Blood Glucose (Actual Answer = 100 mg/dl) Bayer HealthCare is testing a new glucose meter to be sold to the public. They tested a standard solution that contains 100 mg of glucose/dl of liquid. The results are shown below. Trial # Amount of Glucose 1 98 mg/dl 2 99 mg/dl 3 100 mg/dl Average 99 mg/dl 1. Are the results accurate? 2. Are the results precise?
2. Measuring Blood Glucose (Actual Answer = 100 mg/dl) The workers at Bayer wanted to add a new feature to the glucose meter. They tested the meter with the added feature in the same 100 mg/dl standard in the example above. The results are shown below. Trial # Amount of Glucose 1 79 mg/dl 2 99 mg/dl 3 119 mg/dl Average 1. Are the results accurate? 3. Measuring Iron in Cereal (Actual Answer = 18 mg) Total claims that each serving of cereal contains 18 mg of iron. Bob did an experiment to see if this was true. His results are shown below. Trial # Amount of Iron 1 5 mg 2 4 mg 3 5 mg Average 1. Are Bob s results accurate? 2. Are Bob s results precise? 2. Are the results precise?