ࡱ> ;=:j {"bjbjWW 4b=={88888LLLLlL1LLLLL" 0000000$2r508/^088LL0www28L8L0w0ww-/LP2D.00011.6F6(/68/dw001F16 : Introduction to Math CALCULATOR EXERCISE- use your calculator to solve each calculation. Report your answer using exponential notation with three digits. 1. (3.14 x 10-5) (6.112 x 10-1) = (3.22 x 10-3) ( 9.08 x 103) 2. 8.22 x 10-3 + 1.59 x 10-5 = 3. (6.54 x 10-3) - (8.02 x 106) = (5.19 x 103) (7.67 x 10-5) SCIENTIFIC NOTATION To be in scientific notation, a number must written in decimal form with only one nonzero digit to the left of the decimal point and this number must be multiplied by 10 raised to some power. Put the following numbers in scientific notation: a. 0.0045 = b. 3693 = c. 40.4 = d. 0.0000053 = e. 25.6 x 10-3 = e. 636.25 x 105 = Put the following numbers in expanded form: a. 9.35 x 106 = _____ ___ b. 3.10 x 10-8 = _ c. 7.31 x 103 = d. 4.76 x 10-3 = SIGNIFICANT FIGURES Calculators will display a large number of digits, but scientists must only report those that are SIGNIFICANT based upon how the measurements were taken. Reporting too many digits implies a greater degree of accuracy than is true. Use these rules for limiting your answer to the proper number of significant figures. Rules for counting significant figures: A digit is significant if it is a: 1. Nonzero digits Example: 56.239 0.043781 both have 5 sig figs 2. Captive zeros- zeros that are between two nonzero digits, or after a nonzero digit and before a decimal Example: 3.06 404 700. All have three sig figs 3. Trailing zeros-zeros that are after a decimal and after a nonzero digit Example: 0.400 2.50 both have three sig figs 4. An exact number is a number determined by counting or from definitions. They are not used to determine the number of significant digits. Example: 2( 10 cm = 1 dm 1 in = 2.54 cm 1. Indicate how many significant figures are in each of the following numbers: a. 0.0012 b. 437,000 c. 900.0 d. 0.001060 e. 100 f. 1.0 x 102 g. 1.00 x 103 OPERATIONS WITH NUMBERS IN SCIENTIFIC NOTATION 1. Multiplying and dividing- the answer reported must have no more significant figures than the least number of significant figures in the measurements. a. (3.0070)(9020) = _________ b. (20.0)(0.00030)/(5.61)(0.00991) = 2. Adding and subtracting- the result has the same number of decimal places as the least precise measurement (fewest decimal places) used in the calculation a. 30.906 + 22.1= b. 3.02 X 10-2 + 8.543 X 10-3 = Review of the METRIC SYSTEM Working units of the metric (SI) system Length meters(m) Volume liters (L) Mass grams (g) Time seconds (s) Metric Prefixes Kilo Hecto Dekka Base Unit deci centi milli x 10+3 x 10+2 x 10+1 x 100 x 10-1 x 10-2 x 10-3 King Hector Drove Unicorns down chocolate mountain These conversion factors should be memorized.  1 in = 2.54 cm 1 L = 1.06 qt 454 g = 1 lb 1 cm3 = 1 mL VI. DIMENSIONAL ANALYSIS Conversion factors are fractions that express equalities and can be used to convert from one quantity to another. Since the top and bottom of the fraction are always equal, one can invert the conversion factor whenever needed. example: "2.54 cm = 1 in" can be written  EMBED Equation.3  or  EMBED Equation.3  PROCEDURE FOR WORKING PROBLEMS BY DIMENSIONAL ANALYSIS:  Step 1. Start with the measurement, usually has only one unit. Step 2. Multiply by your conversion factor with the starting measurements unit on the bottom so that it will be cancelled out. Step 3. Multiply numerators. Divide by denominators to get an answer. Step 4. Put your answer in scientific notation. Step 5. Round off to the least number of digits in your problem.  EMBED Equation.3  Note: It is assumed that you know these definitions.  Length: 12 in = 1 ft 3 ft = 1 yd 5280 ft = 1 mi Volume: 2 pt = 1 qt 4 qt = 1 gal Mass: 16 oz = 1 lb 2000 lb = 1 ton 1. How many mg in a Kg? 2. How many cm in a dm? 3. How many L in a mL? 4. How many g in a mg? 5. 63.2 mL = daL 6. 5489 mg = cg 7. 0.00063 Km = dm 8. 756 mL = L 9. 0.0064 m = cm 10. 56.23 dg = dag 11. 2.25 Kg = g 12. 761 m = mm 14. 5.23 mL = cm3 Report your answer to 3 significant digits. 15. How many centimeters long is a newborn baby measuring 22.5 in? 16. Calculate the number of liters in 5.03 gal of gasoline. 17. A 175 lb person has 9.00 pints of blood. Calculate his blood volume in liters. 18. The shortest person in the NBA is 5 feet 5 inches. Calculate his height in meters. 19. Calculate the mass of a 1.75 lb brain in kilograms. 20. If your blood sugar level is determined to be 20.5 mg per dL of blood, calculate the number of grams of sugar in 1.00 L of your blood. 21. If the density of mercury is 13.8 g/cm3, calculate the mass in kilograms of 17.4 mL of mercury. 22. Convert the speed of a car going 70.0 mph to km/s. 23. The speed of light is 3.00 X 108 m/s. How many miles can light travel in 2.5 years? 24. Convert 35.5 square inches to square cm. 25. A room contains 684 m3 of air. Determine the volume of the room in cubic feet. 26. A 75.0 kg child is to receive medication at a dosage rate of 10.0 mg of drug per kilogram of body weight. Calculate the number milligrams of medication the child should receive. 27. A medication is supplied in a mixture that contains 7.50 mg of medication per milliliter of solution. The dosage rate is 10.0 mg of active ingredient per kilogram of body weight. Calculate the number of milliliters of medication that should be given to a patient weighing 205 lb. VII. TEMPERATURE SCALES- complete the chart below  FAHRENHEIT F CELSIUS C KELVIN K WATER BOILS   100  WATER FREEZES  32   ABSOLUTE ZERO    0 BODY TEMPERATURE  98.6   ROOM TEMPERATURE  77 25 298 Algebra Practice Solve each equation for x being certain to include the units. 1. (6.00  EMBED Equation.3 )(3.00  EMBED Equation.3 ) = x ( 0.0821  EMBED Equation.3 ) ( 298  EMBED Equation.3 ) 2.  EMBED Equation.3  3.  EMBED Equation.3  4.  EMBED Equation.3 , where R = 8.314  EMBED Equation.3 , T=525  EMBED Equation.3 , and M = 40.02 x10-3  EMBED Equation.3  5. 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