Chapter Vocabulary Co Curricular Data Analysis Review Base Unit Second (s) Meter (m) Kilogram (kg) Kelvin (K) Derived unit Liter Density Scientific notation Dimensional analysis (Equality) not in book Conversion factor Accuracy Precision Significant Figures Chapter Analyzing Data Units of measure Base units: A defined unit in a system of measurement that is based on an object or event in the physical world and is independent of other units. Examples: time (sec), mass (gram), length (meter) Derived units: combinations of base units such as volume (length 3 ), velocity (length/time), and density (mass/volume). Temperature: Either Celsius (⁰C) or Kelvin (K). It is notation used to express very large or very small numbers using powers of 10. Proper format: (1 Number<10) x 10 n Examples 175 L = 1.75 x 10 L 15,000,000 g = 1.5 x 10 7 g 0.00000000530 m = 5.30 x 10-9 m 3 4 and Commonly Used Metric Prefixes Prefix Symbol Meaning Factor Makes Unit BIGGER! mega M 1 million times larger than the unit it precedes 10 6 kilo k 1000 times larger than the unit it precedes 10 3 Makes Unit smaller! deci d 10 times smaller than the unit it precedes 10-1 centi c 100 times smaller than the unit it precedes 10 - milli m 1000 times smaller than the unit it precedes 10-3 micro μ 1 million times smaller than the unit it precedes 10-6 nano n 1 billion times smaller than the unit it precedes Examples: 1 kilometer = 1000 meters 1 millimeter = 0.001 meters (10-3 m) 10-9 5 Metric Units of Length Comparison Unit Symbol Relationship Example kilometer km 1 km = 10 3 m Length of about 5 city blocks 1 km 10-3 km = 1 m meter m Base unit Height of doorknob from the floor 1 m decimeter dm 10 1 dm = 1 m Diameter of a large orange 1 dm 1 dm = 10-1 m centimeter cm 10 cm = 1 m Diameter of a shirt button 1 cm 1 cm = 10 - m millimeter m 10 3 mm = 1 m 1 mm = 10-3 m Thickness of a dime 1 mm Micrometer μ 10 6 μm = 1 m 1 μm = 10-6 m nanometer n 10 9 nm = 1 m 1 nm = 10-9 m Diameter of a bacteria cell 1 μm Human hair 5 μm Thickness of RNA molecule 1 nm Example: 13,000 m = 13 x 10 3 m = 13 km 6 1
Metric Units of Volume Comparison Metric Units of Mass Comparison Unit Symbol Relationship Example Liter L Base unit Quart of milk 1 L milliliter ml 10 3 ml = 1 L 1 ml = 10-3 L 0 drops of water 1 ml Cubic centimeter cm 3 or cc 1 cm 3 = 1 ml 10 3 cm 3 = 1 L microliter μl 10 6 μm= 1 L 1 μm = 10-6 L Cube of sugar 1 cm 3 Crystal of table salt 1 μl Drop of water from a needle 1 μl Example: Break up number into groups of 3. 0.000005 L = 0.000 005 L = 5 x 10-6 L = 5 μl (10-6 ) 7 Unit Symbol Relationship Example kilogram kg 1 kg = 10 3 g A small textbook 1 kg gram g Base unit Dollar bill 1 g milligram mg 10 3 mg = 1 g Ten grains of salt 1 mg microgram μg 10 6 μg = 1 g 1 particle of baking powder 1 μg Example 1: 43,000 g = 43 x 10 3 g = 43 kg Notice we are not putting in proper scientific notation, but in an order of magnitude that corresponds to a prefix. Example : 0.0000033 g = 3.3 x 10-6 g = 3.3 μg 8 Practice Express in Scientific notation: 38000 m 5060 s 0.0054 g Convert: 4500 m to km 0.00000533 g to μg 777 μl to L Unit to measure: Thickness of a quarter? Mass of a car? Volume of soda can? 3.8 x 10 4 m 5.06 x 10 3 s 5.4 x 10-3 g 4.5 km 5.33 μg 777 x 10-6 L or 7.77x10-4 L mm (millimeter) kg (kilogram) ml (milliliter) Addition and Subtraction 1. Make sure numbers are in the same order of magnitude (You don t have to have them in proper format to add and subtract.). Then add or subtract as usual, carry down the exponent and the unit. 9 10 Addition and Subtraction Example Add 3.553 x 10 4 ft+. x 10 3 ft 3.553 x 10 4 ft + 0. x 10 4 ft 3.775 x 10 4 ft Subtract 4.753 x 10 6 m 8.5 x 10 5 m 47.53 x 10 5 m - 8.5 x 10 5 m 39.01 x 10 5 m 11 Rules of Exponents You can use the Rules of Exponents to multiply or divide numbers in scientific notation. The Rules of Exponents: (10 m )(10 n ) = 10 m+n (10 m ) n = 10 m*n 10 m /10 n = 10 m-n 10 -m = 1/10 m 10 0 = 1 1
Multiplication and Division For multiplication, multiply the two first factors, then add the exponents. Multiply the units too. Ex: (6.5 x 10 ft)(.0 x 10 ft) = 13 x 10 4 ft or 1.3 x 10 5 ft For division, divide the two first factors, than subtract the denominator from the numerator. Keep units in same position. Ex: 1.5 x 10 4 g 3.0 x 10 3 cm 3 = 1.5/3.0 x 10 1 g/cm 3 = 0.50 x 10 1 or 5.0 g/cm 3 More Practice Solve: 5 x 10-5 m + x 10-5 m 7 x 10-5 m 1.6 x 10 4 kg +.5 x 10 3 kg 1.51 x 10 4 kg 5.36 x 10-1 kg 7.40 x 10 - kg 4.6 x 10-1 kg (4 x 10 cm) x (1 x 10 8 cm) 4 x 10 10 cm (6 x 10 g) / ( x 10 1 cm 3 ) 3 x 10 1 g/cm 3 13 14 Dimensional analysis is a method of problem solving that focuses on the units to describe what you are looking at. 15 It uses a conversion factor, which is the ratio of equivalent values (equalities) used to express the same quantity with different units. Example: 1 mile = 580 ft so 1 mile = 1 and 580 ft = 1 580 feet 1 mile When using them, put the unit given in the denominator and the unit you want in the numerator. New Unit Old (Given) Unit 16 If you are using a derived unit, such as density, the equality will show the relationship between units that measure different properties. Example: If the density of iron is 7.87 g/cm 3, that really means: Every 7.87 g of iron will take up 1 cm 3 Or 7.87 g = 1 cm 3 (for iron) Remember that units work like variables. Example:.54b 8.00a * 0. 3b a.54cm 8.00in* 0. 3cm 1in Same as: 17 18 3
Remember that units work like variables. Example: 1b 1b 3.50a * * 0.00350 b 100 a 100 a Same as: cm 1m 1m * 0.00350 100cm 100cm 3.50 * m Practice Convert: 1.0 feet to inches 1.5 meters to centimeters 500 cm to m 65 miles/hr to ft/s 144 inches 150 cm 0.5 m 95 ft/s 19 0 Reliability of Measurements With scientific measurements, you want to know accuracy, precision and certainty. Accuracy How close a measurement is to an accepted value Precision How close a measurement is to other measurements of the same thing. Reliability of Measurements Percent Error How far you are off from an accepted measurement. Percent Error Error Accepted Value x100 Error = obtained value accepted value The error is the absolute difference. It doesn t matter if the error is above or below the accepted value. 1 Accuracy Example A student runs an experiment three times and obtains values of 6.54 g, 6.60 g, and 6.65 g. Ideally, they should have gotten 6.55 g as a result. Determine the overall accuracy of the experiment. The average of the three results is: 6.54 + 6.60 + 6.65 = 6.60 g 3 6.60 6.55 x 100 = 0.7% error 6.55 Precision Example A. One set of balances give the following readings: 10.05 g, 9.9 g, 10.77 g for a 10.00 g mass. B. Another set of balances give these readings: 9.95g, 10.0 g, and 10.00 g. Which set, A or B, is more precise? 3 4 4
Significant Figures (Sig Figs) For any measured value, sig figs are all of the certain digits plus an uncertain digit. The last digit is an estimate and is off by at least +1. Example: 5. really means between 5.1 and 5.3. 10.53 really means between 10.5 and 10.54 Significant Figures! 5 6 1. All non zero digits (1,,3,4,5,6,7,8, and 9) are. Trailing zeros to the right of the decimal point are Example 34.554 m has 5 SF s $.00 has 3 SF s, both trailing zero s are 0.05410 has 4 SF s 7 3. Zeros between two significant digits are 4. Zeros used as placeholders are not Example 38.00 kg has 5 SF s 00 m has 1 SF 0.00 g has only 1 SF But, 500. s has 3 SF s 8 Example 5. For numbers in scientific notation, all of the digits before the x 10 n are 6. Counting numbers and defined constants are considered to have an infinite number of significant figures. 5.3 x 10 5 km has 3 SF s 6 coins.54 cm/1 in 9 7. When you add or subtract values, your final answer must have the same number of digits to the right of the decimal place as the value with the fewest number of decimal places. Example: 4.66 km +10.5 km 15.16 15. km 30 5
(Cont d) 8. When you multiply or divide, your final answer can only have the same number of sig figs as the measurement with the fewest sig figs. Example: 3.444 m*.11 m= 7.584 m which becomes 7.6 m Note: For simplicity, report 3 sig figs for all x and / calculations. 9. Figuring out the number of significant figures is the LAST thing you do. If you have more than one step, carry more digits than you think you need while you re doing the calculation. This will minimize errors due to rounding. 31 3 Rounding Rules 1. If the digit to the right of the last significant figure is less than five, do not change the last significant figure. Ex. 4.433 4.43. If the digit to the immediate right of the last significant figure is equal to or greater than five, round up the last significant figure. Ex. 5.446 5.45 Ex. 3.335 3.34 Significant Figure Rules of Thumb When multiplying or dividing, report answer to 3 sig figs. This represents 3 orders of magnitude and your measuring device (meter stick, balance, graduated cylinder, etc.) will give you 3 or 4 sig figs. Start with first nonzero digit and report 3 digits, regardless of where the decimal point is. Example 1: 0.1 g/53.3 ml = 0.00398 g/ml Example : 45.8 mm x 53. mm = 436.56 mm 440 mm Note that 45.7 mm x 53.1 mm = 46.67 mm 430 mm Remember that the last digit represents an estimated value. 33 34 More Practice Convert and give answer w/correct # of sig figs 14. hours to seconds 1.50 ft to in 17.8 ft 3 to gallons 5110 s 5.1 x 10 4 s 16 in 133 gallons Significant Figures why they are important!! Densities of Metals Zinc: 7.14 g/cm 3 Chromium: 7.0 g/cm 3 Iron: 7.87 g/cm 3 Zirconium: 6.51 g/cm 3 Tin: 7.31 g/cm 3 Manganese: 7.47 g/cm 3 Three Student students Mass, measure g the Volume, mass and volume Density, of an g/cm unknown 3 metal. They will try and determine cm 3 which metal it is by its density. 1 14 7 14.1.0 7.1 3 14.14 1.96 7.1 35 36 6