Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Chapter 1 Measurement F. Morales 1 CHAPTER OUTLINE Scientific Method Measurements/SI Units Volume & Density Conversion of Units Scientific Notation Significant Figures 2 The Nature of Science —Scientific Method - Science is NOT a body of knowledge, but a method to understand nature & how it works Results Science accepts nothing on faith CONTRADICT: descard The ultimate judge is always the experiment Many observations over time Hypothesis From trends, we come up w/Models or HYPOTHESIS Require further testing, EXPERIMENT Results AGREE w/prediction: Hypothesis needs to survive more experiments to be accepted as a good description of nature 3 SCIENTIFIC METHOD The scientific method is a process of creative thinking and testing aimed at objective and verifiable discoveries. Knowledge gained through the scientific method is self-correcting and improves over time. 4 MEASUREMENTS SI UNITS Measurements are made by scientists to determine size, length and other properties of matter. For measurements to be useful, a measurement standard must be used. A standard is an exact quantity that people agree to use for comparison. SI is the standard system of measurement used worldwide by scientists. 5 SI BASE UNITS Quantity Measured Units Symbol Meter m Mass Kilogram kg Time Seconds s Temperature Kelvin K Electric current Ampere A Mole mol Candela cd Length Amount of substance Intensity of light 6 DERIVED UNITS In addition to the base units, several derived units are commonly used in SI system. Quantity Measured Units Symbol Volume Liter L Density grams/cc g/cm3 7 VOLUME Volume is the amount of space an object occupies. Common units are cm3 or liter (L) and milliliter (mL). 1 L = 1000 mL 1 mL = 1 cm3 8 DENSITY Density is mass per unit volume of a material. Common units are g/cm3 (solids) or g/mL (liquids). Density is indirectly related to the volume of an object. Which has greatest density? Density is directly related to the mass of an object. 9 CONVERSION OF UNITS The SI system of units is easy to use because it is based on multiples of ten. Common prefixes are used with the base units to indicate the multiple of ten that the unit represents. Prefixes megakilocentimillimicro- Symbol M k c m Multiplying factor 1,000,000 1000 0.01 0.001 0.000,001 10 CONVERSION OF UNITS How many cm mmare areininaakm? cm? 100000 10x10x10x10x10 10 or 105 11 CONVERSION OF UNITS Any unit can be converted into another by use of the appropriate conversion factor. beginning unit x final unit = final unit beginning unit Conversion factor 12 Example 1: The length of a football field is 100 yards. What is the length of the field in meters? (1m = 1.094 yd) m 1 = 91.4 m 100 yd x 1.094 yd 13 Example 2: The thickness of a book is 2.5 cm. What is this measurement in mm? 2.5 cm x 10 mm = 25 mm 1 cm 14 Example 3: How many centimeters are in 2.0 ft? (1 in = 2.54 cm) ft ® in ® cm 12 in x 2.0 ft x 1 ft 2.54 cm = 61 cm 1 in 15 Example 4: How many seconds are there in 1 day? day ® hr ® min ® sec 24 hr 1 day x x 1 day 60 1 min s 60 x 1 min hr = 86400 s 16 Example 5: If the density of gold is 19.3 g/cm3, how many grams does a 5.00 cm3 nugget weigh? 5.00 cm3 x g 1 cm 3 19.3 = 96.5 g 17 Example 6: What volume of mercury has a mass of 60.0 g if its density is 13.6 g/mL? 1 mL = 4.41 mL 60.0 g x 13.6 g 18 IS UNIT CONVERSION IMPORTANT? In 1999 Mars Climate orbiter was lost in space because engineers failed to make a simple conversion from English units to metric, an embarrassing lapse that sent the $125 million craft fatally close to the Martian surface. Further investigation showed that engineers at Lockheed Martin, which built the aircraft, calculated navigational measurements in English units. When NASA’s JPL engineers received the data, they assumed the information was in metric units, causing the confusion. 19 SCIENCTIFIC NOTATION Scientific Notation is a convenient way to express very large or very small quantities. Its general form is A x 10n coefficient n = integer 1 < A < 10 20 SCIENTIFIC NOTATION To convert from decimal to scientific notation: Move the decimal point so that it’s located after the first nonzero digit. Follow the new number by a multiplication sign and 10 with an exponent (power). The exponent is equal to the number of places that the decimal point was shifted. 75000000 7.5 x 10 7 21 SCIENTIFIC NOTATION For numbers smaller than 1, the decimal moves to the left and the power becomes negative. 0 00642 6.42 x 10 3 22 Example 1: Write 6419 in scientific notation. decimal after first nonzero digit power of 10 6419. 6.419 x 103 23 Example 2: Write 0.000654 in scientific notation. decimal after first nonzero digit power of 10 -4 0.000654 6.54 x 10 24 CALCULATIONS WITH SCIENTIFIC NOTATION To perform multiplication or division with scientific notation: 1. Change numbers to exponential form. 2. Multiply or divide coefficients. 3. Add exponents if multiplying, or subtract exponents if dividing. 4. If needed, reconstruct answer in standard exponential form. 25 Example 1: Multiply 30,000 by 600,000 Convert Multiply Reconstruct Add to exponential exponents coefficients answerform (3 x 104) (6 x 105) = 18 x 10 9 1.8 x 1010 26 Example 2: Divide 30,000 by 0.006 Convert Subtract Reconstruct Divide to exponential coefficients exponents answerform 4) (3 x 10 3 4 -3 (3 x 10 ) / (6 x 10 ) = (6 x 10-3) = x 104-(-3) 6 = 0.5 x 7 10 5 x 106 27 SIGNIFICANT FIGURES Two kinds of numbers are used in science: Counted or defined: exact numbers; have no uncertainty Measured: are subject to error; have uncertainty Every measurement has uncertainty because of instrument limitations and human error. 28 UNCERTAINTY IN MEASUREMENTS certain certain What is this measurement? uncertain 8.65 8.6 uncertain What is this measurement? The last digit in any measurement is the estimated one. 29 SIGNIFICANT FIGURES RULES Significant figures are the certain and uncertain digits in a measurement. 1. All non-zero digits are significant. 2. All sandwiched zeros are significant. 3. Leading zeros (before or after a decimal) are NOT significant. 4. Trailing zeros (after a decimal) are significant. 0 . 0 0 4 0 0 4 5 0 0 30 Examples: Determine the number of significant figures in each of the following measurements: 461 cm 3 sig figs 1025 g 4 sig figs 0.705 mL 3 sig figs 93.500 g 5 sig figs 0.006 m 1 sig fig 5500 km 2 sig figs 31 ROUNDING OFF NUMBERS If rounded digit is less than 5, the digit is dropped. 51.234 Round to 3 sig figs 1.875377 Round to 4 sig figs Less than 5 Less than 5 32 ROUNDING OFF NUMBERS If rounded digit is equal to or more than 5, the digit is increased by 1. 51.369 51.369 4 5.4505 5.4505 1 Round to 3 sig figs Round to 4 sig figs More than 5 Equal to 5 33 SIGNIFICANT FIGURES & CALCULATIONS The results of a calculation cannot be more precise than the least precise measurement. In multiplication or division, the answer must contain the same number of significant figures as in the measurement that has the least number of significant figures. 34 MULTIPLICATION & DIVISION 3 sig figs 4 sig figs Calculator answer (9.2)(6.80)(0.3744) = 23.4225 2 sig figs The answer should have two significant figures because 9.2 is the number with the fewest significant figures. The correct answer is 23 35 SIGNIFICANT FIGURES & CALCULATIONS The results of an addition or a subtraction must be expressed to the same precision as the least precise measurement. The result must be rounded to the same number of decimal places as the value with the fewest decimal places. 36 ADDITION & SUBTRACTION Add 83.5 and 23.28 Least precise number Calculator answer Correct answer 83.5 23.28 106.78 106.8 37 Example 1: 5.008 + 16.2 + 13.48 = 34.688 7 Least precise number Round to 38 Example 2: 3 sig figs 3.15 x 1.53 2 = 6.1788 0.78 2 sig figs Round to 39 THE END 40