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Chapter 2: Measurements and Calculations

Chapter 2: Measurements and Calculations. Ch 2.1 Scientific Method. Steps to the Scientific Method (1) Make observations-- Use your 5 senses to gather information. (2) Propose a hypothesis-- Make an “educated guess” for what is happening.

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Chapter 2: Measurements and Calculations

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  1. Chapter 2: Measurements and Calculations

  2. Ch 2.1 Scientific Method Steps to the Scientific Method (1) Make observations-- Use your 5 senses to gather information. (2) Propose a hypothesis-- Make an “educated guess” for what is happening. (3) Perform experiments-- This tests your hypothesis. Many experiments are sometimes needed to test a hypothesis. The same experiment must give similar results if the experiment is to be reliable. (4) Make a theory-- This should explain the results of your experiments. Theories may change or be rejected over time because of results from new experiments.

  3. Models: are a part of theory that is an explanation of how phenomena occur and how data or events are related. • Qualitative Data: non-numerical data (ex. Green car) • Quantitative Data: numerical data (ex. 12 cars)

  4. Ch 2.2 Measurement

  5. Every measurement must have a unit.

  6. Base Units • There are 7 base units in SI. • A Base unit is a defined unit in a system of measurement that is based on an object

  7. Metric System • An easy way to move within the metric system is by moving the decimal point one place for each “step” desired • Example: change meters to centimeters • Use Prefixes!!! To convert to a smaller unit, move decimal point to the right or multiply. Kilo 1000 Hecto 100 Deka 10 Basic Unit Deci 10 To convert to a bigger unit, move decimal point to the left or divide. Centi 100 Milli 1000

  8. Metric System • 400000 centimeters = _________kilometers • 500 kilometers = __________meters To convert to a smaller unit, move decimal point to the right or multiply. Kilo 1000 Hecto 100 Deka 10 Basic Unit Deci 10 To convert to a bigger unit, move decimal point to the left or divide. Centi 100 Milli 1000

  9. Derived Units A unit that is defined by a combination of base units is called a derived unit. Examples are Area, Volume, Density, Molar Mass, Molar Volume, and Energy. The two derived units we will be working with in this chapter are volume and density.

  10. Volume Volume is the space occupied by an object. The derived unit for volume is the cubic centimeter (cm3); used for solid objects. Liters (L) are used to measure the amount of liquid in a container. For the smaller quantities of liquids, volume is measured in milliliters (mL). 1 mL = 1 cm3

  11. Density • Density is a ratio that compares the mass of an object to its volume • The units for density: • grams per cubic centimeter(g/cm3) for solids • grams per milliliter (g/mL) for liquids

  12. The density of an object will determine if it will float or sink in another phase. If an object floats, it is less dense than the other substance. If it sinks, it is more dense. • The density of water is 1.0 g/ml.

  13. Example 1 A sample of aluminum metal has a mass of 8.4 g. The volume of the sample is 3.1 cm3. Calculate the density of aluminum. Answer 2.7 g/cm3

  14. A conversion factor is a ratio of equivalent values used to express the same quantity in different units.

  15. A conversion factor is always equal to 1. • Because a quantity does not change when it is multiplied or divided by 1, conversion factors change the units of a quantity without changing its value. • This is also known as dimensional analysis and it will be used a lot throughout the year. The key to doing dimensional analysis is making sure that your units cancel out!

  16. Example 2 • Express a mass of 5.712 grams in milligrams and kilograms • Grams to milligrams 1 g = 1000 mg • Grams to kilograms 1 kg = 1000 g

  17. Answer • 5712 mg • 0.005712 kg

  18. Temperature • The temperatureof an object is a measure of how hot or cold the object is relative to other objects. • Temperature scales - scientists use two temperature scales • Celsius (oC) scale was devised by Anders Celsius • Freezing point of water – 0 oC • Boiling point of water – 100 oC • the Kelvin (K) scale was devised by William Thomson and is the SI base unit of temperature • On the Kelvin scale water freezes at 273 K and boils at 373 K • °C + 273 = K • K – 273 = °C

  19. Example Convert the following Celsius temperatures to Kelvin. A. 42oC B. 100oC C. 68oC

  20. Ch 2.3 Using Scientific Measurements • A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.

  21. Precision and Accuracy • Accuracyrefers to the agreement of a particular value with the truevalue. • Precisionrefers to the degree of agreement among several measurements made in the same manner. Precise but not accurate Precise AND accurate Neither accurate nor precise

  22. Percent Error • Experimental values are measured during an experiment • Accepted value = true value • Error = (Experimental value - accepted value) • When you calculate percent error, you ignore plus and minus signs • The lower the % error means lab technique is good.

  23. Significant Figures Scientist indicate the precision of measurements by the number of digits they report - Significant figures or Sig Figs A value of 3.52 g is more precise than a value of 3.5 g.

  24. 3 2 3 4 5 3 3 4 Rules for Counting Significant Figures in a Measurement Here is how you count the number of sig. figs. in a given measurement: #1 (Non-Zero Rule): All digits 1-9 are significant. *Examples: 2.35 g =_____S.F. 2200 g = _____ S.F. #2 (Straddle Rule): Zeros between two sig. figs. are significant. *Examples: 205 m =_____S.F. 80.04 m =_____S.F. 7070700 cm =_____S.F. #3 (Righty-Righty Rule): Zeros to the right of a decimal point AND anywhere to the right of a sig. fig. are significant. *Examples: 2.30 sec. =_____S.F. 20.0 sec. =_____S.F. 0.003060 km =_____S.F.

  25. 4 2 ∞ ∞ ∞ ∞ Rules for Counting Significant Figures in a Measurement #4 (Bar Rule): Any zeros that have a bar placed over them are sig. (This will only be used for zeros that are not already significant because of Rules 2 & 3.) *Examples:3,000,000 m/s =_____S.F. 20 lbs =____S.F. #5 (Counting Rule): Any time the measurement is determined by simply counting the number of objects, the value has an infinite number of sig. figs. (This also includes any conversion factor involving counting.) *Examples:15 students =_____S.F. 29 pencils = ____S.F. 7 days/week =____S.F. 60 sec/min =____S.F.

  26. Sig Fig Practice #1 How many significant figures in each of the following? 1.0070 m  5 sig figs 17.10 kg  4 sig figs 100,890 L  5 sig figs 3.29 x 103 s  3 sig figs 0.0054 cm  2 sig figs 3,200,000  2 sig figs

  27. Rules for Significant Figures in Mathematical Operations • Addition and Subtraction: use the leastnumber of places after the decimal between all the numbers you are adding or subtracting. • 6.8 + 11.934 = • 18.734  18.7 (3 sig figs)

  28. Sig Fig Practice #2 Calculation Calculator says: Answer 10.24 m 3.24 m + 7.0 m 10.2 m 100.0 g - 23.73 g 76.3 g 76.27 g 0.02 cm + 2.371 cm 2.39 cm 2.391 cm 713.1 L - 3.872 L 709.228 L 709.2 L

  29. Rules for Significant Figures in Mathematical Operations • Multiplication and Division:use theleastnumber of sig figs between the numbers you are measuring. • 6.38 x 2.0 = • 12.76 13 (2 sig figs)

  30. Sig Fig Practice #3 Calculation Calculator says: Answer 22.68 m2 3.24 m x 7.0 m 23 m2 100.0 g ÷ 23.7 cm3 4.22 g/cm3 4.219409283 g/cm3 0.02 cm x 2.371 cm 0.05 cm2 0.04742 cm2 710 m ÷ 3.0 s 236.6666667 m/s 240 m/s

  31. Scientific Notation Cartoon courtesy of NearingZero.net

  32. Scientific Notation • Scientific notation is a way of representing really large or small numbers using powers of 10. *Examples:5,203,000,000,000 miles = 5.203 x 1012 miles 0.000 000 042 mm = 4.2 x 10−8 mm Steps for Writing Numbers in Scientific Notation (1) Write down all the sig. figs. (2) Put the decimal point between the first and second digit. (3) Write “x 10”

  33. (4) Count how many places the decimal point has moved from it’s original location. This will be the exponent...either + or −. (5) If the original # was greater than 1, the exponent is +, and if the original # was less than 1, the exponent is - ....(In other words, large numbers have + exponents, and small numbers have - exponents.)

  34. Scientific Notation • Practice Problems: Write the following measurements in scientific notation or back to their expanded form. 4.77 x 108 9.10 x 10−4 6,310,000,000 0.00000388 477,000,000 miles = _______________miles 0.000 910 m = _________________ m 6.31 x 109 miles = ___________________ miles 3.88 x 10−6 kg = __________________ kg

  35. PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION ADDITION AND SUBTRACTION

  36. IF the exponents are the same, we simply add the numbers in front and bring the exponent down unchanged. 4 x 106 + 3 x 106 7 x 106

  37. The same holds true for subtraction in scientific notation. 4 x 106 - 3 x 106 1 x 106

  38. If the exponents are NOT the same, we must move a decimal to make them the same. 4.00 x 106 + 3.00 x 105

  39. 4.00 x 106 4.00 x 106 + .30 x 106 + 3.00 x 105 4.30 x 106 Move the decimal on the smaller number!

  40. A Problem for you… 2.37 x 10-6 + 3.48 x 10-4

  41. Solution… 002.37 x 10-6 2.37 x 10-6 + 3.48 x 10-4

  42. Solution… 0.0237 x 10-4 + 3.48 x 10-4 3.5037 x 10-4 3.50 x 10-4

  43. MULTIPLYING AND DIVIDING

  44. Multiply the front factors first. Then add the exponents. 4.0 x 106 X 3.0 x 105

  45. 4.0 x 106 x 3.0 x 105 12.0 x 1011 = 1.2 x 1012 Make sure that only one number is in front of the decimal at the end of the problem.

  46. Divide the front factors first. Then subtract the exponents. 4.0 x 106 ÷ 3.0 x 105

  47. 4.0 x 106 ÷ 3.0 x 105 1.3 x 101

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