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Analyzing Data

Analyzing Data. Chapter 2. Units and Measurement . 2.1 x. 2.1 Objectives. Define SI base units for time, length, mass, volume, and temperature Explain how a prefix changes a metric unit Convert within metric units Compare derived units Calculate using D=m/V. Review Vocabulary.

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Analyzing Data

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  1. Analyzing Data Chapter 2

  2. Units and Measurement 2.1 x

  3. 2.1 Objectives Define SI base units for time, length, mass, volume, and temperature Explain how a prefix changes a metric unit Convert within metric units Compare derived units Calculate using D=m/V

  4. Review Vocabulary Metric system Mass SI unit Second Meter Gram Prefix

  5. New Vocabulary Kelvin Derived unit Liter Cubic centimeter Density Mole Temperature

  6. SI Prefixes There are some that are missing! You must still account for them!

  7. SI Base Units The quantity symbol appears in the equation while the unit symbol appears in the answer!

  8. Time • SI Unit: second (s) • Common units: ??

  9. Length • SI Unit: meter (m) • Other common units: ??

  10. Mass • SI Unit: kilogram (kg) • Other common units: ?? • Differs from weight

  11. Temperature • SI Unit: Kelvin (K) • Other units: ?? • K = °C + 273.15 • Absolute zero

  12. Which is larger? • Millimeter or kilometer • Microgram or nanogram • 120 seconds or 1/60th of an hour • 30 K or 30°C • 1 L or 1 m3 • 1 m or 100mm

  13. SI Derived Units 1m3=1,000,000 cm3 & 1 cm3=1mL

  14. Volume • SI Unit: liter (L) • Can be a derived unit • (length)3 (lwh) • 1 mL = 1 cm3 • 1 L = 1 dm3

  15. Density • Tells the amount of a substance in a given volume • Always a mass/volume • Water has a density of 1 g/mL • Constant for a substance at a given pressure and temperature

  16. Density • The ratio of mass to volume or the amount of mass in a given amount of material • SI unit: kg/m3 • Usable unit: g/mL or g/cm3 • Varies with temperature

  17. Density • Water has a density of 1g/mL • D<1 will float in water • D>1 will sink in water If it is the same egg, what must have happened?

  18. Kloock’s foolproof way to solve science problems… • State what you know. • State what you want to know. • Find an equation that contains those variables. • Solve the equation for what you want to know. • Plug and chug!

  19. Density = mass/volume • D=m/V • What is the density of an object with a mass of 250 g and a volume of 10.0 mL?

  20. What is the density of an object with a mass of 250g and a volume of 10.0 mL? • State what you know. • m = 250 g • V = 10.0 mL • State what you want to know. • D = ?

  21. What is the density of an object with a mass of 250g and a volume of 10.0 mL? • m = 250g V = 10.0 mL D = ? 3. Find an equation that contains those variables. D=m/V 4. Solve the equation for what you want to know. D=m/V

  22. What is the density of an object with a mass of 250g and a volume of 10.0 mL? • D= 250g/10.0 mL = 25 g/mL Will this object float or sink in water? • m = 250g V = 10.0 mL D = ? D=m/V

  23. What is the density of a block with a mass of 12 g that measures 2 cm long, 2 cm wide and 2 cm deep? • m=12g, v=(2cm)(2cm)(2cm)=8cm3 • D=m/v=12g/8cm3= • 1.5g/cm3

  24. What is the density of a substance with a mass of 6g and a volume of 2cm3? • m=6g, v=2cm3 • D=m/v=6g/2cm3= • 3g/cm3

  25. Can you… Define SI base units for time, length, mass, volume, and temperature Explain how a prefix changes a metric unit Convert within metric units Compare derived units Calculate using D=m/V

  26. Scientific Notation and Dimensional ANalaysis

  27. 2.2 Objectives Express numbers in scientific notation Convert between units using dimensional analysis

  28. Review Vocabulary Quantitative data Qualitative data Coefficient Exponent

  29. New Vocabulary Scientific notation Dimensional analysis Conversion factor

  30. Scientific Notation An ordinary penny contains about 20,000,000,000,000,000,000,000 atoms. The average size of an atom is about 0.00000003 centimeters across. The length of these numbers in standard notation makes them awkward to work with. Scientific notationis a shorthand way of writing such numbers.

  31. Scientific Notation In scientific notation the number of atoms in a penny is 2.0  1022, and the size of each atom is 3.0  10–8 centimeters across. The sign of the exponent tells which direction to move the decimal. A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left.

  32. 1.35  10 5 5 10 = 100,000 Additional Example 1A: Translating Scientific Notation to Standard Notation Write the number in standard notation. A. 1.35  105 1.35  100,000 Think: Move the decimal right 5 places. 135,000

  33. –3 2.7  10 1 –3 10 = 2.7  1000 1 1000 Additional Example 1B: Translating Scientific Notation to Standard Notation Continued Write the number in standard notation. –3 B. 2.7  10 2.7 1000 Divide by the reciprocal. 0.0027 Think: Move the decimal left 3 places.

  34. 4 4 10 = 10,000 –2.01  10 –2.01  10,000 Additional Example 1C: Translating Scientific Notation to Standard Notation Continued Write the number in standard notation. C. –2.01  104 –20,100 Think: Move the decimal right 4 places.

  35. 2.87  10 9 10 = 1,000,000,000 9 Try This: Example 1A Write the number in standard notation. A. 2.87  109 2.87  1,000,000,000 2,870,000,000 Think: Move the decimal right 9 places.

  36. 1 –5 10 = 100,000 1 1.9  100,000 –5 1.9  10 Try This: Example 1B Write the number in standard notation. B. 1.9  10–5 1.9 100,000 Divide by the reciprocal. 0.000019 Think: Move the decimal left 5 places.

  37. 8 –5.09  10 10 = 100,000,000 8 Try This: Example 1C Write the number in standard notation. C. –5.09  108 –5.09  100,000,000 –509,000,000 Think: Move the decimal right 8 places.

  38. 7.09  10 So 0.00709 written in scientific notation is 7.09  10–3. Check 7.09  10–3 = 7.09  0.001 = 0.00709 Additional Example 2: Translating Standard Notation to Scientific Notation Write 0.00709 in scientific notation. Move the decimal to get a number between 1 and 10. 0.00709 7.09 Set up scientific notation. Think: The decimal needs to move left to change 7.09 to 0.00709, so the exponent will be negative. Think: The decimal needs to move 3 places.

  39. 8.11  10 So 0.000811 written in scientific notation is 8.11  10–4. –4 Check 8.11  10 = 8.11  0.0001 = 0.000811 Try This: Example 2 Write 0.000811 in scientific notation. Move the decimal to get a number between 1 and 10. 0.000811 8.11 Set up scientific notation. Think: The decimal needs to move left to change 8.11 to 0.000811, so the exponent will be negative. Think: The decimal needs to move 4 places.

  40. Try This: Example 3 An oil rig can hoist 2,400,000 pounds with its main derrick. It distributes the weight evenly between 8 wire cables. What is the weight that each wire cable can hold? Write the answer in scientific notation. Find the weight each cable is expected to hold by dividing the total weight by the number of cables. 2,400,000 pounds ÷ 8 cables = 300,000 pounds per cable Each cable can hold 300,000 pounds. Now write 300,000 pounds in scientific notation.

  41. 3.0  10 5 Each cable can hold 3.0  10 pounds. Try This: Example 3 Continued Set up scientific notation. Think: The decimal needs to move right to change 3.0 to 300,000, so the exponent will be positive. Think: The decimal needs to move 5 places.

  42. 5.3  10–3 Lesson Quiz Write in standard notation. 1. 1.72  104 17,200 2. 6.9  10–3 0.0069 Write in scientific notation. 3. 0.0053 5.7  107 4. 57,000,000 5. A human body contains about 5.6 x 106microliters of blood. Write this number in standard notation. 5,600,000

  43. Scientific Notation • Text age 43: 15 and 16

  44. Dimensional Analysis • Text book page 45: 17-20

  45. Uncertainty in Data

  46. What’s the difference? Accuracy Precision a measure of how close a series of measurements are to one another. • a measure of how close a measurement comes to the actual or true value of whatever is measured.

  47. Which of the following are more precise? • 65.41g, 65.38g, 65.40g or • 65.41g, 64.98g, 65.23g? • Do the math!!

  48. What time is it? • Someone might say “1:30” or “1:28” or “1:27:55” • Each is appropriate for a different situation • In science we describe a value as having a certain number of “significant digits” • The # of significant digits in a value includes all digits that are certain and one that is uncertain • “1:30” has 2, 1:28 has 3, 1:27:55 has 5 • There are rules that dictate the # of significant digits in a value

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