Lecture 3.1- Measurements (HP)
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Lecture 3.1- Measurements (HP)

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Section 3.1 Lecture for Honors Chemistry

Section 3.1 Lecture for Honors Chemistry

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  • The distribution of darts illustrates the difference between accuracy and precision. a) Good accuracy and good precision: The darts are close to the bull’s-eye and to one another. b) Poor accuracy and good precision: The darts are far from the bull’s-eye but close to one another. c) Poor accuracy and poor precision: The darts are far from the bull’s-eye and from one another.
  • The scale below has not been properly zeroed, so the reading obtained for the person’s weight is inaccurate. There is a difference between the person’s correct weight and the measured value. Calculating What is the percent error of a measured value of 114 lb if the person’s actual weight is 107 lb?
  • Three differently calibrated meter sticks are used to measure the length of a board. a) A meter stick calibrated in a 1-m interval. b) A meter stick calibrated in 0.1-m intervals. c) A meter stick calibrated in 0.01-m intervals. Measuring How many significant figures are reported in each measurement?

Lecture 3.1- Measurements (HP) Lecture 3.1- Measurements (HP) Presentation Transcript

  • Lecture 3.1- Measurements
  • SCIENTIFIC NOTATION is used to represent very large or very small numbers
  • SCIENTIFIC NOTATION 6.02 x 1023
  • SCIENTIFIC NOTATION 6.02 x 1023 must be between 1-10
  • SCIENTIFIC NOTATION 6.02 x 1023 must be The power of ten between determines the size of 1-10 the number
  • SCIENTIFIC NOTATION 6.02 x 1023 must be The power of ten between determines the size of 1-10 the number Positive power = big number(greater than 10) Negative power = small number(less than one)
  • SCIENTIFIC NOTATION 6.02 x 1023 must be The power of ten between determines the size of 1-10 the number Positive power = big number(greater than 10) Negative power = small number(less than one) EX. 0.00567g = 5.67 x 10-3g a small number 437,850g = 4.3785 x 105g a large number
  • To convert from standard notation to scientific notation move the decimal point to make a number between 1 and 10 then count how many spaces you moved it. positive because it is a big number negative because it is a small number
  • Accuracy and Precision • Accuracy measures how close a measurement comes to the actual value. • Precision measures how close a series of measurements are to each another.
  • 3.1
  • Just because a measuring device works, you cannot assume it is accurate. The scale has not been properly zeroed, so the reading obtained for the person’s weight is inaccurate.
  • Significant digits When measuring we record all certain digits plus one uncertain digit
  • Significant digits When measuring we record all certain digits plus one uncertain digit, so there is always some degree of uncertainty in measurement.
  • Significant digits When measuring we record all certain digits plus one uncertain digit, so there is always some degree of uncertainty in measurement. In science we account for this by using significant digits or significant figures
  • The more significant digits in a measurement the more accurate the measuring device was.
  • The more significant digits in a measurement the more accurate the measuring device was.
  • The more significant digits in a measurement the more accurate the measuring device was.
  • The number of significant digits tells us how accurate the measuring device was.
  • COUNTING THE NUMBER OF SIGNIFICANT DIGITS 3 rules
  • COUNTING THE NUMBER OF SIGNIFICANT DIGITS 3 rules 1. Non-zero integers are always significant 101,300 0.0003020
  • COUNTING THE NUMBER OF SIGNIFICANT DIGITS 101,300 0.0003020
  • COUNTING THE NUMBER OF SIGNIFICANT DIGITS 101,300 0.0003020 2. Zeros- captive zeros (in between non-zero integers) are ALWAYS significant
  • COUNTING THE NUMBER OF SIGNIFICANT DIGITS 101,300 0.0003020 2. Zeros- captive zeros (in between non-zero integers) are ALWAYS significant leading zeros (in front) are NEVER significant
  • COUNTING THE NUMBER OF SIGNIFICANT DIGITS 101,300 0.0003020 2. Zeros- captive zeros (in between non-zero integers) are ALWAYS significant leading zeros (in front) are NEVER significant trailing zeros (at the end) are ONLY significant IF there is a decimal point.
  • COUNTING THE NUMBER OF SIGNIFICANT DIGITS 3. Exact numbers are considered to have infinite significant figures
  • COUNTING THE NUMBER OF SIGNIFICANT DIGITS 3. Exact numbers are considered to have infinite significant figures Exact numbers come from counting or from definitions
  • COUNTING THE NUMBER OF SIGNIFICANT DIGITS 3. Exact numbers are considered to have infinite significant figures Exact numbers come from counting or from definitions Counting  there are 15 students in the library Definition  1m = 1000mm 15, 1, and 1000 are exact numbers in these situations
  • Reporting calculations with the correct number of significant digits
  • Reporting calculations with the correct number of significant digits Our calculations are only as precise as our least precise measurement.
  • Our calculations are only as precise as our least precise measurement
  • Our calculations are only as precise as our least precise measurement If 30 beans have a mass of 17.3g what is the average mass?
  • Our calculations are only as precise as our least precise measurement If 30 beans have a mass of 17.3g what is the average mass? 17.3g/30 =
  • Our calculations are only as precise as our least precise measurement If 30 beans have a mass of 17.3g what is the average mass? 17.3g/30 = 0.576666666666666666g
  • Our calculations are only as precise as our least precise measurement If 30 beans have a mass of 17.3g what is the average mass? 17.3g/30 = 0.576666666666666666g Does it really make sense to claim such precision when we only measured out to one tenth of a gram?
  • 17.3g/30 = 0.576666666666666666g This number has three significant digits
  • 17.3g/30 = 0.576666666666666666g This This number number has infinite has three significant significant digits digits
  • 17.3g/30 = 0.576666666666666666g This This number number has infinite has three significant significant digits digits The least precise number has 3 significant digits so the answer should have only 3 significant digits.
  • 17.3g/30 = 0.576666666666666666g This This number number has infinite has three significant significant digits digits The least precise number has 3 significant digits so the answer should have only 3 significant digits. 0.577g
  • For multiplication and division report the number of significant digits in the least precise measurement.
  • For multiplication and division report the number of significant digits in the least precise measurement. 4.56 x 1.4 = 6.4 two sig figs in result
  • For multiplication and division report the number of significant digits in the least precise measurement. 4.56 x 1.4 = 6.4 two sig figs in result 4 x 7.65321 = 3 x 101 one sig fig in result
  • For multiplication and division report the number of significant digits in the least precise measurement. 4.56 x 1.4 = 6.4 two sig figs in result 4 x 7.65321 = 3 x 101 one sig fig in result For addition and subtraction report the same number of DECIMAL PLACES as the least precise measurement.
  • For multiplication and division report the number of significant digits in the least precise measurement. 4.56 x 1.4 = 6.4 two sig figs in result 4 x 7.65321 = 3 x 101 one sig fig in result For addition and subtraction report the same number of DECIMAL PLACES as the least precise measurement. 18 + 32.657 = 51 result is a whole number
  • For multiplication and division report the number of significant digits in the least precise measurement. 4.56 x 1.4 = 6.4 two sig figs in result 4 x 7.65321 = 3 x 101 one sig fig in result For addition and subtraction report the same number of DECIMAL PLACES as the least precise measurement. 18 + 32.657 = 51 result is a whole number 18.1 + 32.657 = 50.8 report to tenths place
  • ROUNDING OFF RESULTS When performing a chain of calculations round off your answers only at the end. 13.44 round down 13.4 13.45 round up 13.5