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Scientific Measurements

Scientific Measurements. Ch. 3 Go to teacherweb.com to print a copy of these for yourself. The International System of Measurement - SI. is commonly called the metric system in the United States. 1960: General Conference of Weights and Measures set standard for length, chose prefixes.

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Scientific Measurements

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  1. Scientific Measurements Ch. 3 Go to teacherweb.com to print a copy of these for yourself.

  2. The International System of Measurement - SI • is commonly called the metric system in the United States. • 1960: General Conference of Weights and Measures set standard for length, chose prefixes.

  3. The International System of Measurement - SI • Base Units: a defined unit in a system of measurement that is based on an object or event in the physical world. • Prefixes are used when referring to amounts greater than or smaller than the base unit • The prefixes are based on multiples of ten. • Regardless of the base unit, the entire metric system uses the same prefixes.

  4. Standards • Time: frequency of microwave radiation given off by a cesium-133 atom • Length: distance light travels through a vacuum in 1/299792458 of a second. • Mass: a platinum – iridium metal cylinder

  5. Never write a number without its units.

  6. SI Units & Prefixes • Know the units and prefixes for SI. • Be able to arrange measurements from largest to smallest and convert related SI units.

  7. Derived Units • a unit that is defined by a combination of base units. Ex. Volume, density • Volume: the space occupied by an object • solid objects with regular dimensions • Unit = cubic meter, m3, cm3 • Liquids and irregular shapes: • Unit = liter • 1mL = 1cm3

  8. Density • Density - “heavy” vs. “light” • Ratio of mass per unit volume. • Unit = g/cm3 or g/mL • D = mass volume • Can be used to identify an unknown sample of matter • Ex) Every sample of pure Aluminum has the same density.

  9. Temperature • Thermometer: liquids expand when heated & contract when cooled. • Celsius Scale: Anders Celsius. • Water Freezing point is 0C • Water Boiling point is 100C

  10. Temperature • Kelvin Scale: Lord Kelvin (William Thomson) • Kelvin(K): SI unit for temperature • Water freezes at 273K • Water boils at 373K

  11. Convert K and °C • Kelvin to °C: subtract 273. • Ex) 254K – 273 = -19°C • °C to Kelvin: add 273 • Ex) 45 °C + 273 = 318K

  12. Convert the following 5. 298K to °C 6. 16 °C to K 7. 98 °C to K 8. 344K to °C 9. 209 °C to K 5. 25 °C 6. 289 K 7. 371 K 8. 71 °C 9. 482 K

  13. Scientific Notation • Expresses numbers as a multiple of 2 factors: • a number greater than 1 but less than 10 and • 10 raised to a power, or exponent. • Tells you how many times the first factor must be multiplied by ten.

  14. When a number larger than 1 is written in scientific notation, the exponent is POSITIVE • When numbers smaller than 1 are written in scientific notation, the exponent is NEGATIVE

  15. 1,567,000,000 m • Move the decimal point to the left  (There should be 1 number that is not a 0 – to the left of the decimal) • Count the number of places the decimal point is moved: that # is the exponent. • 1.567 x 109 m • If the Decimal moves to the Left: Positive (+) exponent

  16. 0.0000000000001567m • Move the decimal point to the right  (There should be 1 number that is not 0 – to the left of the decimal) • Count the number of places the decimal point is moved: that # is the exponent. • 1.567 x 10-13 m • If the Decimal moves to the right: Negative (-) exponent

  17. Write the following numbers in scientific notation: 10) 5.69x105 11) 2.58 x10-6 12) 8.9x106 13) 2.5x10-3 14) 8.4x10-4 10) 569,000 11) 0.00000258 12) 8,900,000 13) 0.0025 14) 0.00084

  18. Calculators and Scientific Notation • Look for a button with either EXP or EE on it or as its second function • Enter the first part of the number • Ex. 4.32 • Press the exp button and enter the exponent. • DO NOT enter x10 or use the caret button – this will make your answers wrong!! • The calculator knows x10 is there – it just doesn’t have to enter it

  19. Math with Scientific Notation • Addition and Subtraction • Only if the exponents are the same • Move decimals to get the same exponents • Exponents do nothing when added/subtracted • Multiplication • Exponents are added • Division • Exponents are subtracted (denominator from the numerator)

  20. Addition and Subtraction 15) 8 x 104 + 6 x 104 = 14 x 104 = 1.4 x 105 = 1400000 16) 1.2 x 10-4 – 5 x 10-5 = 12 x 10-5 – 5 x 10-5 = 7 x 10-5 17) 5 x 106 + 3 x 107 = 5 x 106 + 30 x 106 = 35 x 106 = 3.5 x 107

  21. Multiplication 18) (3 x 105)(5 x 102) =15 x 107 = 1.5 x 108 19) (5.8 x 103) (6.2 x 104) =35.96 x 107 =3.596 x 108

  22. Division

  23. Accuracy and Precision • Accuracy: how close a measured value is to an accepted value • Precision: how close a series of measurements are to one another. • Not necessarily accurate!

  24. Percent Error • The ratio of an error to an accepted value • To evaluate the accuracy of experimental data, you can calculate the percent error. • Percent Error is the difference between an experimental value and an accepted value

  25. Percent Error = error x 100 accepted value The error: Known value minus Experimental value

  26. 37. Calculate the percent error. The known density of a metal is 2.5g/mL. In the lab, the density was found to be 2.04g/mL. • The error: Known minus Experimental • 2.5-2.04 = 0.46 • % Error = 0.46 x 100 =18.4% 2.5

  27. 38. Three measurements of 34.5m, 38.4m, and 35.3m are taken. If the accepted value of the measurement is 36.7m, what is the percent error for each measurement? 5.99%, 4.63%, 3.81%

  28. 39. Three measurement of 12.3mL, 12.5mL and 13.1mL are taken. The accepted value for each measurement is 0.0128L. Calculate the percent error for each measurement. 3.91%, 2.34%, 2.34%

  29. Significant Figures • A measurement is a number that consists of all known digits (read from the instrument)and one estimated digit. • Needed for calculations since a final answer can’t be any more accurate than the least accurate measurement/number that was used to find that answer.

  30. Rules for Significant Digits 1. Nonzero numbers are always significant 2. Zeros between nonzero numbers are always significant. 3. All final zeros to the right of the decimal place are significant.

  31. 4. Zeros that act as placeholders are not significant. Convert quantities to scientific notation to remove the placeholder zeros. 5. Counting numbers and defined constants have an infinite number of significant figures. Ex. Pi, speed of light 6. Watch the location of decimals when counting sig figs. Ex. 100 vs. 100.

  32. Examples of significant figures:

  33. Sig Figs in Calculations: • Addition & Subtraction • Add or subtract the numbers as needed. • Determine what is the SMALLEST number of digits behind the decimal in the numbers added/subtracted. • Round the answer to have this many numbers after the decimal OR add zeros at the end after the decimal if needed

  34. Multiplication & Division • Multiply or divide the numbers as needed. • Determine what is the smallest amount of sig figs in the numbers used to get the answer. • Round the final answer to have this number of sig figs. • Combo of add/subtract & multiply divide in the same problem: • Do the math as normal. • Round the final answer to appropriate number of sig figs like normal for multiply/divide problems.

  35. Graphs

  36. Graph: a visual display of information or data.

  37. Types of Graphs

  38. Pie Graphs • Pie • Used to show how some fixed quantity is broken down into parts • Circle represents the total

  39. Bar Graphs 2. Bar • Used for comparing information collected by counting

  40. Line Graphs 3. Line • Used to show trends or how data changes over time.

  41. Line Graph • Independent variable • plotted on the horizontal x-axis • Ex) Time in seconds • Dependent variable • plotted on the vertical y-axis • Ex) Distance in meters or centimeters

  42. Are the speeds constant? How can you tell? • Yes, the lines are straight.

  43. How to construct a line graph on paper. • 1. Identify the variables • 2. Determine the variable range. • Subtract the lowest data value from the highest value. • Do each variable separately! • 3. Number & label each axis.

  44. 4. Plot the data points. • Place a dot on the graph for each value. 5. Draw the graph. • Draw a curve or line that best fits the data points. 6. Title the graph. • Title should be about data

  45. Remembering Metric Units • Giant Mighty Kangaroos Have Dirty Underwear During Cold Months Maybe Not Probably • Giga, Mega, Kilo, Hecto, Deca, base Unit, Deci, Centi, Milli, Micro, Nano, Pico

  46. Convert the Following 32. 225 cg to kg 33. 52 Gg to dg 34. 9500 nL to mL 35. 32 ML to GL 36. 9 ng to pg

  47. 32. 0.00225 kg 33. 5,200,000,000,000 dg 34. 0.0095 mL 35. 0.032 GL 36. 9000 pg

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