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Quantitative vs. Qualitative

Quantitative vs. Qualitative. Make a quantitative observation about your textbook Make a qualitative observation about your textbook. Quantitative vs. Qualitative. Quantitative observation: Qualitative observation:. Precision vs. Accuracy…. Archery Activity. Precision vs. Accuracy.

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Quantitative vs. Qualitative

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  1. Quantitative vs. Qualitative • Make a quantitative observation about your textbook • Make a qualitative observation about your textbook

  2. Quantitative vs. Qualitative • Quantitative observation: • Qualitative observation:

  3. Precision vs. Accuracy… • Archery Activity

  4. Precision vs. Accuracy • Which is more precise for measuring volume, a beaker or a graduated cylinder?

  5. Precision vs. Accuracy • Accuracy: refers to the closeness of measurements to the correct or accepted value of the quantity measured. • Precision: refers to the closeness of a set of measurements of the same quantitiy made in the same way.

  6. Precision vs. Accuracy • Measured values that are accurate are close to the accepted value • Measured values that are precise are close to one another but not necessarily close to the accepted value

  7. Darts within small area = High precision Area covered on bull’s-eye = High accuracy

  8. Darts within small area = High precision Area far from bull’s-eye = Low accuracy

  9. Darts within large area = Low precision Area far from bull’s-eye = Low accuracy

  10. Darts within large area = Low precision Area centered around bull’s-eye = High accuracy (on average)

  11. Unit conversions • Copy metric conversion from book

  12. Unit Conversions • Practice problems: 750 km = __________m? 283 m = __________km 112 Mwatt = __________Kwatt? 112 Mwatt = __________Gwatt

  13. Scientific Notation & Significant Figures

  14. Unit Estimation

  15. Scientific Notation • Used to make numbers more usable • 1,000,000,000 = 1x109 • 0.0000000001=1x10-10

  16. How do you figure this out? • You move the decimal until you have only one digit in front of the decimal. • If you move right, then the exponent will be NEGATIVE based on the number of places your decimal moved. • If you move left, then the exponent will be POSITIVE based on the number of places your decimal moved.

  17. Practice • Give the following in scientific notation • 6,289,030,987 • 0.004500678 • 5.60987 • 568.2365400 • 35.98340002 • 0.23476

  18. Practice 6,289,030,987 = 0.004500678 = 5.60987 = 568.2365400 = 35.98340002 = 0.23476 = 6.289030987x109 4.500678x10-3 5.60987 5.682365400x102 3.59834002x10 2.3476x10-1 Give the following inscientific notation…

  19. 1.3487x105 = 4.9800456x104 = 2.345x101 = 5.6789x10-3 = 3.591x10-1 = 2.0080x10-2 = 134,870 49,800.456 23.45 0.0056789 0.3591 0.020080 Going the other way…

  20. Try For Yourself • 7.234x10-5=? • 8.234x103=? • 5.000x10-4=? • 9.99998x10-2=? • 8.555x106=?

  21. ANSWERS 7.234x10-5 = 0.000 072 34 8.234x103 = 8,234 5.000x10-4 = 0.000 500 0 9.99998x10-2 = 0.099 999 8 8.555x106 = 8,555,000

  22. Significant Digits - What is it? • When we take measurements in science, we can only be sure of our numbers to a certain point • The numbers we are sure of are called significant digits or significant figures (“sig figs”)

  23. Sig Figs - How do we use them? • Two types • Measured • You actually measure and record your answer to a certain digit • Calculated • You use already measured numbers to compute an answer

  24. Measured Sig Figs • Questions you can answer: • How long is your book? • Measure it with a meterstick and read the length. • What is the mass of an orange? • Put it on a scale and read the mass. • How much milk is in the carton? • Pour the milk into a graduated cylinder and read the volume.

  25. Calculated Sig Figs • Sometimes, you’ve collected the data and you need to calculate a final answer • Example - you find the length, width and height of your book and you want to find the volume. • You need to multiply the three numbers together to get an answer.

  26. Determining what counts…Sig Fig Rules! • All non-zero numbers are significant • Example 1,2,3,…,9 • All zeros between non-zero numbers are significant • Example 1080.305 • All zeros before a written decimal are significant • Example 600.

  27. More Rules… • All zeros following non-zero numbers, after a decimal are significant • Example 1.00 0.003470030 • These rules are to determine what counts when you are looking at a number.

  28. Practice • How many sig figs are in the following numbers? • 2.341 • 0.0004580 • 560 • 560. • 560.0003

  29. Answers 2.341 has 4 sig figs All the numbers are non-zero digits, so they all count!

  30. Answers 0.0004580 has 4 sig figs The three non-zero numbers 458 and the zero following this set The first four zeros are place holders - they get the 4 into ten thousands place

  31. Answers Another way to think about 0.0004580 having four sig figs is to write it in scientific notation 0.0004580=4.580x10-4 When you write in scientific notation, you only write the sig figs before you write the x10whatever So here you see that you wrote the 4, 5, 8, and 0. Those are the sig figs!

  32. Answers 560 has 2 sig figs This one is tricky. Notice that there is no decimal, so the zero is just a place holder to get the 6 into the tens spot.

  33. Answers 560. Has 3 sig figs. This time the zero counts because the decimal means it was actually measured.

  34. Answers 560.0003 has 7 sig figs All zeros are between non-zero digits, so they are all significant.

  35. How do you know when to stop? • When you’re measuring, you know when to stop based on your equipment. • If your equipment reads to the tens, then you can guess up to one more place. You can read to the ones… • Let’s look at it.

  36. Multi step calculations • Keep One Extra Digit in Intermediate Answers • When doing multi-step calculations, keep at least one more significant digit in intermediate results than needed in your final answer. • For instance, if a final answer requires two significant digits, then carry at least three significant digits in calculations. If you round-off all your intermediate answers to only two digits, you are discarding the information contained in the third digit, and as a result the second digit in your final answer might be incorrect. (This phenomenon is known as "round-off error.")

  37. 2 Greatest Sins in Sig Figs • Writing more digits in an answer (intermediate or final) than justified by the number of digits in the data. • Rounding-off, say, to two digits in an intermediate answer, and then writing three digits in the final answer.

  38. Reading the right number of digits. • Ruler/Meterstick • Graduated Cylinder • Beaker • Scale

  39. Calculations - The rules!!! • Addition/Subtraction • Your answer should have the same number of decimal places as the number with the least number of decimal places • Multiplication/Division • Your answer should have the same number of sig figs as the number with the least number of sig figs • Always follow the order of operations!

  40. Practice • 2.786 + 3.5 = • 0.0004 x 3001 = • 65 + 45.32 x 90 = • 45.6 - 34.23 = • 900.3/30.2450 =

  41. Percent Error • Percent error determines how accurate an experimental value is compared quantitatively with the correct or accepted value. • Percent error: calculated by subtracting the experimental value from the accepted value, dividing the difference by the accepted value, and then multiplying by 100

  42. Percent Error Percent error = Valueaccepted – Valueexperimental x 100 Valueaccepted Percent error can have a positive or negative value

  43. Percent Error A student measures the mass and volume of a substance and calculates its density as 1.40 g/mL. The correct, or accepted value of the density is 1.36 g/mL. What is the percent error of the student’s measurement? = 1.36g/mL – 1.40 g/mL x 100 = -2.9% 1.36 g/mL

  44. Percent Error What is your percent error from the lab when you found the density of water? = 1.00g/mL – g/mL x 100 = -2.9% 1.00 g/mL Your experimental value

  45. Percent Error – pg. 45 Two technicians independently measure the density of a new substance. Technician A Records: 2.000, 1.999, 2.001 g/mL Technician B Records: 2.5, 2.9, and 2.7 g/mL The correct value is found to be: 2.701 g/mL. Which Technician is more precise? Which is more accurate? B A

  46. Go Through Answers on Packet

  47. Directly Proportional • Two quantities are directly proportional if… • Dividing one by the other gives a constant value • y/x = k • k = constant • You can rearrange above equation by saying : y = kx • If one increases…the other increases at the same rate (doubling one constant = doubles the othr • 2y/2x = k (constant)

  48. Directly Proportional All directly proportional relationships produce linear graphs that pass through the origin

  49. Inverse Proportions • Two quantities are inversely proportional if… • Their product is constant • xy = k • k = constant • The greater the speed = less time to travel a given distance • Double speed (2x) = ½ required time • Halving the speed (½) = 2 times the time

  50. Inverse Proportional

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