Scientific Measurement

1. Scientific Measurement

2. Do you have a calculator with you today? • Yes • No

3. Accuracy - How close a measurement is to the true value Precision - How close a set of measurements are to one another.

4. How accurate or precise was this person? • Accurate • Precise • Both • Neither

5. Precise or Accurate? • Accurate • Precise • Both • Neither

6. Precise or Accurate? • Accurate • Precise • Both • Neither

7. Dealing with numbers in science

8. :00 Answer Now Write each power of ten in standard notation. • 30 • 100 • 1000 103

9. Write each power of ten in standard notation. 60 1000000 10000 :00 Answer Now 106

10. Write each power of ten in standard notation. .01 -20 100 :00 Answer Now 10-2

11. Write each power of ten in standard notation. -.0004 .0004 10000 :00 Answer Now 10-4

12. There are 325,000 grains of sand in a tub. Write that number in scientific notation. Setting the Stage

13. What is the exponent to the 10 for 325,000 grains of sand? • 3 • 4 • 5 • 6 • -6 • -5 • -4 0

14. Definition • Scientific notation- is a compact way of writing numbers with absolute values that are very large or very small. • Glencoe McGraw-Hill. Math connects cours 3. pages 130-131

15. Scientific Notation • all numbers are expressed as whole numbers between 1 and 9 multiplied by a whole number power of 10. • If the absolute value of the original number was between 0 and 1, the exponent is negative. Otherwise, the exponent is positive. • Ex. 125 = 1.25 x 102 • 0.00004567 = 4.567 x 10-5

16. What is the exponent of 10 for3,450,000 • -6 • 6 • -5 • 5 • 4 • -4 0

17. What is the exponent of 10 for0.0002345 • -6 • 6 • -5 • 5 • 4 • -4 0

18. :10 Answer Now What is 2.85 x 104 written in standard form • .000285 • 285 • 28500 • 2850

19. What is 3.085 x 107 written in standard form .0000003085 30,850,000 3085 308,500,000 :00 Answer Now

20. What is 1.55 x 10-3 written in standard form .00155 155 1550 .000155 :00 Answer Now

21. What is 2.7005 x 10-2 written in standard form 270.05 27005 .27005 .027005 :10 Answer Now

22. You try some... Write the following numbers in scientific notation: A) 5,000 E) 0.0145 B) 34,000 F) 0.000238 C) 1,230,000 G) 0.0000651 D) 5,050,000,000 H) 0.000000673

23. Closure / Summary • Explain why 32.8 x 104 is not correctly written in scientific notation. • What does a negative exponent tell you about writing the number in standard form.

24. Significant Figures or Digits Significant Figures are used to show the accuracy and precision of the instruments used to take the measurement.

25. What is the measurement? 1 0 • 0.55 • 0.7 • 0.6 • 0.8

26. What is the measurement? 1 0 • 0.55 • 0.70 • 0.67 • 0.65

27. Measurements • To show how precise the instrument is: • Read the measurement to one decimal place what the instrument is marked

28. Read the water level • 4.85 • 7.2 • 4.3 • 4.35

29. Read the water level • 17.0 • 16.8 • 15.18 • 15.2

30. Counting Significant Digits • Non-zero digits are always significant 1,2,3,4,5,6,7,8,9 are always significant • Rules for Zeros: • Leading Zeros never count as significant 0.0000456 0.0032 • Captive zeros (zeros between non-zero digits) are always significant 10,034 0.005008 • Trailing Zeros are significant ONLY IF there is a decimal in the number. 234,000 234,000.0 0.045600

31. If we want to write the number 700 with 3 significant digits we can do so using the following two methods: 700. OR 7.00×102

32. How many significant digits does the following number have?20 • 1 • 2 • 3 • 0

33. How many significant digits does the following number have?22.0 • 0 • 1 • 2 • 3

34. How many significant digits does the following number have?0.000354 • 3 • 1 • 6 • 7

35. How many significant digits does the following number have?56,000 • 0 • 1 • 2 • 3

36. How many significant digits does the following number have?75,000. • 2 • 5 • 1 • 3

37. How many significant digits does the following number have?7.00 • 1 • 2 • 3 • 4

38. How many significant digits does the following number have?4.30 x 108 • 1 • 2 • 3 • 4

39. How many significant digits does the following number have?0.00040050 • 5 • 8 • 2 • 4

40. How many significant digits does the following number have?0.00043 • 5 • 8 • 2 • 4

41. How many significant digits does the following number have?10,023,000 • 3 • 8 • 4 • 5

42. Rounding Numbers to the Correct Significant Figures Count (from left to right) how many significant figures you need. Look at the next number to see if you need to round your last sig. fig. up or down. Round the following to 3 sig. figs 1,344 0.00056784 24,500 12,345 2.45678 x 10-3

44. Significant Digit Calculations We have two ways of categorizing sig. fig. calculations: • Addition and Subtraction B) Multiplication, Division, other math

45. Addition and Subtraction Rules When we add and subtract we are only worried about the number of decimal places involved in the numbers present. We do not care about the number of actual significant digits. We will always pick the number that has the least decimal places.

46. You try some... A) 14.0 + 2.45 B) 12 + 7.2 C) 0.00123 + 1.005 D) 100 – 5.8 E) 2.5 – 1.25 F) 43.786 – 32.11

47. Multiplication, Division, other math If we are multiplying, dividing, using exponents, trigonometry, calculus, etc we must use the least number of significant digits of the numbers in the set. For example...

48. You try some... A) 12 × 5.00 F) 119 / 32 B) 8.45 × 4.3 G) 756.2 / 29.8 C) 0.0125 × 7.532 H) 0.976 / 0.0044 D) 5.6 × 11.7 I ) 981 / 756.23 E) 34.1 × 0.55 J) 43.2 / 12.45

49. Density Density – the amount of matter present in a given volume of a substance, the ratio of the mass of an object to its volume. D = mass Volume

50. Percent Error