1. Scientific Measurements
Significant Figures & Scientific Notation

2. No Starter – Lab Safety Test Today!!
Get out a blank piece of paper.
Put your name and class period in the upper right hand corner.
Do not write on the test it is a classroom copy.
Put your test number in the upper right hand corner.

3. Large and Small Numbers
Scientists often deal with numbers that are either extremely large or extremely small
Examples
the speed of light = meters per second
hydrogen atoms has a mass of g
These numbers are cumbersome to write and use!

4. Scientific Notation
Scientific Notation: a system used to write large or small numbers more compactly and precisely

5. Scientific Notation
There are 2 parts to a number written in scientific notation:
a coefficient - a number equal to or greater than 1 and less than 10
an exponential part - a base which is always 10, raised to an exponent (n)

6. Is it written in scientific notation?
x 103

7. Is it written in scientific notation?
No x 103 The coefficient is not between 1-10

8. Is it written in scientific notation?
837 x 102

9. Is it written in scientific notation?
No 837 x 102 The coefficient is not between 1-10

10. Is it written in scientific notation?
2.894 x 10-3

11. Is it written in scientific notation?
Yes
2.894 x 10-3
The coefficient is 1-10 and it is multiplied by 10 to a power

12. Is it written in scientific notation?
x 52

13. Is it written in scientific notation?
x 52
Must be multiplied by the base of 10

14. Scientific Notation Steps
Put the decimal after the first significant digit
Indicate how many places the decimal moved by the power of 10 (the number of places the decimal moved becomes the exponent)
A positive power of 10 indicates the decimal moved to the left
A negative power of 10 indicates the decimal moved to the right

15. Scientific Notation Steps

16. Scientific Notation Steps

17. Convert to scientific notation
15237

18. Convert to scientific notation
x 10-3
15237

19. Convert to scientific notation
x 10-3
x 104

20. Convert to scientific notation
x 10-3
x 104
x 107

21. Convert to scientific notation
x 10-3
x 104
x 107
x 102

22. Convert to scientific notation
x 10-3
x 104
x 107
x 102
x 10-5

23. Addition and Subtraction
To add or subtract using scientific notation first write each quantity using the same exponent
Add or subtract the quantity and leave the exponent the same
Example:
(4.3 x 104) + (3.9 x 103) =

24. Addition and Subtraction
To add or subtract using scientific notation first write each quantity using the same exponent
Add or subtract the quantity and leave the exponent the same
Example:
(4.3 x 104) + (3.9 x 103)
(4.3 x 104) + (0.39 x 104) = 4.69 x 104

25. Multiplication and Division
To multiply numbers expressed in scientific notation, multiply the numbers in the usual way, then add the exponents together.
Example:
(8.0 x 104) x (5.0 x 102) =

26. Multiplication and Division
To multiply numbers expressed in scientific notation, multiply the numbers in the usual way, then add the exponents together.
Example:
(8.0 x 104) x (5.0 x 102) =
8.0 x 5.0 and =

27. Multiplication and Division
To multiply numbers expressed in scientific notation, multiply the numbers in the usual way, then add the exponents together.
Example:
(8.0 x 104) x (5.0 x 102) =
8.0 x 5.0 and =
= 40 x 106

28. Multiplication and Division
To divide using scientific notation, divide the numbers as usual and subtract the exponents.
Example:
(6.9 x 107) =
(3.0 x 10-5)

29. Multiplication and Division
To divide using scientific notation, divide the numbers as usual and subtract the exponents.
Example:
6.9 and 107 – (-5)
(6.9 x 107) =
3.0
(3.0 x 10-5)

30. Multiplication and Division
To divide using scientific notation, divide the numbers as usual and subtract the exponents.
Example:
6.9 and 107 – (-5)
(6.9 x 107) =
3.0
(3.0 x 10-5) =
2.3 x 1012

31. Calculator Time
Try plugging these into your scientific calculator. Put all answers in scientific notation.
37,000 x 7,000 x
(7x106) x (8x105)

32. Calculator Time
Try plugging these into your scientific calculator. Put all answers in scientific notation.
37,000 x 7, x 108
x x 10-7
(7x106) x (8x105) 5.6 x 1012

33. Accuracy and Precision
Accuracy: how close a measurement is to the true value
Example: weighing a 50g mass
50.00 g = accurate
32.18g = not accurate
49.99g = accurate

34. Accuracy and Precision
Precision: how close multiple measurements are to each other
Example: weighing a 50g mass
50.00g, 49.99g, 50.00g = precise
32.18g, 51.02g, 63.44g = not precise

35. Accuracy and Precision
An Easy way to remember ACcurate = Correct Precision = Reproducibility

36. Percent Error
Percent Error: the difference between the measured value and the accepted value in a %.
Example:
You measured the temperature of boiling water in the lab at 99.1oC. The accepted value of boiling water is 100oC.

37. Percent Error Formula | 99.1 oC - 100oC | x 100% 100oC
You measured the temperature of boiling water in the lab at oC. The accepted value of boiling water is 100oC.
| 99.1 oC - 100oC |
x 100%
100oC

38. Percent Error Formula | 99.1 oC - 100oC | x 100% 100oC = 0.9%
You measured the temperature of boiling water in the lab at oC. The accepted value of boiling water is 100oC.
| 99.1 oC - 100oC |
x 100%
100oC
= 0.9%

39. Significant Figures
You can read the temperature to the nearest degree.
You can also estimate the temperature to the nearest tenth of a degree by noting the closeness of the liquid inside the lines – but this would involves some amount of uncertainty.

40. Significant Figures
Significant Figure: the number that is known precisely in a measurement, plus a last estimated digit.
When using significant numbers, the last digit is understood to be uncertain

41. Significant Figures Example
We might measure the volume to be 6mL.
The actual volume is the range of 5mL to 7mL (6 + 1)

42. Significant Number Rules

43. Significant Figure Rules 1
All nonzero digits are significant.
Examples:
1.05
Significant Figure Rules 1

44. Significant Figure Rules 2
Sandwiched zeros (zeros between two numbers) are significant.
Examples:
4.0208
50.1
Significant Figure Rules 2

45. Significant Figure Rules 3
Leading zeros (zeros to the left of the 1st nonzero number) are not significant.
Examples:
only has 1 significant digit, the 5
Significant Figure Rules 3

46. Significant Figure Rules 4
Trailing zeros (zeros to the right of a nonzero number) after the decimal are significant.
Examples:
5.10
3.00
Significant Figure Rules 4

47. Significant Figure Rules 5
Trailing zeros (zeros to the right of a nonzero number) before the decimal are significant.
If they are at the rightmost end of an understood decimal as a place holder, they are not significant.
Examples:
50.00 significant
significant
300 not significant
Significant Figure Rules 5

48. Significant Figure Rules 6
A number that is counted is exact and can have unlimited significant figures.
Significant Figure Rules 6

50. How many significant digits?
5.703 70
100.
395830
0.0101
21.0

51. How many significant digits? 70
100.
395830
0.0101
21.0

52. How many significant digits?
100.
395830
0.0101
21.0

53. How many significant digits?
395830
0.0101
21.0

54. How many significant digits?
0.0101
21.0

55. How many significant digits?
21.0

56. How many significant digits?

57. Significant Figures in Calculations
Rounding
Round down if the last digit is 4 or less
Round up if the last digit is 5 or more

58. Significant Figures in Calculations
Addition and Subtraction
The answer is written with the same number of decimal places as the measurement with the fewest decimal places
89.332
one digit after the decimal point
round answer off to 90.4

59. Significant Figures in Calculations
Multiplication and Division
The answer is expressed with the same number of significant figures as the number with the fewest significant figures
2.8 x =
2 significant figures round off to 13
6.85
112.04 =
3 significant figurers round off to

60. Significant Figures in Calculations
Example:
3.489 x ( )
Complete the subtraction first
5.67 – 2.3 = 3.37
Use the subtraction rule to determine the significant figurers
3.489 x 3.4 =
Complete the multiplication
3.489 x 3.4 =
Use the multiplication rule to determine the significant figures 12
Multiplication/Division and Addition/Subtraction
In calculations involving both multiplication/division and addition/subtraction, do the steps in the () first.