1. 1.2 Measurements and Uncertainties

2. 1.2.1 State the fundamental units in the SI system
In science, numbers aren’t just numbers.
They need a unit. We use standards for this unit.
A standard is:
a basis for comparison
a reference point against which other things can be evaluated
Ex. Meter, second, degree

3. 1.2.1 State the fundamental units in the SI system
The unit of a #, tells us what standard to use.
Two most common system:
English system
Metric system
The science world agreed to use the International System (SI)
Based upon the metric system.

4. 1.2.1 State the fundamental units in the SI system

5. 1.2.1 State the fundamental units in the SI system
Conversions in the SI are easy because everything is based on powers of 10

6. Units and Standards
Ex. Length.
Base unit is meter.

7. 1.2.2 Distinguish between fundamental and derived units and give examples of derived units.
A derived unit is a unit which can be defined in terms of two or more fundamental units.
For example speed(m/s) is a unit which has been derived from the fundamental units for distance(m) and time(s)

8. Some derived units don’t have any special names
1.2.2 Distinguish between fundamental and derived units and give examples of derived units.
Some derived units don’t have any special names
Quantity Name
Quantity Symbol
Unit Name
Unit Symbol
Area A
Square meter
Volume V
Cubic meter
Acceleration a
Meters per second squared
Density p
Kilogram per cubic meter

9. Others have special names
1.2.2 Distinguish between fundamental and derived units and give examples of derived units.
Others have special names
Quantity Name
Quantity Symbol
Special unit name
Special unit Symbol
Frequency f Hz
Force F N
Energy/Work
E, W J
Power P W
Electric Potential V

10. Common conversions 2.54 cm = 1 in 4 qt = 1 gallon
5280 ft = 1 mile 4 cups = 48 tsp
2000 lb = 1 ton
1 kg = lb
1 lb = g
1 lb = 16 oz
1 L = 1.06 qt

11. 1.2.3 Convert between different units of quantities
Convert your age into seconds.
Most people can do that if given a few minutes. But do you know what you were doing.
Write what you know.

12. 1.2.3 Convert between different units of quantities
Let’s break it down.
Write what you know.
The unit you are coming from goes on bottom.
The unit you are going to is placed on top.
Multiply on the top and bottom and simplify!

13. 1.2.3 Convert between different units of quantities
Let’s break it down.
32ft = ______in
100lbs = ______ kg
85cm = _______ in

14. 1. 2. 4 State unites in the accepted SI format 1. 2
1.2.4 State unites in the accepted SI format State values in scientific notation and in multiples of units with appropriate prefixes
Scientific Notation
A short-hand way of writing large numbers without writing all of the zeros.

15. Scientific notation consists of two parts:
A number between 1 and 10
A power of 10
N x 10x

16. The Distance From the Sun to the Earth
93,000,000 miles

17. Step 1 93,000,000 = 9.3000000 Move the decimal to the left
Leave only one number in front of decimal
93,000,000 =

18. Step 2
Write the number without zeros
93,000,000 = 9.3

19. Step 3 7 93,000,000 = 9.3 x 10 Count how many places you moved decimal
Make that your power of ten
93,000,000 = 9.3 x 10 7

20. The power of ten is 7 because the decimal moved 7 places. 7
93,000,000 = 9.3 x 10 7

21. 93,000, Standard Form
9.3 x Scientific Notation

22. Practice Problem -----> -----> -----> ----->
Write in scientific notation.
Decide the power of ten.
98,500,000 = 9.85 x 10?
64,100,000,000 = 6.41 x 10?
279,000,000 = 2.79 x 10?
4,200,000 = 4.2 x 10?
9.85 x 107
----->
6.41 x 1010
----->
2.79 x 108
----->
----->
4.2 x 106

23. More Practice Problems
On these, decide where the decimal will be moved.
734,000,000 = ______ x 108
870,000,000,000 = ______x 1011
90,000,000,000 = _____ x 1010
Answers
3) 9 x 1010
7.34 x 108
2) 8.7 x 1011

24. Complete Practice Problems
Write in scientific notation.
50,000
7,200,000
802,000,000,000
Answers
1) 5 x 104
2) 7.2 x 106
3) 8.02 x 1011

25. Scientific Notation to Standard Form
Move the decimal to the right
3.4 x 105 in scientific notation
move the decimal
--->
340,000 in standard form

26. Practice: Write in Standard Form
Move the decimal to the right.
6.27 x 106
9.01 x 104
6,270,000
90,100

27. 1.2.7 Distinguish between precision and accuracy
Accuracy is how close to the “correct” value
Precision is being able to repeatedly get the same value
Measurements are accurate if the systematic error is small
Measurements are precise if the random error is small.
Examples: groupings on 4 different targets

28. Example of precision and accuracy
A voltmeter is being used to measure the potential difference across an electrical component. If the voltmeter is faulty in some way, such that it produces a widely scattered set of results when measuring the same potential difference, the meter would have low precision. If the meter had not been calibrated correctly and consistently measured 0.1V higher than the true reading (zero offset error), it would be in accurate.

29. There are two types of error, random and systematic.
1.2.6 Describe and give examples of random and systematic errors Explain how the effects of random errors may be reduced.
There are two types of error, random and systematic.
Random Errors - occur when you measure a quantity many times and get lots of slightly different readings.
Examples - misreading apparatus, Errors made with calculations, Errors made when copying collected raw data to the lab report
Can be reduced by repeating measurements many times.
Measurements are precise if the random error is small

30. 1. 2. 6 Describe and give examples of random and systematic errors. 1
1.2.6 Describe and give examples of random and systematic errors Explain how the effects of random errors may be reduced.
There are two types of error, random and systematic.
Systematic error – when there is something wrong with the measuring device or method
Examples – poor calibration, a consistently bad reaction time on the part of the recorder, parallax error
Can be reduced by repeating measurements using a different method, or different apparatus and comparing the results, or recalibrating a piece of apparatus
Measurements are accurate if the systematic error is small.

31. Graphs can be used to help us identify different types of error.
Low precision is represented by a wide spread of points around an expected value.
Low accuracy is represented by an unexpected intercept on the y-axis. Low accuracy gives rise to systematic errors.

32. Accurate or Precise?

33. Accurate or Precise?

34. Accurate or Precise?

35. Accurate or Precise?

36. 1.2.9 Calculate quantities and results of calculations to the appropriate number of significant figures
The numbers reported in a measurement are limited by the measuring tool 
Significant figures in a measurement include the known digits plus one estimated digit

37. 1.2.9 Calculate quantities and results of calculations to the appropriate number of significant figures
The number of sig figs should reflect the precision of the value of the input data.
If the precision of the measuring instrument is not known then as a general rule, give your answer to 3 sig figs.

38. Three Basic Rules Non-zero digits are always significant.
523.7 has ____ significant figures
Any zeros between two significant digits are significant.
23.07 has ____ significant figures
A final zero or trailing zeros if it has a decimal, ONLY, are significant.
3.200 has ____ significant figures
200 has ____ significant figures

39. Practice How many sig. fig’s do the following numbers have?
38.15 cm _________
5.6 ft ____________
2001 min ________
50.8 mm _________
25,000 in ________
200. yr __________
0.008 mm ________
oz ________

40. Exact Numbers
Can be thought of as having an infinite number of significant figures
An exact number won’t limit the math.
1. 12 items in a dozen
2. 12 inches in a foot
3. 60 seconds in a minute

41. Example Video
4:45

42. Multiplying and Dividing
Round to so that you have the same number of significant figures as the measurement with the fewest significant figures. 
two sig figs
x three sig figs
453.6  answer
450 two sig figs

43. Practice: Multiplying and Dividing
In each calculation, round the answer to the correct number of significant figures.
A X 4.2 =
1) 9    2) 9.2   3) 9.198 
B ÷ 0.07 =          
1)    2) 62   3) 60

44. Adding and Subtracting
Base your answer on which number column is lacking significance.   
  25
26.34  Calculated Answer
26 Rounded answer based on sig figs

45. Practice: Adding and Subtracting
In each calculation, round the answer to the correct number of significant figures.
A =          
1)   2) 256.8  3) 257    
B  =          
1)   2) 40.73  3) 40.7 
 

46. 1.2.9 Calculate quantities and results of calculations to the appropriate number of significant figures
Practice
How many sig figs are in each number listed?
A) D) 0.060
B) E) 90210
C) F)
Calculate, giving the answer with the correct number of sig figs.
12.6 x 0.53
(12.6 x 0.53) – 4.59
(25.36 – 4.1) ÷ 2.317

47. 1.2.9 Practice 13(Dickinson)
A meter rule was used to measure the length, height and thickness of a house brick and a digital balance was used to measure its mass. The following data were obtained.
Length = 20.5cm, height = 8.4cm, thickness 10.2cm, mass = g
Calculate the density of the house brick and give your answer to an appropriate number of sig figs.

48. 1.2.9 Practice 13(Dickinson) Solution Density = (mass/volume)
Density = g cm-3
Density = 1.8 g cm-3

49. 1.2.10 State uncertainties as absolute, fractional and percentage uncertainties.
Random uncertainties(errors) due to the precision of a piece of apparatus can be represented in the form of an uncertainty range.
Experimental work requires individuals to judge and record the numerical uncertainty of recorded data and to propagate this to achieve a statement of uncertainty in the calculated results.

50. Analogue instruments = +/- half of the limit of reading
State uncertainties as absolute, fractional and percentage uncertainties.
Rule of Thumb
Analogue instruments = +/- half of the limit of reading
Ex. Meter stick’s limit of reading is 1mm so it’s uncertainty range is +/- 0.5mm
Digital instruments = +/- the limit of the reading
Ex. Digital Stopwatch’s limit of reading is 0.01s so it’s uncertainty range is +/- 0.01s

51. 1.2.10 State uncertainties as absolute, fractional and percentage uncertainties.
We can express this uncertainty in one of three ways- using absolute, fractional, or percentage uncertainties
Absolute uncertainties are constants associated with a particular measuring device.
(Ratio) Fractional uncertainty = absolute uncertainty
measurement
Percentage uncertainties = fractional x 100%

52. Example A meter rule measures a block of wood 28mm long.
Absolute = mm +/- 0.5mm
Fractional = 0.5mm = mm +/
28mm
Percentage = x 100% =
28mm +/- 1.79%

53. 1.2.10 State uncertainties as absolute, fractional and percentage uncertainties.
Random uncertainties(errors) due to the precision of a piece of apparatus can be represented in the form of an uncertainty range.
Experimental work requires individuals to judge and record the numerical uncertainty of recorded data and to propagate this to achieve a statement of uncertainty in the calculated results.