1. Day 2. SI Units

2. International System of Units (SI)
Over hundreds of years, physicists (and other
scientists) have developed traditional ways (or
rules) of expressing their measurements.
If we can’t trust the measurements, we can put no faith in reports of scientific research.
the International System of Units (SI) is used
for scientific work throughout the world –
everyone accepts and uses the same rules, and
understands that there are limitations to the
rules.

3. SI
SI Rules
In the SI system all physical quantities can be expressed as some combination of fundamental units, called base units. (i.e., mol, m, kg, …..) . For example:
1N = 1 kg•m/s => unit for force
1 J = 1 kg•m2/s2 => unit for energy

4. SI SI Rules The SI convention includes both quantity and unit symbols.
Note: these are symbols (e.g., 60 km/h) and are not abbreviations (e.g., mi./hr/)
When converting units, the method most commonly used is multiplying by conversion factors, which are memorized or referenced (e.g., 1 m = 100 cm, 1 h = 60 min = 3600 s)
It is also important to pay close attention to the units, which are converted by multiplying by a conversion factor (e.g., 1 m/s = 3.5 km/h)

5. SI (handout)
Useful conversion factors!

6. copy
SI Units
It is easiest to keep track of your units if you use ratios/conversion factors to convert your units.
Example problems:
Convert 34.5 mm to m.
Convert 23.6 mm to km.
(HINT: You can avoid careless mistakes by first converting from mm into m, and then converting from m to km.)
3) Convert 5 km/h into m/s

7. SI Units Practice Convert 12.5 cm into mm
An athlete completed a 5-km race in 19.5 min. Convert this time into hours.
A train is travelling at 95 km/h. Convert 95 km/h into metres per second (m/s)

8. worksheet

9. Day 3. Uncertainty and Significant Digits

10. Uncertainty in Measurements:
There are two types of quantities used in
science: exact values and measurements.
Exact values include defined quantities (1 m = 100cm) and counted values (5 beakers or 10 trials).
Measurements, however, are not exact ………there is always some uncertainty or error associated with every measurement. Because of this, there is an international agreement about the correct way to record measurements

11. Significant Digits
The certainty of any measurement is communicated by the number of significant digits in the measurement.
In a measured or calculated value, significant digits are the digits that are known for certain and include the last digit that is estimated or uncertain.
There are a set of rules that can be used to determine whether or not a digit is significant (handout)

12. Significant Digits Rules:
(on handout)
Rules:
All non-zero digits are significant: N has four significant digits
In a measurement with a decimal point, zeroes are placed before other digits are not significant: has two significant digits
Zeroes placed between other digits are always significant: 7003 has four significant digits
Zeroes placed after other digits behind a decimal are significant: km and kg each has four significant digits

13. Significant Digits In a calculation:
(on handout)
In a calculation:
When adding or subtracting measured quantities, the final answer should have no more than one estimated digit (the answer should be rounded off to the least number of decimals in the original measurement) **number of decimal places matter
When multiplying or dividing, the final answer should have the same number of significant digits as the original measurement with the least number of significant digits ** significant digits matter
**when doing long calculations, record all of the digits until the final answer is determined, and then round off the answer to the correct number of significant digits (ADD TO HANDOUT)

14. Significant Digits
Practice:

15. Significant digits

16. Precision
Measurements also depend on the precision of the measuring instruments used – the amount of information that the instrument provides
For example, cm is more precise than 2.86 cm
Precision is indicated by the number of decimal places in a measured or calculated value

17. Precision Rules for precision:
All measured quantities are expressed as precisely as possible. All digits shown are significant with any error or uncertainty in the last digit.
For example, in the measurement cm, the uncertainty lies with the digit 4

18. Precision
The precision of a measuring instrument depends on its degree of fineness and the size of the unit being used
For example, a ruler calibrated in millimetres is more precise than a ruler calibrated in centimetres

19. Precision
Any measurement that falls between the smallest divisions on the measurement instrument is an estimate. We should always try to read any instrument by estimating tenths of the smallest division.

20. Precision
4. The estimated digit is always shown when recording the measurement.
Eg. The 7 in the measurement 6.7 cm would be the estimated digit

21. Precision
5. Should the object fall right on a division mark, the estimated digit would be 0.

22. Precision

26. worksheet

27. Day 4. Error

28. Error in Measurement
Many people believe that all measurements are reliable (consistant over many trials), precise (to as many decimal places as possible), and accurate (representing the actual value). But there are many things that can go wrong when measuring. For example:

29. Error in Measurement
There may be limitations that make the instrument or its use unreliable (inconsistent)
The investigator may make a mistake or fail to follow the correct techniques when reading the measurement to the available precision (number of decimal places)
The instrument may be faulty or inaccurate; a similar instrument may give different readings

30. What are three things you can do during an experiment to help eliminate errors?
To be sure that you have measured correctly, you should repeat your measurement at least three times
If your measurements appear to be reliable, calculate the mean and use that value
To be more precise about the accuracy, repeat the measurements with a different instrument

31. Two Types of Error
Random error results when an estimate is made to obtain the last digit for an measurement
The size of the random error is determined by the precision of the measuring instrument
For example, when measuring length with a measuring tape, it is necessary to estimate between the marks on the measuring tape
If these marks are 1 cm apart, the random error will be greater and the precision will be less than if the marks were 1 mm apart.
Such errors can be reduced by taking the average of several readings

32. Two Types of Error RANDOM ERROR
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RANDOM ERROR
Results when the last digit is estimated
Reduced by taking the average of several readings

33. Systemic Error
is associated with an inherent problem with the measuring system, such as the presence of an interfering substance, incorrect calibration, or room conditions.
For example, if a balance is not zeroed at the beginning, all measurements will have a systemic error; using a slightly worn metre stick will also introduce error
Such errors are reduced by adding or subtracting the known error or calibrating the instrument

34. Due to a problem with the measuring device
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SYSTEMIC ERROR
Due to a problem with the measuring device
Reduced by adding/subtracting the error or calibrating the device

35. Accuracy & Precision
In everday usage, “accuracy” and “precision” are used interchangeably to descibe how close a measurement is to a true value, but in science it is important to make a distinction between them

36. Accuracy & Precision Accuracy:
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Accuracy & Precision
Accuracy:
- Refers to how closely a measurement agrees with the accepted value of the object being measured
Precision:
Describes how it has been measurement
Depends on the precision of the measurement

37. Percentage Error
No matter how precise a measurement is, it still may not be accurate.
Percentage Error is the absolute value of the different between experimental and accepted values expressed as a percentage of the accepted value

38. Percentage Difference
Sometimes if two values of the same quantity are measured, it is useful to compare the precision of these values by calculating the percentage difference between them

39. Practice
Worksheet – math skills