Significant Figures and 0’s
Two tutorials on significant figures two supplement the “Significant Figures and 0’s” section of these notes.
[youtube=http://www.youtube.com/watch?v=5UjwJ9PIUvE&feature=related]
[youtube=http://www.youtube.com/watch?v=PNH7_nDE6SQ]
For a more in-depth explanation of “Significant Figures and 0’s” http://en.wikipedia.org/wiki/Significant_figures#Identifying_significant_digits is a good resource.
► All digits from 1 – 9 are significant, no matter where they are in a number.
► Zeroes between the digits 1 – 9 are significant.
→e.g. 3009 has 4 sig digs 140012 has 6 sig digs
► “Leading zeroes” (zeroes in front of a number) are not significant. They are “place holders”.
→e.g. 0.00231 has 3 sig digs 0.1003 has 4 sig digs
► If there is NO decimal point in the number, then trailing zeroes (zeroes at the end of a number) are not significant.
→e.g. 100 has only 1 sig dig 45300 has 3 sig digs
► If there IS a decimal point in the number, then trailing zeroes (zeroes at the end of a number) are significant.
→e.g. 103.00 has 5 sigs digs 0.02480 has 4 sig digs 250. has 3 sig digs
Concerning Calculators:
►Do not round with your calculator
→Round your answer only once
→Round only to the correct number of significant digits
►Do not use ^ on your calc, it does not recognize the order of operations in all cases
►Buttons used for scientific notation in your calc can go by these names: EXP, EE, x10, S.N.
Expressing Error
►Error is a fundamental part of science
►you need to have a way to tell in which cases an error is and is not important
e.g. If you are 80cm off measuring a person’s height it makes a big difference, but not when you are 80cm off when measuring the distance from Vancouver to Kamloops
►There are usually 3 reasons for error
→Physical errors in the measuring device (the device is not accurate)
→Sloppy measuring (you can avoid this one with care)
→Changing ambient conditions
→→e.g. This means the measuring device is altered(such as a metal meter stick because they expand or contract in different temps)
►Error is taken to be half the smallest division on your measuring device
Calculated Errors
►There are two different possibilities:
1.Absolute error
2.Percentage error
Absolute Errror
►This is how off you are from the actual answer
ex.50km off from 400k to Kamloops
►Equation: absolute error= measured-accepted
►positive number means your over the accepted value
►negative means your under the accepted value
►Accepted value can also be your predicted value
►Percentage error is used to measure to determine the importance of the difference
Percent Error
(Song video to remember the equation)
[youtube=http://www.youtube.com/watch?v=DmB5ZuYhFmE&feature=related]
►Most common mistakes are made here
►Equation:
Percent error= absolute error/ accepted value
►Equation an a calculator:
%error= ([measured-accepted]/accepted)x100
%error= ([observed-theoretical]/theoretical)x100
►The “( )” in the equations above represent absolute value(even if answer is negative it can be switched to a positive)
Practice/Example Question:
You measure the weight of an orange to be 15n. the actual weight is 17.5 N, what is the % difference? Round to the nearest tenth.
ANSWER
-14.28%>round to>14.30%
Process
Dimensional Analysis
want to know what 100km/h is in miles/hour? Read these notes!
►Conversion rates help us find this out, they never change unlike currency
► Just like converting between currencies in chemistry it is usually necessary to convert between units
►This process is called dimensional analysis
STEPS
1. Find a unit equality
2. Find the conversion factors
3. Apply conversion factors
4. Cancel units
►You can skip 1,2,3 as long as 4 is correct
Practice/Example Question:
How many miles are there in 120km?
1.[unit equality] 1mi=1.6km
2.[conversion factor] 1=(1mi/1.6km)
3.[apply the conversion factor] (120km)(1mi/1.6km)
4.[cancel units] (120)(1/1.6)
[answer] 75