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1
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- Warning!
Lots of math
(not tough math, but lots of it)
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2
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- Remember there are qualitative and quantitative observations
- This chapter deals with the quantitative!
- called measurements
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3
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- these measurements are not just numbers
- they have units
- as in
5 millimeters,
75 people,
16 mph, etc.
- but first…
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4
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- Some numbers are just too darn big or too small to deal with reasonably
- Scientific Notation is a method for making very large or very small
numbers more compact and easier to write.
- as in: 64,400,000,000 can be written 6.44 x 1010
- it’s easy! :)
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5
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- Description: scientific notation must be written as the product of a number
between 1 and 10 and the appropriate power of 10
- just count how many times you have to move the decimal point to get a
number between 1 and 10
- if the number is getting
smaller the exponent will
compensate by getting
bigger
and vice versa
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6
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- 238,000
- 1,500,000
- 0.00043
- 0.135
- 357
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7
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- go into a restaurant, sit down, just tell the waitress “two,” and see
what you get
- Units are used everyday to give meaning to numbers
- people have used them since, like, forever…
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8
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- the English system is used in the US; the metric system is used everywhere
else
- scientists everywhere use metric and standardized it into the International
System (SI)
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9
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- these are the basic units of SI
- know them,
love them,
marry them
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10
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- and these are the prefixes we use to make them even more convenient
- “1 mm” is easier to use &
write than “one thousandth of a meter”
- know them, love them, marry them
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11
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- length is based on the meter
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12
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- volume is how much 3D space something takes up
- SI unit is the m3
- one thousandth of that is the dm3, aka the liter
- 0.001 of that is cm3 or ml
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13
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- we mostly measure volume with a
- graduated cylinder
- but also these critters, all of
- which are marked on the side
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14
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- Remember that when you use the Graduated cylinder to read the bottom of
the meniscus
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15
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- mass is measured in grams (even though SI unit is kg)
- measured with a balance
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16
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- this is a table to get you better acquainted with it all
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17
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- many measurements are made of objects that make us estimate
- so, we’ll always argue about the last number or two
- the ones we agree on are called certain, the argued ones uncertain
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18
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- every measuring device has some degree of uncertainty
- the certain numbers + the one uncertain one are called significant…
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19
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- which instrument gives us more sigfigs?
- that’s the one you want to use (but it probably costs a lot more!)
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20
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- the whole rest of your science/math life must reflect the measuring
devices you use. Therefore, you
need to know about significant figures (aka: sigfigs)
- so what about zero’s and what not?
- there are rules! yippee! ready?
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21
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22
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23
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- the mass of an eyelash
is 0.000304 g
- 3
- the length of the skidmark was 1.270 x 102 m
- 4
- A 125-g sample of chocolate chip cookie contains 10 g of chocolate
- 3, 1
- the volume of soda remaining in a can after a spill is 0.09020 L
- 4
- a dose of antibiotic is 4.0 x 10-1 cm3
- 2
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24
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- yes, there are rules even for this
- remember to use only the first digit to the right of the last sigfig to
help you decide
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25
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- there are only two basic rules here, one to do with multiplication and
division, the other addition and subtraction…
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26
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- Multiplying and dividing
- answer will have as many sigfigs as the working number w/ the fewest
- examples
- 2.34 • 3.2 = 7.488?
- smallest number of s/d is 2 so 7.5
- 35.0 / 6.734 = 5.1975051975?
- smallest number of s/d is 3 so 5.20
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27
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- addition and subtraction…
- first add them up! don’t worry about sigfigs until the end!
- 3.75 + 4.1 = 7.85
- you can only go to where all numbers have something to contribute, so
can only go to 7.9
- 3.987 + 4.60 = 8.587
- but can only go to 0.01, so 8.59
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28
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- I have to buy 72 CostCo muffins, but they only sell them by the dozen.
Do I just give up? May it never be!
- I convert into dozens!
- but I have to know the relationship b/t individuals and dozens!
- called a conversion factor!
- here 1 dozen = 12
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29
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- unit1 x conversion factor = unit2
- we’ll…
1) make a
starting point,
2) determine
where we’re going,
then…
3) build a bridge
to it with the
conversion factor
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30
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- 1) write down what you know (given),
2) where you’re going, then
3) build a bridge (your book calls the bridge an equivalence
statement) between them…
- Change 100 mm into m.
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31
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32
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33
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- Change 45mm into km.
- (Hint: you might make this a 2-stepper.)
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34
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- here we learn both the different temp scales and how to convert between
them
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35
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- the Big Three Temp Scales are Fahrenheit, Celsius, and Kelvin
- in science we use almost exclusively C and K
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36
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- a degree C and K are the same amount; they just differ by their starting
points
- they only differ by 273
- thus, and simply
- TC + 273 = TK
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37
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- What is 70˚C in kelvins?
- TC + 273 = TK
- 70 + 273 = 343 K
- Nitrogen boils at 77 K. What is that in C?
- TC + 273 = TK
- TC = TK - 273
- TC = 77 - 273
- TC = -196 ˚C
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38
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- here we have different size units and different starting points! yikes!
- short story:
TF = 1.80TC + 32
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39
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- It’s 28˚C outside. What is that in F?
- TF = 1.8TC + 32
- TF = 1.8(28) + 32
- TF = 50. + 32
- TF = 82 ˚F
- It’s -40˚C in that lab freezer. What’s that in F?
- TF = 1.8TC + 32
- TF = 1.8(-40) + 32
- TF = -72 + 32
- TF = -40˚F (!)
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40
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- You have a 101˚F fever. What is that in C?
- TF = 1.8TC + 32
- 101 = 1.8TC + 32
- 69 = 1.8TC
- 38 = TC
- Page 142 has a bunch of cutesy conversion equations
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41
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- density is just how much stuff is crammed into a certain space
- in science speak it’s mass/volume:
- D = m/V
- finding mass is no problem; how do you find volume?
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42
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- one can either use dimensions (like lxwxh) or volume displacement for
irregular objects
- take volume before, volume after - tada!
the difference is the volume of your object
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43
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44
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45
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Notes
