1. chapter 5 Measurements & Calculations
Warning! Lots of math (not tough math, but lots of it)

2. Remember there are qualitative and quantitative observations
This chapter deals with the quantitative!
called measurements

3. these measurements are not just numbers
they have units
as in 5 millimeters, 75 people, 16 mph, etc.
but first…

4. 5.1 scientific notation
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! :)

5. 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

6. examples
238,000
2.38 x 105
1,500,000
1.5 x 106
4.3 x 10-4
0.135
1.35 x 10-1
357
3.57 x 102

7. 5.2 units Units are used everyday to give meaning to numbers
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…

8. 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)

9. these are the basic units of SI
know them, love them, marry them

10. m 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

11. 5.3 measurements of length, volume, and mass
length is based on the meter

12. 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

13. graduated cylinder we mostly measure volume with a
but also these critters, all of
which are marked on the side

14. Remember that when you use the Graduated cylinder to read the bottom of the meniscus

15. mass is measured in grams (even though SI unit is kg)
measured with a balance

16. this is a table to get you better acquainted with it all

17. 5.4 uncertainty in measurement
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

18. 31.7
31.8
31.6
every measuring device has some degree of uncertainty
the certain numbers + the one uncertain one are called significant…

19. which instrument gives us more sigfigs?
that’s the one you want to use (but it probably costs a lot more!)

20. 5.5 significant figures there are rules! yippee! ready?
the whole rest of your science/math life must reflect the measuring devices so you’se all gotta know dese tings called sigfigs
so what about zero’s and what not?
there are rules! yippee! ready?

22. one more thing…

23. examples the mass of an eyelash is 0.000304 g 3
the length of the skidmark was 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 L
a dose of antibiotic is 4.0 x 10-1 cm3 2

24. rounding off 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

25. determining sigfigs in calculations
there are only two basic rules here, one to do with multiplication and division, the other addition and subtraction…

26. examples 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 / = ?
smallest number of s/d is 3 so 5.20

27. addition and subtraction…
first add them up! don’t worry about sigfigs until the end!
= 7.85
you can only go to where all numbers have something to contribute, so can only go to 7.8
= 8.587
but can only go to 0.01, so 8.59

28. 5.6 problem solving and dimensional analysis
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

29. 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

30. 1) write down what you know (given), 2) where you’re going, then 3) build a Bob/Eddie bridge (your book calls the bridge an equivalence statement) between them…
Change 100 mm into m.
bridge
where you’re going
given
100mm x 1 m
0.1 = m
BOB 
1000 mm
EDDIE

31. 5460 = 546cm x 10 mm mm  1 cm Change 546 cm into mm. bridge
where you’re going
given
546cm x 10 mm
5460 = mm
BOB  1 cm
EDDIE

32. 7.75x106 = µg 7.75g x 106 µg  g 1 or 7,750,000 Convert 7.75g to µg.
bridge
where you’re going
given µg
7.75g x
106
7.75x106
or 7,750,000 = µg  g 1

33. Change 45mm into km.
(Hint: you might make this a 2-stepper.) km 1
45mm 1 m =
1000
1000 m mm
4.5x10-5 or km

34. 5.7 temperature conversions: an approach to problem solving
here we learn both the different temp scales and how to convert between them

35. the Big Three Temp Scales are Fahrenheit, Celsius, and Kelvin
in science we use almost exclusively C and K

36. converting between K and C
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 = TK

37. examples What is 70˚C in kelvins? TC + 273 = TK 70 + 273 = 343 K
Nitrogen boils at 77 K. What is that in C?
TC = TK - 273
TC =
TC = -196 ˚C

38. converting between F and C
here we have different size units and different starting points! yikes!
short story: TF = 1.80TC + 32

39. examples TF = 1.8TC + 32 It’s 28˚C outside. What is that in F?
TF = 82 ˚F
It’s -40˚C in that lab freezer. What’s that in F?
TF = 1.8(-40) + 32
TF =
TF = -40˚F (!)

40. examples TF = 1.8TC + 32 You have a 101˚F fever. What is that in C?
Page 142 has a bunch of cutesy conversion equations

41. 5.8 density
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?

42. 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

43. d.m.v helper m D V

44. d.m.v helper m D V

45. d.m.v helper m D V