1. Scientific measurement
Chapter 3
Scientific measurement

2. Types of measurement Quantitative- (quantity) use numbers to describe
Qualitative- (quality) use description without numbers
4 meters
extra large
Hot
100ºC
Quantitative
Qualitative
Qualitative
Quantitative

3. Which do you Think Scientists would prefer
Quantitative- easy check
Easy to agree upon, no personal bias
The measuring instrument limits how good the measurement is

4. How good are the measurements?
Scientists use two word to describe how good the measurements are
Accuracy- how close the measurement is to the actual value
Precision- how well can the measurement be repeated

5. Differences
Accuracy can be true of an individual measurement or the average of several
Precision requires several measurements before anything can be said about it
examples

6. Let’s use a golf anaolgy

7. Accurate? No
Precise?
Yes

8. Accurate?
Yes
Precise?
Yes

9. Precise? No
Accurate? NO

10. Accurate?
Yes
Precise?
We cant say!

11. Reporting Error in Experiment
A measurement of how accurate an experimental value is
(Equation) Experimental Value – Accepted Value
Experimental Value is what you get in the lab
accepted value is the true or “real” value
Answer may be positive or negative

12. | experimental – accepted value | x 100
Reporting Error in Experiment
% Error =
| experimental – accepted value | x 100
accepted value
OR | error| x 100
Answer is always positive

13. Example: A student performs an experiment and recovers 10.50g of NaCl product. The amount they should of collected was 12.22g on NaCl.
Calculate Error
Error = g g
= g
Calculate % Error
% Error = | -1.72g | x 100
12.22g
= % error

14. Convert to Scientific Notation And Vise Versa
Example: 2.5x10-4 (___) is the coefficient
and ( ___) is the power of ten
2.5 -4
Convert to Scientific Notation And Vise Versa
= ____________
3.44 x = ____________
2.16 x 103 = ____________
= ____________
5.5 x 106
0.0344
2160
1.75 x 10-3

15. Multiplying and Dividing Exponents using a calculator
(3.0 x 105) x (3.0 x 10-3) = _________________
(2.75 x 108) x (9.0 x 108) = ________________
(5.50 x 10-2) x (1.89 x 10-23) = ____________
(8.0 x 108) / (4.0 x 10-2) = ________________
9.00 x 102
2.475 x 1017
1.04 x 10-24
2.0 x 1010

16. Adding and Subtracting Exponents using a calculator
7.5 x x 109 = __________________
5.5 x x 10-5 = _________________
5.498 x 10-2

17. Significant figures (sig figs)
How many numbers mean anything
When we measure something, we can (and do) always estimate between the smallest marks.
4.5 inches 2 1 3 4 5

18. Significant figures (sig figs)
Scientist always understand that the last number measured is actually an estimate
4.56 inches 1 2 3 4 5

19. Sig Figs
What is the smallest mark on the ruler that measures cm?
142 cm?
140 cm?
Here there’s a problem does the zero count or not?
They needed a set of rules to decide which zeroes count.
All other numbers do count
Tenths place
Ones place
Yikes!

20. Which zeros count?
Those at the end of a number before the decimal point don’t count
12400
If the number is smaller than one, zeroes before the first number don’t count
0.045
= 3 sig figs
= 2 sig figs

21. Which zeros count? Zeros between other sig figs do. 1002
zeroes at the end of a number after the decimal point do count
If they are holding places, they don’t.
If they are measured (or estimated) they do
= 4 sig figs
= 6 sig figs

22. Sig Figs Only measurements have sig figs. Counted numbers are exact
A dozen is exactly 12
A a piece of paper is measured 11 inches tall.
Being able to locate, and count significant figures is an important skill.

23. Sig figs. How many sig figs in the following measurements? 458 g

24. Sig Figs. 405.0 g 4050 g 0.450 g 4050.05 g 0.0500060 g = 4 sig figs

25. Question 50 is only 1 significant figure
if it really has two, how can I write it?
A zero at the end only counts after the decimal place.
Scientific notation
5.0 x 101
now the zero counts.
50.0
= 3 sig figs

26. Adding and subtracting with sig figs
The last sig fig in a measurement is an estimate.
Your answer when you add or subtract can not be better than your worst estimate.
have to round it to the least place of the measurement in the problem

27. For example
27.93
6.4 +
First line up the decimal places
27.93
6.4 +
27.93
6.4
Find the estimated numbers in the problem
Then do the adding
34.33
This answer must be rounded to the tenths place

28. Rounding rules look at the number behind the one you’re rounding.
If it is 0 to 4 don’t change it
If it is 5 to 9 make it one bigger
round to four sig figs
to three sig figs
to two sig figs
to one sig fig
= 45.46
= 45.5
= 45
= 50

29. Practice
= = 11.7
6.0 x x 103
6.0 x x 10-3
= = 615
= = 2.118
= 3198 = 3.2 x 103
= 2.12 = 2.1
= = 6.2
= 374
= = 5.6 x 10-2

30. Multiplication and Division
Rule is simpler
Same number of sig figs in the answer as the least in the question
3.6 x 653
2350.8
3.6 has 2 s.f. 653 has 3 s.f.
answer can only have 2 s.f.
2400

31. Multiplication and Division
practice
4.5 / 6.245
4.5 x 6.245
x .043
3.876 / 1983
16547 / 714
= = 0.72
= = 28
= = 0.42
= =
= = 23.2

32. The Metric System Easier to use because it is …… a decimal system
Every conversion is by some power of ….
10.
A metric unit has two parts
A prefix and a base unit.
prefix tells you how many times to
divide or multiply by 10.

33. Base Units Length - meter more than a yard - m
Mass - grams - a bout a raisin - g
Time - second - s
Temperature - Kelvin or ºCelsius K or C
Energy - Joules- J
Volume - Liter - half f a two liter bottle- L
Amount of substance - mole - mol

34. Prefixes Kilo K 1000 times Hecto H 100 times Deka D 10 times
deci d 1/10
centi c 1/100
milli m 1/1000
kilometer - about 0.6 miles
centimeter - less than half an inch
millimeter - the width of a paper clip wire

35. Converting K H D d c m
King Henry Drinks (basically) delicious chocolate milk
how far you have to move on this chart, tells you how far, and which direction to move the decimal place.
The box is the base unit, meters, Liters, grams, etc.

36. k h D d c m Conversions 5 6 Change 5.6 m to millimeters
starts at the base unit and move three to the right.
move the decimal point three to the right 5 6

37. k h D d c m Conversions convert 25 mg to grams convert 0.45 km to mm
convert 35 mL to liters
It works because the math works, we are dividing or multiplying by 10 the correct number of times (homework)
= g
= 450,000 mm
= L

38. Volume calculated by multiplying L x W x H
Liter the volume of a cube 1 dm (10 cm) on a side
so 1 L =
10 cm x 10 cm x 10 cm or 1 L = 1000 cm3
1/1000 L =
1 cm3
Which means 1 mL = 1 cm3

39. Volume 1 L about 1/4 of a gallon - a quart
1 mL is about 20 drops of water or 1 sugar cube

40. Mass weight is a force, Mass is the amount of matter.
1gram is defined as the mass of 1 cm3 of water at 4 ºC.
1 ml of water = 1 g
1000 g =
1000 cm3 of water
1 kg = 1 L of water

41. Mass 1 kg = 2.5 lbs 1 g = 1 paper clip
1 mg = 10 grains of salt or 2 drops of water.

42. Density how heavy something is for its size
the ratio of mass to volume for a substance
D = M / V M D V

43. Density is a Physical Property The density of an object remains
_________ at _______ ________
Therefore it is possible to identify an unknown by figuring out its density.
Story & Demo (king and his gold crown)
constant
constant
temperature

44. What would happen to density if temperature decreased?
As temperature decreases molecules
______ _____
And come closer together therefore making volume _________
The mass ______ ____ _______
Therefore the density would _______
Exception _____________________
Therefore Density decreases ICE FLOATS
slow
down
decrease
STAYS
THE
SAME
INCREASE
WATER, because it expands.

45. Units for Density
1. Regularly shaped object in which a ruler is used. ______
2. liquid, granular or powdered solid in which a graduated cylinder is used ______
3. irregularly shaped object in which the water displacement method must be used _____
g/cm3
g/ml
g/ml

46. Sample Problem:
What is the density of a sample of Copper with a mass of 50.25g and a volume of 6.95cm3?
D = M/V
D = 50.25g / 6.95 cm3
= = 7.23 cm3

47. Sample Problem 2. A piece of wood has a density of
0.93 g/ml and a volume of 2.4 ml What is its mass? M
M = D x V D V
M = 0.93 g/ml x 2.4 ml
= = 2.2 g

48. Problem Solving or Dimensional Analysis
Identify the unknown
What is the problem asking for
List what is given and the equalities needed to solve the problem.
Ex. 1 dozen = 12
Plan a solution
Equations and steps to solve
(conversion factors)
Do the calculations
Check your work:
Estimate; is the answer reasonable
UNITS
All measurements need a NUMBER & A UNIT!!

49. Dimensional Analysis
Use the units (__________) to help analyze (______) the problem.
Conversion Factors: Ratios of equal measurements.
Numerator measurement = Denominator measurement
Using conversion factors does not change the value of the measurement
Examples; 1 ft = _____ (_________)
1 ft__ or in (_____________ __________)
12 in ft
dimensions
solve
12 in
equality
Conversion
factors

50. What you are being asked to solve for in the problem will determine which conversion factors need to be used.
Common Equalities and their conversion factors:
1 lb = _____oz
1 mi = ______ft
1 yr = ______days
1 day = ____hrs
1 hr = ____min
1 min = ____sec 16
5280
365 24 60 60

51. Sample Problems using Conversion Factors:
How many inches are in 12 miles?
Equalities: 1 mi = 5280 ft
1 ft = 12 in
12miles X X =
sig figs = 760,000 inches
760,320 inches
12 in
1 ft
5280 ft
1 mi

52. 2. How many seconds old is a 17 year old?
Equalities: 1 yr = 365 days; 1 day = 24 hrs; hr = 60 min; 1 min = 60 sec
17 yrs X X X X
= 536,112,000 sec
Sig figs = 540,000,000 sec
365 day
1 yr
24 hrs
1 day
60 min
1 hr
60 sec
1 min

53. 3. How many cups of water are in 5.2 lbs of water?
Equalities: 1 lb = 16 oz; 8 oz = 1 cup
5.2 lbs X X =
= 10.4 cups
Sig figs = 1.0 x 101 cups
83.2 cup 8
16 oz
1 lb
1 cup
8 oz

54. Equalities: 1 g = 1000 mg; 1 L = 1000 ml X X = 13.6 g 1 ml 1000 mg 1 g
3. If the density of Mercury (Hg) at 20°C is 13.6 g/ml. What is it’s density in mg/L?
Equalities: 1 g = 1000 mg; 1 L = 1000 ml
X X =
13.6 g
1 ml
1000 mg
1 g
1000 ml
1 L
13,600,000 mg/L
13.6 x 107 mg/L