1. Scientific Measurement & Data Analysis
Chapter 2
Scientific Measurement & Data Analysis

2. It depends upon the units!!!
Units of Measurement
Which is bigger?
5 or
5 quarters and 120 pennies
5 pennies and 120 quarters
It depends upon the units!!!

3. Units of Measurement – English
English – Developed from common use.
Lacks uniformity
Lacks coherency
Not easy to use
Metric – Developed in France in 1795.
Simple base units
Interchangeable prefixes
Decimal (base 10) system

5. Metric Prefixes Prefix Symbol Meaning kilo- k hecto- h deca- da deci-
centi- c
milli- m
1000
1 km = m
100
1 hm = 100 m 10
1 dam = 10 m .1
10 dm = 1 m
.01
100 cm = 1 m
.001
1000 mm = 1 m

6. Making Metric Your Own When you see Think of Liter (L) half a 2L pop
meter (m) inches longer than a yard stick
decimeter (dm) length of a pack of gum
centimeter (cm) thickness of a pack of gum
millimeter (mm) thickness of DVD
kilometer (km) more than 1/2 a mile (about .6)
gram (g) less than half a dime

7. Units of Measurement – History
SI (International System of Units) – Developed by scientists in 1960.
Only 7 fundamental units
Derived units based on fundamental units

8. Units of Measurement – SI Base Units
Quantity
Unit
Symbol
Length
meter m
Mass
kilogram kg
Time
second s
Temperature
kelvin K
Amount of Substance
mole
mol
Electrical current
ampere A
Luminous intensity
candela cd

9. kilogram per cubic meter
Units of Measurement – SI Derived Units
Quantity
Unit
Symbol
Derivation
Units
Area
square meter m2
length  width
m  m
Volume
cubic meter m3
length  width  height
m  m  m
Density
kilogram per cubic meter
kg/m3
mass
volume kg
Velocity
meter per second
m/s
length/time m s
Force
newton N
(mass  length)
(time  time)
kg  m s2
Pressure
pascal Pa
force
area
N = kg
m2 m  s2
Energy
joule J
force  length
N  m = kg  m2

10. Metric Conversions
kilo hecto deca base unit deci centi milli-
(k) (h) (da) (d) (c) (m)
Meter (m)
Liter (L)
Gram (g)
Second (s)
/ / /1000
To convert from 1 prefix to another, just move the decimal to the left or right that many places!

11. 5000 cg How many centigrams (cg) are in 5dag?1 2 3
kilo hecto deca base unit deci centi milli-
(k) (h) (da) (d) (c) (m)
Meter (m)
Liter (L)
Gram (g)
Second (s)
How many centigrams (cg) are in 5dag?
Just move the decimal ___ places to the ________! 5 3
right
5000 cg

12. .012 km 1 2 3 left How many kilometers (km) are in 12 meters m?
kilo hecto deca base unit deci centi milli-
(k) (h) (da) (d) (c) (m)
Meter (m)
Liter (L)
Gram (g)
Second (s)
How many kilometers (km) are in 12 meters m?
Just move the decimal ___ places to the ________!
1 2 3
left
.012 km

13. Scientific Notation Scientific Notation 1100000 m = 1.1 × 106 m
exponent
coefficient
(Integer)
( 1 and  10)
g = 2.3 × 10-8 g

14. How reliable are Measurements?
Accuracy, Precision
Accuracy – how close a measurement is to the true value.
Precision – how close a group of measurements are to each other.

15. How reliable are Measurements?
How do you make a measurement?
With most measuring devices, you should be able to estimate to one decimal place more than the smallest division on the device.
The smallest division is a _____ of a centimeter, so you can guess to the __________ (or ___ decimal places like 1.24).
tenth
hundredth 2

16. Using A Ruler
= cm
= cm
= 1.5 cm

17. 1 2 3
1 =
5.73 mL
2 =
3.0 mL
3 =
.35 mL

18. Measurement – Significant Figures
All of the known digits plus the estimated digit are significant – they are not placeholders.
When we measured the volume of cylinder 1 on the last slide we got:
5.73 mL
known estimated
This would mean 3 significant figures.

19. 100
200
300
100
200
300
120 mL
120 mL

20. Measurement – Significant Figures
Significant Figure Rules
Every nonzero is significant.
123.2 g
Zeros between nonzero digits are significant.
1004 m
Zeros to left of nonzero are NOT significant.
0.01 g
4 sig figs
4 sig figs
1 sig figs

21. Measurement – Significant Figures
4. Zeros to the right of nonzero digits are significant ONLY when the decimal is shown.
12.00 m
1200. m
1200 m
1.20 ×103 m
5. Counting numbers and defined quantities have unlimited significant digits.
3 gold atoms unlimited
1 hour = 60 minutes 1 and 60 unlimited
4 sig figs
4 sig figs
2 sig figs
3 sig figs

22. Significant Figures in Calculations
An answer can’t have more significance than the measurements upon which it is based.
YOUR ANSWER IS ONLY AS GOOD AS YOUR WORST MEASUREMENT!

23. Significant Figures in Calculations
Addition Subtraction
Round your answer to the same number of decimal places as your least significant number.
Think of it as the leftmost uncertainty. m m m m
540 m

24. Significant Figures in Calculations
Multiplication and Division
Round answer to the same number of significant digits as the measurement with the least number of significant digits. m
× m 5 3 m2
2860 m2

25. Temperature What does your body sense? temperature or heat
What contains more heat?
a glass of boiling water or an iceberg
What does your body sense?
temperature or heat

26. Temperature
Heat – type of energy transferred because of a difference in temperature.
Can’t be measured directly
Temperature – measure of the average kinetic energy of the particles in a sample of matter.
Determines the direction of heat transfer

27. Temperature Scales
Fahrenheit (F) – zero based on equal mix of snow and ammonium chloride.
32F = freezing point of water
212F = boiling point of water
Celsius (C) – based on water
0C = freezing point of water
100C = boiling point of water

28. Temperature Scales
Kelvin (K) - only temperature scales that is proportional to the speed of the particles.
0 K = all particle motion stops
273 K = freezing point of water
373 K = boiling point of water

29. Temperature Conversion
T(K) = T(C) + 273
T(C) = T(K) – 273
What is 25C (room temp.) in Kelvin?
T(K) = 25C = 298 K

30. Density mass Density volume = The density of water is 1.00 g/mL!!! D M

31. Density - Problem mass = (2.7 g/mL) × (19.5 mL – 12.4 mL)
A piece of aluminum (density 2.7 g/mL) is added to a graduated cylinder with 12.4 mL of water in it. The volume of the water rises to 19.5 mL, what is the mass of the aluminum? D M V
(volume)
(volume)
mass = (2.7 g/mL) × (19.5 mL – 12.4 mL)
mass = (2.7 g/mL)(7.1 mL)
mass = g
19g

32. How reliable are Measurements?
Error (measuring experimental accuracy)
Error = accepted value – experimental value
Percent Error = |error|
accepted value
× 100

33. How reliable are Measurements?
Experimentally, the boiling point of a substance is found to be °C. The actual value of the substance is °C. Find the error and percent error of the measured value. °C °C
.88 °C -
Error = accepted - experimental
= °C °C
= .88 °C
.9 °C
= °C × 100
100.0 °C
% error = |error| × 100
accepted
= .9%

34. Graphing
Using data to create a graph can help to reveal a pattern if one exists.
A graph is a visual display of data.

35. Circle Graph
A circle graph is sometimes called a pie chart because it is divided into wedges like a pie or pizza.
A circle graph is useful for showing parts of a fixed whole.
The parts are usually labeled as percents with the circle as a whole representing 100%.

36. Bar Graph
A bar graph often is used to show how a quantity varies with factors such as time, location, or temperature.
In those cases, the quantity being measured appears on the vertical axis (y-axis).
The independent variable appears on the horizontal axis (x-axis).
The relative heights of the bars show how the quantity varies.

37. Line Graph
In chemistry, most graphs that you create and interpret will be line graphs.
The points on a line graph represent the intersection of data for two variables.
The dependent variable is plotted on the y-axis and the independent variable on the x-axis.
Remember that the independent variable is the variable that a scientist deliberately changes during an experiment.

38. Line Graph
Sometimes points are scattered, the line cannot pass through all the data points.
The line must be drawn so that about as many points fall above the line as fall below it.
This line is called a best fit line.

39. Line Graph
If the best fit line is straight, there is a linear relationship between the variables and the variables are directly related.
This relationship can be further described by the steepness, or slope, of the line.
If the line rises to the right, the slope is positive.
A positive slope indicates that the dependent variable increases as the independent variable increases.

40. Line Graph If the line sinks to the right, the slope is negative.
A negative slope indicates that the dependent variable decreases as the independent variable increases.

41. Line Graph
Either way, the slope of the graph is constant. You can use the data points to calculate the slope of the line.
The slope is the change in y divided by the change in x.

42. Interpreting Graphs
An organized approach can help you understand the information on a graph.
First, identify the independent and dependent variables.
Look at the ranges of the data and consider what measurements were taken.
If a graph has multiple lines or regions, study one area at a time.
Decide if the relationship between the variables is linear or nonlinear.
If the relationship is linear, is the slope positive or negative?

43. Interpreting Graphs
When points on a line graph are connected, the data is considered continuous.
You can read data from a graph that falls between measured points.
This process is called interpolation.

44. Interpreting Graphs
You can extend the line beyond the plotted points and estimate values for the variables.
This process is called extrapolation.
Why might extrapolation be less reliable than interpolation?
The trend might change!