1. Chapter 2 Data Analysis 2.1 Units of Measurement
2.2 Scientific Notation and Dimensional Analysis
2.3 How reliable are measurements

2. 2.1 Units of Measurement Objectives
Define SI base units for time, length, mass, and temperature.
Explain how adding a prefix changes a unit.
Compare the derived units for volume and density.

3. SI Units
International System of Units (SI Units)has seven base units of measure:
Length – meter (m)
Time – second (s)
Amount of substance – mole (mol)
Electric current – Ampere (A)
Temperature – Kelvin (K)
Luminous Intensity – Candela (cd)
Mass – kilogram (kg)

4. Time The SI base unit for time is the second (s).
The frequency of microwave radiation given off by a cesium-133 (Cs- 133) atom is the physical standard used to establish the length of a second.
Cesium clocks are more reliable than the ones we use every day.
Many chemical reaction take place in less than a second.

5. Length The SI base unit for length is the meter (m).
A meter is the distance that light travels through a vacuum in 1/ of a second.

6. Mass Kilogram (kg) is the SI base unit for mass.
Kilogram is defined by the platinum-iridium metal sphere kept in Sevres, France.
It is the only base unit whose standard is currently a physical object.

7. Prefixes Used with SI Units
Symbol
Factor
Scientific Notation
Example
giga G
1,000,000,000
109
gigameter(Gm)
mega M
1,000,000
106
megameter(Mm)
kilo k
1,000
103
kilometer(km)
deci d
1/10
10-1
decimeter(dm)
centi c
1/100
10-2
centimeter(cm)
milli m
1/1000
10-3
millimeter(mm)
micro
1/1,000,000
10-6
micrometer(µm)
nano n
1/1,000,000,000
10-9
nanometer(nm)
pico p
1/1,000,000,000,000
10-12
picometer(pm)

8. Derived Units
Derived units are units defined by a combination of base units.
Speed m/s (distance and time)
Volume is the space occupied by an object – cm3
Volume of liquid is measured in mL (1 mL is equal to 1cm3)
Density is the ratio that compares the mass of an object to its volume.
g/ cm3
D=m/V
1000 mL Volume of cotton balls and 1000 mL Volume of marbles….Do they have the same density? Why?

9. Density of Aluminum Mass – 13.5 g Volume – 5.0 cm3
Density = mass/Volume
D= 13.5g/5.0 cm3
D=2.7g/cm3

10. Temperature Hot or cold are qualitative descriptions of temperature.
In order to get a quantitative description you need a thermometer.
A thermometer is a narrow tube with a liquid that expands when heated and contracts when cooled.

11. Celsius Celsius Devised by Anders Celsius, a Swedish astronomer.
Uses the temperature at which water freezes and boils to establish his scale.
0ºC
100ºC

12. Kelvin
Kelvin scale was devised by William Thomson, a Scottish physicist and mathematician, who was known as Lord Kelvin.
Water freezes at 273K and boils at 373K
Kelvin is the SI unit for temperature.

13. Kelvin  Celsius or Celsius  Kelvin
10ºC = 283 K
293 K – 273 = 20ºC

14. 2.2 Scientific Notation and Dimensional Analysis
Express numbers in scientific notation
Use dimensional analysis to convert between units.

15. Scientific Notation
Scientific notation expresses numbers as a multiple of two factors: a number between 1 and 10; and ten raised to a power, or exponent.
The exponent tells you how many times the first factor must be multiplied by ten.
Greater than 1 – positive exponent
Less than 1 – negative exponent

16. Scientific Notation
1,392,000

17. Adding and subtracting using scientific notation
When adding or subtracting using scientific notation the exponents must be the same.
Ex x 102 m x 102 m = 9.78 x 102 m

18. Let’s try
15.6 x x x 107
2.4 x 103 – 0.23 x 104

19. Multiplying and dividing using scientific notation
When multiplying or dividing the exponents do not have to be the same.
For multiplication
First multiply the first factors
Then add the exponents
For division
First divide the first factors
Then subtract the exponents

20. Example
Multiplication
(2 x 103) x (3x102)
Division
(9x108) ÷ (3x10-4)

21. Dimensional Analysis
Dimensional Analysis is a method of problem-solving that focuses on the units used to describe matter.
A conversion factor is a ratio of equivalent values used to express the same quantity in different units.
Often used in dimensional analysis

22. Example
Convert 48 km to m
Convert 550m/s to km/min

23. 2.3 How reliable are measurements Objectives
Define and compare accuracy and precision.
Use significant figures and rounding to reflect the certainty of data.
Use percent error to describe the accuracy of experimental data.

24. ACCURACY/PRECISION Accuracy Precision
How close a measurement is to the actual value
Precision
How close a set of measurements are to each other

25. Accuracy and Precision
The density of a white solid was determined by students. The same was sucrose, which has a density of 1.59 g/cm3
Who collected the most accurate data? Who collected the most precise data?
Student A
Student B
Student C
Trial 1
1.54g/cm3
1.40g/cm3
1.70g/cm3
Trial 2
1.60g/cm3
1.68g/cm3
1.69g/cm3
Trial 3
1.57g/cm3
1.45g/cm3
1.71g/cm3
Average
1.51g/cm3

26. Percent Error
Percent error is the ratio of an error to an accepted value.
Percent error = error/accepted value x 100
Student A
Student B
Student C
Trial 1
-0.05g/cm3
-0.19g/cm3
+0.11g/cm3
Trial 2
+0.01g/cm3
+0.09g/cm3
+0.10g/cm3
Trial 3
-0.02g/cm3
-0.14g/cm3
+0.12g/cm3

27. Percent Error – Student A
Trial
Density (g/cm3)
Error (g/cm3) 1
1.54
-0.05 2
1.60
+0.01 3
1.57
-0.02
% error = 0.05 g/cm3/1.59 g/cm3 x 100 = 3.14%
% error = 0.01 g/cm3/1.59 g/cm3 x 100 = 0.63%
% error = 0.02 g/cm3/1.59 g/cm3 x 100 = 1.26%

28. SIGNIFICANT DIGITS or Figures
This is a process used to determine the number of digits to round to when measuring an object.
Use this process when
Measuring mass (on the scale) – g, kg, etc.
Measuring volume (in a graduated cylinder) – ml L, etc.
Measuring length (with a ruler) – cm, m
Is used to communicate to other scientists how accurate your measurement is:
Does your scale measure to the hundredths place, tenths place or whole number?
Referred to as “Sig Figs”

29. How to determine the number of Sig Figs in a measured value
Atlantic-Pacific Method
A = decimal Absent, begin counting from right
P = decimal Present, begin counting from left
Try these:
1,000
1 sig fig
0.001
0.0010
2 sig fig
1000.0
5 sig fig

30. Rules for Using Sig Figs
Multiplication/Division
Do all calculations, then round to the same number of digits as the number with the smallest number of sig figs
4.56 x =
Round to 2 sig figs: 6.4
8.315/298 =
Round to 3 sig figs:
Addition/Subtraction
Do the calculations, then round to the place of the number with the smallest number of decimal places =
Round to 31.1
88.88 – 2.2 = 86.68
Round to (note: if the number after 6 is > 5, round up)

31. Rules for Using Sig Figs
Multiple step calculations
Use an overbar to keep track of the significant figures from step to step.
Round only when reporting the final answer
Example:
88.88 – (calculator
answer)
Based on 2.22, round to 3 sig figs
If the number after the place you want to round to is > 5, round up (in this case 7). Ignore the other 7.
Answer = .0250
The zero after the 5 is significant. You must show it! = =