1. Measurements and Calculations
CHAPTER 2
Measurements and Calculations

2. Scientific Method System Scientific Method
Specific portion of matter that has been selected for study
Scientific Method
Logical approach to solve a problem

3. Scientific Method Steps Observing and collecting data
Use of senses
Quantitative data – numerical
Qualitative data - descriptive
Generalization – statements
Organizing – Graphs, tables, statistics
Hypothesis – testable statement
Law – statement that DESCRIBES facts

4. Scientific Method Steps Theorizing Testing
Statements that EXPLAINS facts
Can never be proven!!
Testing
Experimentation

5. Units of Measurement Unit of Measurement SI
A physical quantity of a defined size
lb, in, ft, g, cm, km SI
International System of Units (metric system)
Adopted in 1960, originated in France

6. SI SI base units – standard of measure Length – meter (m)
Mass – gram (g)
Time – second (s)
Temperature – Kelvin (K)

7. Know the ones in BOLD above!!!
SI Prefixes
Prefix
Symbol
Example
Exponential Factor
Factor
Tera T
Terameter
1012
Giga G
Gigameter
109
Mega M
Megameter
106
Kilo
K or k
Kilometer
103
1000
Hecto H
Hectometer
102
100
Deca D
Decameter
101 10
----
meter
Deci d
Decimeter
10-1
0.1
Centi c
Centimeter
10-2
0.01
Milli m
Millimeter
10-3
0.001
Micro
Micrometer
10-6
Nano n
Nanometer
10-9
Pico p
Picometer
10-12
Know the ones in BOLD above!!!

8. SI Prefixes
Number Line – MEMORIZE!!
K H D d c m _ _ µ_ _ n
Examples:

9. Derived SI Units Derived Unit – obtained from combining base units
Area
L * w ; m2
Volume
L * w * h ; m3
Speed
Length/time ; m/s
Density
Mass/volume ; g/mL or g/cm3

10. Conversion Factors and Factor-Label Method
Factor-Label Method – problem solving method using algebra
Examples:

11. Using Scientific Measurements
Accuracy
Closeness of a measurement to the true or accepted value
Precision
Agreement among the values
Percent Error
Accepted value – Experimental Value x 100%
Accepted Value

12. Significant Figures
Sig Figs – all certain digits plus one uncertain digit
How many sig figs in a number?
Table 2-5 page 47

13. Sig Figs Rules All non-zero numbers ARE significant
3.456 = 4 SF
Sandwich zeros ARE significant
306 = 3 SF
Leading zeros ARE NOT significant
= 3 SF
Trailing zeros:
To the left – ARE NOT significant unless a special sign
300 = 1 SF
300. = 3 SF
To the right – ARE significant
= 4 SF
Scientific Notation
All digits in the number portion ARE significant
2.31 x 103 = 3 SF

14. Significant Figures Using Sig Figs in Math Operations Multiply/Divide
Answer must have number of sig figs as least precise number
2.3 (2 SF) x 5.67 (3 SF) = 13 (2 SF)
16.00 (4 SF) / 8.0 (2 SF) = 2.0 (2 SF)
Add/Subtract
Answer must have number of “columns” as least precise number
1.03 (hundredths)
(ones) 4

15. Significant Figures Rounding off a number – Table 2-6 page 48 Rules –
Decide where the number will be “cut”
Look at number to the right:
If it is a 5 or greater, increase the number by one
If it is less than 5, leave number as is

16. Significant Figures
Examples:

17. Scientific Notation Used to represent very big or very small numbers
Generic form:
M x 10N
M must be greater than 1 and less than 10
If positive (+) N value = a “big” number
If negative (–) N value = a “small” number

18. Scientific Notation Example: 4.21 x 102
 4.21 = number part in standard form (one digit to left of decimal point)
 102 = tells where decimal is
 2 = exponent

19. Scientific Notation Converting TO Scientific Notation
Count the number of spaces needed to get into PROPER form.
This becomes the exponent.
Moving the decimal point left means N is +. Moving the decimal point right means N is -.
Examples:

20. Scientific Notation Converting OUT OF scientific notation:
Move the decimal the number of spaces indicated by the exponent (the number), the correct direction, also indicated by the exponent (the sign)
Examples:

21. Scientific Notation Calculator Type the “M” Hit the EE or EXP button
Type the “N”

22. Scientific Notation Math and scientific notation Add/Subtract Multiply
Exponents MUST be the same!!
Add M values and exponent stays the same
Multiply
Multiply M values and add exponents
Divide
Divide M values and subtract exponents

23. Heat and Temperature Temperature Heat
Measure of the AVERAGE kinetic energy of the particles in a sample
How hot or cold something is
Heat
SUM TOTAL of the kinetic energy of the particles in a sample
More particles = more heat

24. Heat and Temperature Thermometer Device used to measure temperature
Hg or alcohol
Liquid EXPANDS or CONTRACTS
Temp scales
°C – Celsius, 0°C, 100°C
°F – Fahrenheit, 32°F, 212°F

25. Heat and Temperature Kelvin Freezing point of water = 273 K
Boiling point of water = 373 K
K = °C
°C = K –
Examples:

26. Heat and Temperature Units of Heat Joule (J) – SI unit
Calorie (cal) – older, not SI
1 cal = J

27. Problem Solving Analyze Plan Compute Evaluate
Read problem carefully and analyze info
Plan
Develop a plan to solve
Compute
Substitute data and conversion factors into plan and solve
Evaluate
Examine answers – is it reasonable? Does it make sense?

28. Proportionality Variable Directly proportional Inversely proportional
Quantity that can change
Directly proportional
One goes up, other goes up; y=kx
Graph –
Inversely proportional
One goes up, other goes down; y=k/x