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What is Science
• Study of the physical universe
• An organized body of facts
• Experimentation
– Observation
• Cannot be vague
• Avoid inference
Scientific Method – is a
problem solving process
• Define the problem – ask a question
• Form a hypothesis – educated guess
• Test the hypothesis – use the tools of
science
• Accept or reject hypothesis – evaluate
data
• Reformulate hypothesis
• Verify hypothesis - retest
Measurement in Science
• Scientific Notation – a shorthand
method for writing very large and
small numbers
• Metric System – an international
measurement system that uses the
decimal system units of division
(base 10)
• Significant Figures – any
measurement which is reliable
Scientific Notation
• Numbers are expressed as a value
between 1 and 10 (not 10) times 10
raised to a power
– Ex. 2.15 x 10 -7 = 0.000000215
●
Addition and Subtraction – exponents
must have the same value
Multiplication – add exponents
● Division – subtract exponents
●
Addition and Subtraction
7.55 x 10 -7
+2.45 x 10 -5
Must change exponents to match
7.55 x 10 -7
+ 245. x 10 -7
252.55 x 10 -7
Note: the exponent got
smaller so the number
gets bigger
Final correct ans.
2.5255 x 10 -5
Subtraction follows the same rule
Multiplication –
5.39 x 10 5
x 3.21 x 10 3
17.30 x 10 8
add exponents
Note: the answer is not in proper
scientific notation
1.73 x 10 9
Proper Scientific Notation
Division –
subtract exponents
7.26 x 10 5 ÷ 3.21 x 10 3 = 226
Note: the answer is not in proper scientific notation
2.26 x 10 2
Proper Scientific Notation
2.08 x 10 -6
3.21 x 10 -5
= 0.648 x 10 -1
Note: the answer is not in proper scientific notation
6.48 x 10 -2
Proper Scientific Notation
Metric System
• Basic Units
– Meter – length
– Gram – mass
– Cubic decimeter (or Liter) – volume
– Kelvin (or Celsius) – temperature
– Seconds – time
– Joules – energy
Metric System Prefixes
•
•
•
•
•
•
•
kilo - 103 - 1000 times basic unit
hecto - 102 - 100 times basic unit
deka – 101 – 10 times basic unit
deci - 10-1 - 0.1 times basic unit
centi -10-2 - 0.01 times basic unit
milli - 10-3 - 0.001 times basic unit
micro - 10-6 - 0.000001 times basic unit
Metric converter - is helpful when learning
conversions
Metric Converter
Smaller
units
Standard
unit
Prefix
Factor
Scientific Notation
nano (n)
micro (m)
milli (m)
centi (c)
deci (d)
(Meter, Liter,
Gram)
deka (D)
hecto (h)
kilo (k)
mega (M)
giga (G)
1/1,000,000,000
1/1,000,000
1/1000
1/100
1/10
1
10 -9
10 -6
10 -3
10 -2
10 -1
10 0
10
100
1000
1,000,000
1,000,000,000
10 1
10 2
10 3
10 6
10 9
Larger
Units
Decimal Point Movement
Significant Figures (digits)
• Accuracy – difference between a
measured value and the true or
accepted value
• Precision – degree of agreement
between measured values
Accuracy vs. Precision
Accurate
Precise
Accurate
and Precise
Note: The accurate target is not precise but the average of the values
is accurate
Significant Figures
• Rules for defining significant figures
- Leading zeros are not significant
Ex: 0.000025
- Trailing zeros are not significant unless
there is a decimal point following them
Ex: 2500000
Significant Figures (cont.)
- Captive zeros are always significant
Ex: 2003, 70.005, 0.0090006
- Zeros to the right of a decimal and a
non-zero number are always significant
Ex: 0.3500, 0.0000770,
90.000
Significant Figures
• Rules of Operations
– Addition and subtraction – the limiting
term is the one with the smallest
number of places to the right
6.345
+0.125045
6.470
1.00945
- 0.210
0.799
Significant Figures
• Rules of Operation (cont.)
– Multiplication and division – the answer
contains the same number of significant
figures as the value with the smallest number
of significant figures
9.110
x 0.025
0.23
0.4521 = 0.374
1.21
Ans: 2 sig. figs.
Ans: 3 sig. figs