Transcript Slide 1 - Ralph C. Mahar

Scientific Notation
Write 17,500 in scientific notation.
1.75 x 104
Write 0.0050 in scientific notation.
5.0 x 10-3
(3.0 x 105)(5.0 x 10-2)= (3.0 x 5.0) x 105+(-2)
3.5 x 10 5
5 2
3

3
.
5
x
10

3
.
5
x
10
2
1.0 x 10

Addition and subtraction: all numbers
must be changed to the same exponent.
Then add or subtract the numbers,
attaching the common exponent.
ex.: 8.3 x 102 + 5.7 x 103
0.83 x 103
+5.7 x 103
6.53 x 103
6.5 x 103
Metric (SI) Base Units




Length- meter
Mass- kilogram
Volume- liter (displacement)
- cm3 (L x W x H)
Temperature- Celsius C=5/9(F-32)
F = 9/5C +32
- Kelvin
0◦C = 273 K

SI Prefixes
Giga
109
Mega
106
kilo
103
basic unit
deci
10-1
centi
10-2
milli
10-3
micro
10-6
nano
10-9
pico
10-12
From DOE
Significant Figures
Indicate the uncertainty of a
measurement

The significant figures in a measurement
are all the digits that are known with
certainty, plus the first digit that is
uncertain.
Significant Figures


All nonzero digits are significant 43.5
Zeros are significant when. . .




between two nonzero digits 120.01
to the right of a decimal point and to the right
of a nonzero digit. 30.00
to the left of an expressed decimal point and
to the right of a nonzero digit. 19,000.
Not significant when. . .


the zeros to the right of a decimal and to the
left of a nonzero digit. 0.00056
to the right of a nonzero digit but to the left
of an understood decimal 109,000
 Beginning
zeros are not
significant.
 Ending zeros are only significant
when there is a decimal.
Operations with significant figures

Multiplication and division
The answer contains the same number of
significant figures as the measurement with
the least number of significant figures.

Addition and Subtraction
The answer has the same number of decimal
places as the measurement with the least
number of decimal places.
Operations with significant figures

Multiplication and division
Sample 1: 24 cm x 31.8 cm = 763.2 cm2
answer: 760 cm2
Sample 2: 8.40 g ÷ 4.2 ml = 2 g/ml
answer: 2.0 g/ml

Addition and Subtraction
Sample 1: 49.1 g + 8.001 g = 57.101 g
answer: 57.1 g
Sample 2: 81.350 m – 7.35 m = 74 m
answer: 74.00 m
Precision vs. Accuracy


Precision is the agreement between
measurements.
Accuracy is the nearness of a
measurement to its actual value.
x
x
x x
x
x
Not precise, nor accurate
x
x
xx xx
x
x
Precise, not accurate
Precise and accurate
37.53
5.8
These thermometers have different levels of precision. The
increments on the left one are .2 but on the right one
they are 1 . How should their temperatures be recorded?
Percent Error
theoretical – experimental
theoretical
x 100% =
Ex.: You analyze a sample of copper sulfate
and find that it is 68% copper. The
theoretical value is 80%. What is your
percent error?
80-68 x 100% = 15%
80
Derived Units

Measurements derived from basic units.



Area= L x W (m2)
Volume = L x W x H (cm3)
Density = m/V (g/cm3)
Calculations
1. What is the density of a substance whose
mass is 3.0 grams and its volume is
15cm3?
3.0 grams = .20 g/cm3
15 cm3
2. Cobalt has a density of 8.90 g/cm3. What
volume would 17.8 g of cobalt have?
D=m/V so V=m/D
V = 17.8 g
= 2.00 cm3
8.90 g/cm3
Dimensional Analysis
Multiply your starting point by a
conversion factor (equal to 1)
 Units should cross out algebraically,
leaving you with the unit desired.
Ex.: Convert 2hr to min.
Conversion factor is 1hr = 60min
2hr x 60min = 120 min
1 hr

In Switzerland, gas prices are listed
in Swiss Francs per liter. Convert
the Swiss prices below to dollars
per gallon.

Conversion factors needed:


Dollars to Francs: 1 SF = $.83
Liters to gallons: 1 quart = 0.946 L
1 gallon = 4 quarts
1.71 SF x $.83 x .946L x 4 qt = $5.37
1L
1 SF 1 qt
1 gal
gal