Transcript Document

Section 5.1
Scientific Notation and Units
Objectives
1. To show how very large or very small numbers can be
expressed in scientific notation
2. To learn the English, metric, and SI systems of
measurement
3. To use the metric system to measure length, volume
and mass
Section 5.1
Scientific Notation and Units
“Arithmetic is being able to count
up to twenty without taking your
shoes off”
Mickey Mouse
Mickey also says “Do you
remember what an
exponent is?”
Section 5.1
Scientific Notation and Units
A. Scientific Notation
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• Very large or very small numbers can be expressed using
scientific notation
– The number is written as a number between 1 and 10
multiplied by 10 raised to a power.
e.g. 7200 is 7.2 x 103
– The power of 10 depends on:
• The number of places the decimal point is moved.
• The direction the decimal point is moved.
Left  Positive exponent
Right  Negative exponent
Section 5.1
Scientific Notation and Units
A. Scientific Notation
• Representing Large Numbers
93,000,000 miles from the
Earth to the Sun (sunlight
takes 8 minutes to reach us)
93,000,000 = 9.3 x 10,000,000
= 9.3 x 10 x 10 x 10 x 10 x 10 x 10 x 10
= 9.3 x 107 (Decimal point moved 7 digits to the left)
Number between
1 and 10
Appropriate
power of ten
Section 5.1
Scientific Notation and Units
A. Scientific Notation
• Representing Small Numbers
0.000167
To obtain a number between 1 and 10 we
must move the decimal point to the right.
0.000167 = 1.67 10-4
10-4 = 1/10000 (one ten-thousandth)
Section 5.1
Scientific Notation and Units
Convert the following numbers between normal and
scientific notation:
329
700,000
1.7 x 103
2.4503 x 105
20090
0.000034
0.01023
7.9 x 1011
2.8 x 10-3
123.4
7.45 x 10-1
45.607
2.3 x 10-7
Section 5.1
Scientific Notation and Units
Convert the following numbers/sums into correct
scientific notation:
35.9 x 103
556.67 x 104
22.7 x 10-3
0.0348 x 10-1
1845 x 105
123.4 x 1023
0.00345 x 107
Section 5.1
Scientific Notation and Units
Scientific Notation Math - Exponents
103
1/103
10-5
1/105
100
1/10-2
103 x 108
10-3 x 107
10-5 x 10-3
105 / 102
10-7 / 105
10-2 / 10-4
1/10-7
Section 5.1
Scientific Notation and Units
Scientific Notation Math
Multiplication
- multiply the numbers, add the indices
1.2 x 104 multiplied by 5 x 106 =
Division
- divide the numbers, subtract the indices
5.5 x 108 divided by 1.1 x 102 =
(For all operations reconvert answers to full scientific notation)
Section 5.1
Scientific Notation and Units
Scientific Notation Math
• Addition or subtraction:
Convert to the same base and perform the operation
Then reconvert to scientific notation
1.04 x 103 plus 6.8 x 102 =
Section 5.1
Scientific Notation and Units
Combined Operations – Give the answer in scientific
notation
7.5 x 105
__________
3 x 103
2 x 106 x 1.5 x 102
________________________
5 x 103
6.5 x 105 x 4 x 104
________________________
2 x 10-3
7.5 x 10-5
______________________
3 x 103 x 5 x 10-6
Section 5.1
Scientific Notation and Units
B. Units
• Units provide a scale on which to represent the results of a
measurement. What units can you think of?
“Time is God’s way of making sure everything doesn’t
happen at once”
(Unknown)
Section 5.1
Scientific Notation and Units
B. Units
• There are 3 commonly used unit systems.
– English (used in the United States)
– Metric (broadly used across the World)
– SI (most formal version of Metric used in science)
Section 5.1
Scientific Notation and Units
Countries not yet officially metric: USA, Liberia, Myanmar
Section 5.1
Scientific Notation and Units
Metric/SI Prefixes
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Prefixes are used to denote different sizes of each unit:
Multiplication factor
Section 5.1
(scientific notation)
Prefix
Scientific Notation and Units
(1024)
(1021)
(1018) Full List of
(1015)
(1012)
1 000 000 000 (109)
yotta
zetta
Metricexa
Prefixes
peta
tera
giga
Symbol
Y
Z
E
P
T
G
1 000 000 (106)
1000 (103)
100 (102)
10 (101)
0.1 (10-1)
0.01 (10-2)
0.001 (10-3)
0.000 001 (10-6)
0.000 000 001 (10-9)
mega
kilo
hecto
deka
deci
centi
milli
micro
nano
M
k
h
da
d
c
m
µ
n
(10-12)
(10-15)
(10-18)
(10-21)
(10-24)
pico
femto
atto
zepto
yocto
p
f
a
z
y
Section 5.1
Scientific Notation and Units
Metric Dollars
100 dollars
1 hectodollar
1x102
10 dollars
1 dekadollar
1x101
1 dollar
1 dollar
1x100
1 dime
1 decidollar
1X10-1
1 cent
1 centidollar
1X10-2
Section 5.1
Scientific Notation and Units
C. Measurements of Length, Volume and Mass
• Length
– Fundamental unit is the meter
– 1 meter = 39.37 inches
Comparing English and metric systems
Who is taller – a woman 5 ft 6 inches or a man 1.62 meters tall?
Section 5.1
Scientific Notation and Units
C. Measurements of Length, Volume and Mass
*
*
Section 5.1
Scientific Notation and Units
C. Measurements of Length, Volume and Mass
• Volume
– Amount of 3-D space occupied by a
substance
– Fundamental unit is meter3 (m3)
1 liter = 2.11 Pints
250mL of milk is close to ½ Pint, 1 Pint, 1 Quart, 1 Gallon?
Section 5.1
Scientific Notation and Units
C. Measurements of Length, Volume and Mass
• Mass
– Quantity of matter in an object
– Fundamental unit is kilogram = 2.2 lbs
Section 5.1
Scientific Notation and Units
C. Measurements of Length, Volume and Mass
How many quarters in a row to make a meter?
What is the weight in kg of a man who weighs 180 lbs?
How many liters in a six-pack of soda cans?