Transcript Document 7398892

Scientific Notation
Scientific Notation
• Do you know this number, 300,000,000
m/sec.?
• It's the Speed of light !
• Do you recognize this number,
0.000 000 000 753 kg.
• This is the mass of a dust particle!
• Scientists have developed a shorter method to
express very large numbers or very small
numbers.
• This method is called scientific notation.
• The number 123,000,000,000 in scientific
notation is written as :
Scientific Notation
• The first number 1.23 is
called the base. It must be
greater than or equal to 1
and less than 10.
• The second number is
written in exponent form or
10 to some power.
• The exponent is the number
of decimal places needed to
arrive at the bass number.
To write a number in scientific notation:
• Put the decimal after the first digit
and drop the zeroes.
• This gives you the base number.
• In the number 123,000,000,000
The base number will be 1.23
• To find the exponent count the
number of places from the
decimal to the end of the number.
• In 123,000,000,000 there are
11 places
Multiplying Scientific Notated Numbers
• Multiply the base numbers
• Add the exponents of the Tens
• Adjust the base number to have one digit
before the decimal point by raising or
lowering the exponent of the Ten
+
3.25 X 10 3 X
2.50 x10 5 =
3.25 X 2.50
3 + 5= 8
8.125 X 10 8
Dividing Scientific Notation Numbers
• Divide the base numbers
• Subtract the exponents of the Tens
• Adjust the base number to have one digit
before the decimal point by raising or
lowering the exponent of the Ten
Dividing
• Divide 3.5 x 108 by 6.6 x 104
• You may rewrite the problem as:
• 3.5 x 108
6.6 x 104
• Now divide the two base numbers
• Subtract the two powers of 10
• Adjust base number to have one number
before the decimal
3.5 x 108
6.6 x 104
4 is now subtracted
from 8
3.5 is now divided by 6.6 in this order
on the calculator.
0.530303 x 104
Change to correct scientific notation to
get: 5.3 x 103 Note - We subtract one from the exponent
because we moved the decimal one place to the right.
Scientific Notation - Addition and Subtraction
• All exponents MUST BE THE SAME before you
can add and subtract numbers in scientific
notation. The actual addition or subtraction will
take place with the numerical portion, NOT the
exponent.
• You must change the base number on one of the
digits by moving the decimal.
• Always make the powers of ten the same as the
largest.
• Move the decimal on the smallest number until
its power of ten matches that of the largest
exponent.
• Ex. 1 Add 3.76 x 104 and 5.5 x 102
• move the decimal to change 5.5 x 102 to
0.055 x 104
• add the base numbers and leave the
exponent the same: 3.76 + 0.055 = 3.815
x 104
• following the rules for rounding, our final
answer is 3.815 x 104
• Subtraction is done exactly in the same
manor.
Dimensional Analysis
• Dimensional Analysis (also called Factor-Label Method
or the Unit Factor Method) is a problem-solving method
that uses the fact that any number or expression can be
multiplied by one without changing its value. It is a useful
technique.
• Unit factors may be made from any two terms that
describe the same or equivalent "amounts" of what we
are interested in.
• For example, we know that
• 1 inch = 2.54 centimeters
Unit Factors
• We can make two unit factors from this
information:
• When converting any unit to another there
is a pattern which can be used.
• Begin with what you are given and always
multiply it in the following manner.
Want units
• Given units X Given units = Want units
• You will always be able to find a
relationship between your two units.
• Fill in the numbers for each unit in the
relationship.
• Do your math from left to right, top to
bottom.
Want Units
Given units X Given Units = Want units
• (1) How many centimeters are in 6.00 inches?
Metric System of
Measurement
System International
Or
International System of
Measurement
•Based on units of ten
Basic Units of Measure
•
•
•
•
Length – Distance : meter (metre) m
Time – second s
Mass – grams g or kilograms kg
Volume – liter (litre) l
1cc=1cm3=1ml
1dm3=1liter (l)
• Temperature – Celsius C or
•
Kelvin K = C + 273
Metric Prefixes
Prefix:
Symbol:
Magnitude:
Meaning (multiply by):
Yotta-
Y
1024
1 000 000 000 000 000 000 000 000
Zetta-
Z
1021
1 000 000 000 000 000 000 000
Exa-
E
1018
1 000 000 000 000 000 000
Peta-
P
1015
1 000 000 000 000 000
Tera-
T
1012
1 000 000 000 000
Giga-
G
109
1 000 000 000
Mega-
M
106
1 000 000
myria-
my
104
10 000 (this is now obsolete)
kilo-
k
103
1000
hecto-
h
102
100
deka-
da
10
10
-
-
-
-
deci-
d
10-1
0.1
centi-
c
10-2
0.01
milli-
m
10-3
0.001
micro-
u (mu)
10-6
0.000 001
nano-
n
10-9
0.000 000 001
pico-
p
10-12
0.000 000 000 001
femto-
f
10-15
0.000 000 000 000 001
atto-
a
10-18
0.000 000 000 000 000 001
zepto-
z
10-21
0.000 000 000 000 000 000 001
yocto-
y
10-24
0.000 000 000 000 000 000 000 001
Conversion in the Metric System
• If you can remember something silly,
• ("King Henry Died Monday Drinking Chocolate Milk"), the metric
conversions are so easy.
• King Henry Died Monday Drinking Chocolate Milk
• (km) (hm) (dam) (m/unit) (dm)
(cm)
(mm)
• Remember the 1st letter is the symbol for the prefix
and the second is the unit you are measuring in.
• Just sketch the chart above (K, H, D, M, D, C, M) and
place the number you wish to convert under the
proper slot.
• Move the decimal point left or right the correct number
of places to make the conversion.
Example: convert 43.1 cm to km.
• King Henry Died Monday Drinking Chocolate Milk
• (km) (hm) (dam) (m/unit)
(dm)
(cm) (mm)
•
43.1
• This is a move of 5 places to the left filling spaces
with zeros and you get
• .000431 km
Example:convert 43.1 dm to mm.
•King Henry Died Monday Drinking Chocolate Milk
• (km) (hm) (dam) (m/unit) (dm)
(cm)
(mm)
•
43.1
•This is a move of 2 places to the right filling spaces with
zeros and you get
•4310 mm
Significant Digits or Figures
• Significant digits, which are also called
significant figures. Each recorded
measurement has a certain number of
significant digits.
• The significance of a digit has to due with
whether it represents a true measurement
or not.
• Any digit that is actually measured or
estimated will be considered significant
Rules For Significant Digits
1. Digits from 1-9 are always significant.
2. Zeros between two other significant
digits or counting numbers are
always significant.
3. One or more zeros to the right of both
the decimal place and another
significant digit are significant.
Significant Digit Examples
1. All counting numbers: 1,238 there are
4 significant digits in this number.
2. Zero’s between counting number: 123,005
in this number there are 6 significant digits
3. Zero’s to the right of the decimal and the
right or end of the number count as
significant digits: 123.340 in this number
there are 6 significant digits
Significant Digit Rules For
Multiplication and Division Answers
1. Your final answer will have the same
number of digits as that with the least
number of significant digits in the
problem.
2. Ex: 2.43 X 35 = 85.05 since in the
problem the least number of significant
digits is two then your answer will be 85
3. Do not forget to round up or leave where
needed.
Significant Digit Rules for
Subtraction and Addition
1. The correct number of digits in the final answer
will be the same as the least number of
decimal places in the problem.
2. Ex: 123.45
12.456
+1045.4
1181.306 since the least number of
decimal places is one then the final answer is
1181.3
3. Remember to check for round off or not.