Transcript Scientific Notation and Sig Figs

Scientific Notation
So you don’t have to write so
many zeros…Yay!
Standard vs, Scientific
• Standard Notation: no exponents:
– Ex. 102,000
0.00045
1,000,000,000
• Scientific Notation: has exponents:
– Ex. 2.3x10-4
5.6x103
6.022x1023
Of Course There Are Rules!
1. A positive exponent represents a number
bigger than 1.
Ex. 3.8x104 = 38,000
4x102 = 400
Of Course There Are Rules!
2. A negative exponent represents a
number smaller than 1.
Ex. 9.2x10-3 = 0.0092
4x10-2 = 0.04
Of Course There Are Rules!
3. An exponent of 0 does not change the
number because 100=1:
Ex. 2.3x100 = 2.3 x 1 = 2.3
1.6x100 = 1.6
5.8x100 = 5.8
From Standard to Scientific
1. Place a decimal where there would
be ONE real number in front.
2. Count how many places you had to
move it over. This is your
exponent.
3. If the original number is smaller
than 1, put a negative in your
exponent.
From Scientific to Standard
1. If the exponent is negative, move the
decimal left to make the number smaller
than one.
The number of times you move it = the exponent.
2. If the exponent is positive, move the
decimal right to make the number bigger
than one.
The number of times you move it = the exponent.
Since We’re At It…
• SI = Système Internationale
• Universal units of measurement for science.
• Based on 10, so there are exponents
everywhere.
• You’ll need these for next time, so don’t lose
your paper!!
SI Prefixes!!
Symbol
Prefix
Scientific
Standard
M
Mega
106
1,000,000
k
kilo
103
1,000
‘base unit’ = meter, liter, gram, second = 100 = 1
d
deci
10-1
0.1
c
centi
10-2
0.01
m
milli
10-3
0.001
u
micro
10-6
0.000001
n
nano
10-9
0.000000001
Let’s Practice!
• Worksheet for you!! (Get used to it.)
• Do the front only! We’ll do the back at
the end of class.
Significant Figures
More Stuff to Memorize!
Why We Need Significant Figures
• Any measurement has uncertainty.
• Significant figures tell us which digit is
estimated. (usually the last number)
Rule #1
• Any number that is not a zero is
significant. No matter what.
• 34.5 has how many significant figures? 3
Rule #2
• Zeros that come before the non-zero
numbers are never significant.
– These are called “leading zeros.”
• 0.0054 has how many significant figures? 2
Rule #3
• Zeros that are between the non-zero
numbers are always significant.
– These are called “captive zeros.”
• 1.002 has how may significant figures? 4
Rule #4
• Zeros at the end of a number are only
significant if there is a decimal point in your
number.
– These are called “trailing zeros.”
• 1000 has how many significant figures? 1
• 1000. has how many significant figures? 4
• 3.40 x 104 has how many significant figures? 3
Rounding
Do all calculations before you round.
1. Figure out how many sig figs you need.
2. Find the number right after the last sig fig
you need.
3. If that number is less than 5, the digit before
stays the same.
4. If that number is five or more, the last sig fig
goes up by one number.
5. Any extra numbers on the end just go away.
Ex: Round 3.4048 to three significant figures.
3.40
Addition and Subtraction
• The answer has as many significant
figures as the term with the smallest
number of decimal places.
• 12.11+18.0+1.013=?
• How many decimal places should your
answer have? 1
31.123  31.1
Multiplication and Division
• The answer has the same amount of
significant figures as the term with the
smallest number of significant figures.
• 4.56 x 1.4 = ?
• How many significant figures does your
answer need? 2
6.384  6.4
More Practice!
• Finish the back of your worksheet!
• Turn it into the purple crate when you’re
done and move your fish!