Transcript Measurements in Experiments

Scientific Notation and SI Prefixes
Handling the Big and the Small
Powers of Ten
• In science we use
powers of ten to
handle the vast
range of scale in
the universe
• Many physical
quantities can be
very large or very
small
Power Math
Exponent Power of
Ten
-9
10-9
-6
10-6
Value
Name
0.000000001
0.000001
One Billionth
One Millionth
-3
10-3
0.001
One Thousandth
-2
10-2
0.01
One Hundredth
-1
10-1
0.1
One Tenth
0
100
1
One
1
101
10
Ten
2
102
100
Hundred
3
103
1000
Thousand
6
106
1,000,000
Million
9
109
1,000,000,000
Billion
Scientific Notation
• Scientific notation is the standard method of
handling large and small numbers
– SN can handle any number, not just big and small
– SN exists for our convenience
– SN is neither better nor worse than other forms
– We use SN at our discretion for purposes of clarity
and ease of use
– When numbers are expressed in SN, the number of
significant figures is explicit and can no longer be
ambiguous
Standard Form
• The standard form of SN is most often used
• The standard form is just a convention to aid
communication (you don’t have to always use it)
1.23 × 1011
coefficient
base
exponent
1  coefficient  10
base = 10
exponent = any integer
• Examples:
103,000 = 1.03 × 105
0.00022 = 2.2 × 104
Scientific Notation and Calculators
• Scientific calculators have a SN function that
makes our lives much easier! Use it!
• The button usually says either “EE” or “Exp”
• To put in 1.23 × 1011 you type “1.23” then “EE”
then “11” and it will show “1.23E+11”
• It will give answers in the same form:
“5.76E-6” means “5.76 × 106”
• Once you have entered a SN value in this way,
the calculator treats it as one inseparable
number
SI Prefixes
• Another way to handle big and small quantities
is with SI prefixes
• SI prefixes modify units by powers of ten
• For example kilo- (k) can be added to a unit to
make the unit larger by a factor of 1000
One kilometer (km) equals a thousand meters
• In other words, “k” has a value of 1000 or 103
1 km = 1000 m = 103 m
• To convert km to m just substitute 103 for k
Example: 5.2 km = 5.2(103)m = 5.2  103 m
SI Prefixes (cont.)
• We can use kilo- with any unit to create units
a thousand times bigger:
– second (s)  kilosecond (ks)
– gram (g)  kilogram (kg)
– newton (N)  kilonewton (kN)
• Other prefixes like centi- (c) and milli- (m)
make units smaller:
1 cm = (1/100) m = 10-2 m
1 mm = (1/1000) m = 10-3 m
The Full Set of Prefixes
SI Prefixes and Sci. Not.
• SI Prefixes and scientific notation work well
together to offer us more choices for clarity
– Examples:
5.1 × 103 m = 5.1 mm
mill-
meter
9.38 × 105 m = 9.38 × 102 km
= 938 km
kilo-
meter
13700 g = 1.37 × 104 g = 13.7 kg
kilo-
gram
Common Prefixes
• Of the 20 prefixes, only about half of them are
commonly used in science and industry
• Here are the prefixes you should memorize:
Power
109
106
103
102
103
106
109
Prefix
nanomicromillicentikilomegagiga-
Abbreviation
n

m
c
k
M
G
Summary
• Scientific notation uses powers of ten to express
large and small numbers more succinctly
• Calculators help us use scientific notation
• SI Prefixes allow us to create new units that are
powers of ten bigger or smaller
• Scientific notation and unit prefixes together
give us a lot of choices and flexibility
• We should memorize and use the most common
prefixes because they are part of the scientific
language