47.2: Introduction
- Page ID
- 29391
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The system of units used in the physical sciences is based on the metric system. Numbers that describe physical quantities range from the very large to the very small, so a set of standard prefixes are used to designate convenient-sized units that differ by multiples of ten. Every step in the metric system is a multiple of 10.
|
Multiple |
Prefix |
Symbol |
|---|---|---|
|
\(10^{24}\) |
yotta |
Y |
|
\(10^{21}\) |
zetta |
Z |
|
\(10^{18}\) |
exa |
E |
|
\(10^{15}\) |
peta |
P |
|
\(10^{12}\) |
tera |
T |
|
\(10^{9}\) |
giga |
G |
|
\(10^{6}\) |
mega |
M |
|
\(10^{3}\) |
kilo |
k |
|
\(10^{1}\) |
deca |
da |
|
\(10^0\) |
||
|
\(10^{-1}\) |
deci |
d |
|
\(10^{-2}\) |
centi |
c |
|
\(10^{-3}\) |
milli |
m |
|
\(10^{-6}\) |
micro |
μ |
|
\(10^{-9}\) |
nano |
n |
|
\(10^{-12}\) |
pico |
p |
|
\(10^{-15}\) |
femto |
f |
|
\(10^{-18}\) |
atto |
a |
|
\(10^{-21}\) |
zepto |
z |
|
\(10^{-24}\) |
yocto |
y |
The United States continues to use English units. Conversion factors utilize equivalent sized measurements, to change from one unit to another. For example, 1 inch and 2.54 centimeters measure the exact same length. Converting from one unit to another requires multiplying by the appropriate conversion factor.
|
English to Metric |
|---|
|
1 inch = 2.54 centimeter |
|
1 mile = 1609 meters |
|
0.2248 lb = 1 Newton |
Example: [Measurement] x [Conversion Factor] = New Number
\[12 \cancel{\text { inches }} \times \dfrac {2.54 \text { centimeters}}{1 \cancel {\text { inch}}} = 30.48 \text { centimeters} \nonumber \]
The inches in the numerator and the inches in the denominator cancel