Useful Information

This appendix is broken into several tables.

Important Constants1
Symbol Meaning Best Value Approximate Value
[latex]c[/latex] Speed of light in vacuum [latex]2\text{.}\text{99792458}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{8}\phantom{\rule{0.15em}{0ex}}\text{m}/\text{s}[/latex] [latex]3\text{.}\text{00}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{8}\phantom{\rule{0.15em}{0ex}}\text{m}/\text{s}[/latex]
[latex]G[/latex] Gravitational constant [latex]6\text{.}\text{67408}\left(\text{31}\right)\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{11}}\phantom{\rule{0.15em}{0ex}}\text{N}\cdot {\text{m}}^{2}/{\text{kg}}^{2}[/latex] [latex]6\text{.}\text{67}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{11}}\phantom{\rule{0.15em}{0ex}}\text{N}\cdot {\text{m}}^{2}/{\text{kg}}^{2}[/latex]
[latex]{N}_{A}[/latex] Avogadro’s number [latex]6\text{.}\text{02214129}\left(\text{27}\right)\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{\text{23}}[/latex] [latex]6\text{.}\text{02}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{\text{23}}[/latex]
[latex]k[/latex] Boltzmann’s constant [latex]1\text{.}\text{3806488}\left(\text{13}\right)\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{23}}\phantom{\rule{0.15em}{0ex}}\text{J}/\text{K}[/latex] [latex]1\text{.}\text{38}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{23}}\phantom{\rule{0.15em}{0ex}}\text{J}/\text{K}[/latex]
[latex]R[/latex] Gas constant [latex]8\text{.}\text{3144621}\left(\text{75}\right)\phantom{\rule{0.15em}{0ex}}\text{J}/\text{mol}\cdot \text{K}[/latex] [latex]8\text{.}\text{31}\phantom{\rule{0.15em}{0ex}}\text{J}/\text{mol}\cdot \text{K}=1\text{.}\text{99}\phantom{\rule{0.20em}{0ex}}\text{cal}/\text{mol}\cdot \text{K}=0\text{.}\text{0821}\text{atm}\cdot \text{L}/\text{mol}\cdot \text{K}[/latex]
[latex]\text{σ}[/latex] Stefan-Boltzmann constant [latex]5\text{.}\text{670373}\left(\text{21}\right)\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-8}\phantom{\rule{0.15em}{0ex}}\text{W}/{\text{m}}^{2}\cdot \text{K}[/latex] [latex]5\text{.}\text{67}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-8}\phantom{\rule{0.15em}{0ex}}\text{W}/{\text{m}}^{2}\cdot \text{K}[/latex]
[latex]k[/latex] Coulomb force constant [latex]8\text{.}\text{987551788}\text{.}\text{.}\text{.}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{9}\phantom{\rule{0.15em}{0ex}}\text{N}\cdot {\text{m}}^{2}/{\text{C}}^{2}[/latex] [latex]8.99\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{9}\phantom{\rule{0.15em}{0ex}}\text{N}\cdot {\text{m}}^{2}/{\text{C}}^{2}[/latex]
[latex]{q}_{e}[/latex] Charge on electron [latex]-1\text{.}\text{602176565}\left(\text{35}\right)\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{19}}\phantom{\rule{0.15em}{0ex}}\text{C}[/latex] [latex]-1\text{.}\text{60}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{19}}\phantom{\rule{0.15em}{0ex}}\text{C}[/latex]
[latex]{\text{ε}}_{0}[/latex] Permittivity of free space [latex]8\text{.}\text{854187817}\text{.}\text{.}\text{.}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{12}}\phantom{\rule{0.15em}{0ex}}{\text{C}}^{2}/\text{N}\cdot {\text{m}}^{2}[/latex] [latex]8\text{.}\text{85}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{12}}\phantom{\rule{0.15em}{0ex}}{\text{C}}^{2}/\text{N}\cdot {\text{m}}^{2}[/latex]
[latex]{\text{μ}}_{0}[/latex] Permeability of free space [latex]4\pi \phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-7}\phantom{\rule{0.15em}{0ex}}\text{T}\cdot \text{m}/\text{A}[/latex] [latex]1\text{.}\text{26}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-6}\phantom{\rule{0.15em}{0ex}}\text{T}\cdot \text{m}/\text{A}[/latex]
[latex]h[/latex] Planck’s constant [latex]6\text{.}\text{62606957}\left(\text{29}\right)\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{34}}\phantom{\rule{0.15em}{0ex}}\text{J}\cdot \text{s}[/latex] [latex]6\text{.}\text{63}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{34}}\phantom{\rule{0.15em}{0ex}}\text{J}\cdot \text{s}[/latex]
Submicroscopic Masses2
Symbol Meaning Best Value Approximate Value
[latex]{m}_{e}[/latex] Electron mass [latex]9\text{.}\text{10938291}\left(\text{40}\right)×{\text{10}}^{-\text{31}}\text{kg}[/latex] [latex]9\text{.}\text{11}×{\text{10}}^{-\text{31}}\text{kg}[/latex]
[latex]{m}_{p}[/latex] Proton mass [latex]1\text{.}\text{672621777}\left(\text{74}\right)×{\text{10}}^{-\text{27}}\text{kg}[/latex] [latex]1\text{.}\text{6726}×{\text{10}}^{-\text{27}}\text{kg}[/latex]
[latex]{m}_{n}[/latex] Neutron mass [latex]1\text{.}\text{674927351}\left(\text{74}\right)×{\text{10}}^{-\text{27}}\text{kg}[/latex] [latex]1\text{.}\text{6749}×{\text{10}}^{-\text{27}}\text{kg}[/latex]
[latex]\text{u}[/latex] Atomic mass unit [latex]1\text{.}\text{660538921}\left(\text{73}\right)×{\text{10}}^{-\text{27}}\text{kg}[/latex] [latex]1\text{.}\text{6605}×{\text{10}}^{-\text{27}}\text{kg}[/latex]
Solar System Data
Sun mass [latex]1\text{.}\text{99}×{\text{10}}^{\text{30}}\text{kg}[/latex]
average radius [latex]6\text{.}\text{96}×{\text{10}}^{8}\text{m}[/latex]
Earth-sun distance (average) [latex]1\text{.}\text{496}×{\text{10}}^{\text{11}}\text{m}[/latex]
Earth mass [latex]5\text{.}\text{9736}×{\text{10}}^{\text{24}}\text{kg}[/latex]
average radius [latex]6\text{.}\text{376}×{\text{10}}^{6}\text{m}[/latex][latex][/latex]
orbital period [latex]3\text{.}\text{16}×{\text{10}}^{7}\text{s}[/latex]
Moon mass [latex]7\text{.}\text{35}×{\text{10}}^{\text{22}}\text{kg}[/latex]
average radius [latex]1\text{.}\text{74}×{\text{10}}^{6}\text{m}[/latex]
orbital period (average) [latex]2\text{.}\text{36}×{\text{10}}^{6}\text{s}[/latex]
Earth-moon distance (average) [latex]3\text{.}\text{84}×{\text{10}}^{8}\text{m}[/latex]
Metric Prefixes for Powers of Ten and Their Symbols
Prefix Symbol Value Prefix Symbol Value
tera T [latex]{\text{10}}^{\text{12}}[/latex] deci d [latex]{\text{10}}^{-1}[/latex]
giga G [latex]{\text{10}}^{9}[/latex] centi c [latex]{\text{10}}^{-2}[/latex]
mega M [latex]{\text{10}}^{6}[/latex] milli m [latex]{\text{10}}^{-3}[/latex]
kilo k [latex]{\text{10}}^{3}[/latex] micro [latex]\mu[/latex] [latex]{\text{10}}^{-6}[/latex]
hecto h [latex]{\text{10}}^{2}[/latex] nano n [latex]{\text{10}}^{-9}[/latex]
deka da [latex]{\text{10}}^{1}[/latex] pico p [latex]{\text{10}}^{-\text{12}}[/latex]
[latex]{\text{10}}^{0}\left(=1\right)[/latex] femto f [latex]{\text{10}}^{-\text{15}}[/latex]
The Greek Alphabet
Alpha [latex]\text{Α}[/latex] [latex]\alpha[/latex] Eta [latex]\text{Η}[/latex] [latex]\eta[/latex] Nu [latex]\text{Ν}[/latex] [latex]\nu[/latex] Tau [latex]\text{Τ}[/latex] [latex]\tau[/latex]
Beta [latex]\text{Β}[/latex] [latex]\beta[/latex] Theta [latex]\text{Θ}[/latex] [latex]\theta[/latex] Xi [latex]\text{Ξ}[/latex] [latex]\xi[/latex] Upsilon [latex]\text{Υ}[/latex] [latex]\upsilon[/latex]
Gamma [latex]\text{Γ}[/latex] [latex]\gamma[/latex] Iota [latex]\text{Ι}[/latex] [latex]\iota[/latex] Omicron [latex]\text{Ο}[/latex] [latex]ο[/latex] Phi [latex]\text{Φ}[/latex] [latex]\varphi[/latex]
Delta [latex]\text{Δ}[/latex] [latex]\delta[/latex] Kappa [latex]\text{Κ}[/latex] [latex]\kappa[/latex] Pi [latex]\text{Π}[/latex] [latex]\pi[/latex] Chi [latex]\text{Χ}[/latex] [latex]\chi[/latex]
Epsilon [latex]\text{Ε}[/latex] [latex]\epsilon[/latex] Lambda [latex]\text{Λ}[/latex] [latex]\lambda[/latex] Rho [latex]\text{Ρ}[/latex] [latex]\rho[/latex] Psi [latex]\text{Ψ}[/latex] [latex]\psi[/latex]
Zeta [latex]\text{Ζ}[/latex] [latex]\zeta[/latex] Mu [latex]\text{Μ}[/latex] [latex]\mu[/latex] Sigma [latex]\text{Σ}[/latex] [latex]\sigma[/latex] Omega [latex]\Omega[/latex] [latex]\omega[/latex]
SI Units
Entity Abbreviation Name
Fundamental units Length m meter
Mass kg kilogram
Time s second
Current A ampere
Supplementary unit Angle rad radian
Derived units Force [latex]\text{N}=\text{kg}\cdot \text{m}/{\text{s}}^{2}[/latex] newton
Energy [latex]\text{J}=\text{kg}\cdot {\text{m}}^{2}/{\text{s}}^{2}[/latex] joule
Power [latex]\text{W}=\text{J}/\text{s}[/latex] watt
Pressure [latex]\text{Pa}=\text{N}/{\text{m}}^{2}[/latex] pascal
Frequency [latex]\text{Hz}=1/\text{s}[/latex] hertz
Electronic potential [latex]\text{V}=\text{J}/\text{C}[/latex] volt
Capacitance [latex]\text{F}=\text{C}/\text{V}[/latex] farad
Charge [latex]\text{C}=\text{s}\cdot \text{A}[/latex] coulomb
Resistance [latex]\Omega =\text{V}/\text{A}[/latex] ohm
Magnetic field [latex]\text{T}=\text{N}/\left(\text{A}\cdot \text{m}\right)[/latex] tesla
Nuclear decay rate [latex]\text{Bq}=1/\text{s}[/latex] becquerel
Selected British Units
Length [latex]1\phantom{\rule{0.20em}{0ex}}\text{inch}\phantom{\rule{0.20em}{0ex}}\left(\text{in}\text{.}\right)=2\text{.}\text{54}\phantom{\rule{0.20em}{0ex}}\text{cm}\phantom{\rule{0.20em}{0ex}}\left(\text{exactly}\right)[/latex]
[latex]1\phantom{\rule{0.20em}{0ex}}\text{foot}\phantom{\rule{0.20em}{0ex}}\left(\text{ft}\right)=0\text{.}\text{3048}\phantom{\rule{0.20em}{0ex}}\text{m}[/latex]
[latex]1\phantom{\rule{0.20em}{0ex}}\text{mile}\phantom{\rule{0.20em}{0ex}}\left(\text{mi}\right)=1\text{.}\text{609}\phantom{\rule{0.20em}{0ex}}\text{km}[/latex]
Force [latex]1\phantom{\rule{0.20em}{0ex}}\text{pound}\phantom{\rule{0.20em}{0ex}}\left(\text{lb}\right)=4\text{.}\text{448}\phantom{\rule{0.20em}{0ex}}\text{N}[/latex]
Energy [latex]1\phantom{\rule{0.20em}{0ex}}\text{British thermal unit}\phantom{\rule{0.20em}{0ex}}\left(\text{Btu}\right)=1\text{.}\text{055}×{\text{10}}^{3}\phantom{\rule{0.20em}{0ex}}\text{J}[/latex]
Power [latex]1\phantom{\rule{0.20em}{0ex}}\text{horsepower}\phantom{\rule{0.20em}{0ex}}\left(\text{hp}\right)=\text{746}\phantom{\rule{0.20em}{0ex}}\text{W}[/latex]
Pressure [latex]1\phantom{\rule{0.20em}{0ex}}\text{lb}/{\text{in}}^{2}=6\text{.}\text{895}×{\text{10}}^{3}\phantom{\rule{0.20em}{0ex}}\text{Pa}[/latex]
Other Units
Length [latex]1\phantom{\rule{0.20em}{0ex}}\text{light year}\phantom{\rule{0.20em}{0ex}}\left(\text{ly}\right)=9\text{.}\text{46}×{\text{10}}^{\text{15}}\phantom{\rule{0.20em}{0ex}}\text{m}[/latex]
[latex]1\phantom{\rule{0.20em}{0ex}}\text{astronomical unit}\phantom{\rule{0.20em}{0ex}}\left(\text{au}\right)=1\text{.}\text{50}×{\text{10}}^{\text{11}}\phantom{\rule{0.20em}{0ex}}\text{m}[/latex]
[latex]1\phantom{\rule{0.20em}{0ex}}\text{nautical mile}=1\text{.}\text{852}\phantom{\rule{0.20em}{0ex}}\text{km}[/latex]
[latex]1\phantom{\rule{0.20em}{0ex}}\text{angstrom}\left(\text{Å}\right)\phantom{\rule{0.20em}{0ex}}={\text{10}}^{-\text{10}}\phantom{\rule{0.20em}{0ex}}\text{m}[/latex]
Area [latex]1\phantom{\rule{0.20em}{0ex}}\text{acre}\phantom{\rule{0.20em}{0ex}}\left(\text{ac}\right)=4\text{.}\text{05}×{\text{10}}^{3}\phantom{\rule{0.20em}{0ex}}{\text{m}}^{2}[/latex]
[latex]1\phantom{\rule{0.20em}{0ex}}\text{square foot}\phantom{\rule{0.20em}{0ex}}\left({\text{ft}}^{2}\right)=9\text{.}\text{29}×{\text{10}}^{-2}\phantom{\rule{0.20em}{0ex}}{\text{m}}^{2}[/latex]
[latex]1\phantom{\rule{0.20em}{0ex}}\text{barn}\phantom{\rule{0.20em}{0ex}}\left(b\right)={\text{10}}^{-\text{28}}\phantom{\rule{0.20em}{0ex}}{\text{m}}^{2}[/latex]
Volume [latex]1\phantom{\rule{0.20em}{0ex}}\text{liter}\phantom{\rule{0.20em}{0ex}}\left(L\right)={\text{10}}^{-3}\phantom{\rule{0.20em}{0ex}}{\text{m}}^{3}[/latex]
[latex]1\phantom{\rule{0.20em}{0ex}}\text{U.S. gallon}\phantom{\rule{0.20em}{0ex}}\left(\text{gal}\right)=3\text{.}\text{785}×{\text{10}}^{-3}\phantom{\rule{0.20em}{0ex}}{\text{m}}^{3}[/latex]
Mass [latex]1\phantom{\rule{0.20em}{0ex}}\text{solar mass}\phantom{\rule{0.20em}{0ex}}=1\text{.}\text{99}×{\text{10}}^{\text{30}}\phantom{\rule{0.20em}{0ex}}\text{kg}[/latex]
[latex]1\phantom{\rule{0.20em}{0ex}}\text{metric ton}={\text{10}}^{3}\phantom{\rule{0.20em}{0ex}}\text{kg}[/latex]
[latex]1\phantom{\rule{0.20em}{0ex}}\text{atomic mass unit}\phantom{\rule{0.20em}{0ex}}\left(u\right)=1\text{.}\text{6605}×{\text{10}}^{-\text{27}}\phantom{\rule{0.20em}{0ex}}\text{kg}[/latex]
Time [latex]1\phantom{\rule{0.20em}{0ex}}\text{year}\phantom{\rule{0.20em}{0ex}}\left(y\right)=3\text{.}\text{16}×{\text{10}}^{7}\phantom{\rule{0.20em}{0ex}}\text{s}[/latex]
[latex]1\phantom{\rule{0.20em}{0ex}}\text{day}\phantom{\rule{0.20em}{0ex}}\left(d\right)=\text{86},\text{400}\phantom{\rule{0.20em}{0ex}}\text{s}[/latex]
Speed [latex]1\phantom{\rule{0.20em}{0ex}}\text{mile per hour}\phantom{\rule{0.20em}{0ex}}\left(\text{mph}\right)=1\text{.}\text{609}\phantom{\rule{0.20em}{0ex}}\text{km}/\text{h}[/latex]
[latex]1\phantom{\rule{0.20em}{0ex}}\text{nautical mile per hour}\phantom{\rule{0.20em}{0ex}}\left(\text{naut}\right)=1\text{.}\text{852}\phantom{\rule{0.20em}{0ex}}\text{km}/\text{h}[/latex]
Angle [latex]1\phantom{\rule{0.20em}{0ex}}\text{degree}\phantom{\rule{0.20em}{0ex}}\left(°\right)=1\text{.}\text{745}×{\text{10}}^{-2}\phantom{\rule{0.20em}{0ex}}\text{rad}[/latex]
[latex]1\phantom{\rule{0.20em}{0ex}}\text{minute of arc}\phantom{\rule{0.20em}{0ex}}{\left(}^{\text{'}}\right)=1/\text{60}\phantom{\rule{0.20em}{0ex}}\text{degree}[/latex]
[latex]1\phantom{\rule{0.20em}{0ex}}\text{second of arc}\text{}\phantom{\rule{0.20em}{0ex}}{\left(}^{\text{''}}\right)=1/\text{60}\phantom{\rule{0.20em}{0ex}}\text{minute of arc}[/latex]
[latex]1\phantom{\rule{0.20em}{0ex}}\text{grad}=1\text{.}\text{571}×{\text{10}}^{-2}\phantom{\rule{0.20em}{0ex}}\text{rad}[/latex]
Energy [latex]1\phantom{\rule{0.20em}{0ex}}\text{kiloton TNT}\phantom{\rule{0.20em}{0ex}}\left(\text{kT}\right)=4\text{.}2×{\text{10}}^{\text{12}}\phantom{\rule{0.20em}{0ex}}\text{J}[/latex]
[latex]1\phantom{\rule{0.20em}{0ex}}\text{kilowatt hour}\phantom{\rule{0.20em}{0ex}}\left(\text{kW}\cdot h\right)=3\text{.}\text{60}×{\text{10}}^{6}\phantom{\rule{0.20em}{0ex}}\text{J}[/latex]
[latex]1\phantom{\rule{0.20em}{0ex}}\text{food calorie}\phantom{\rule{0.20em}{0ex}}\left(\text{kcal}\right)=\text{4186}\phantom{\rule{0.20em}{0ex}}\text{J}[/latex]
[latex]1\phantom{\rule{0.20em}{0ex}}\text{calorie}\phantom{\rule{0.20em}{0ex}}\left(\text{cal}\right)=4\text{.}\text{186}\phantom{\rule{0.20em}{0ex}}\text{J}[/latex]
[latex]1\phantom{\rule{0.20em}{0ex}}\text{electron volt}\phantom{\rule{0.20em}{0ex}}\left(\text{eV}\right)=1\text{.}\text{60}×{\text{10}}^{-\text{19}}\phantom{\rule{0.20em}{0ex}}\text{J}[/latex]
Pressure [latex]1\phantom{\rule{0.20em}{0ex}}\text{atmosphere}\phantom{\rule{0.20em}{0ex}}\left(\text{atm}\right)=1\text{.}\text{013}×{\text{10}}^{5}\phantom{\rule{0.20em}{0ex}}\text{Pa}[/latex]
[latex]1\phantom{\rule{0.20em}{0ex}}\text{millimeter of mercury}\phantom{\rule{0.20em}{0ex}}\left(\text{mm}\phantom{\rule{0.20em}{0ex}}\text{Hg}\right)=\text{133}\text{.}3\phantom{\rule{0.20em}{0ex}}\text{Pa}[/latex]
[latex]1\phantom{\rule{0.20em}{0ex}}\text{torricelli}\phantom{\rule{0.20em}{0ex}}\left(\text{torr}\right)=1\phantom{\rule{0.20em}{0ex}}\text{mm}\phantom{\rule{0.20em}{0ex}}\text{Hg}=\text{133}\text{.}3\phantom{\rule{0.20em}{0ex}}\text{Pa}[/latex]
Nuclear decay rate [latex]1\phantom{\rule{0.20em}{0ex}}\text{curie}\phantom{\rule{0.20em}{0ex}}\left(\text{Ci}\right)=3\text{.}\text{70}×{\text{10}}^{\text{10}}\phantom{\rule{0.20em}{0ex}}\text{Bq}[/latex]
Useful Formulae
Circumference of a circle with radius [latex]r[/latex] or diameter [latex]d[/latex] [latex]C=2\pi r=\mathrm{\pi d}[/latex]
Area of a circle with radius [latex]r[/latex] or diameter [latex]d[/latex] [latex]A={\mathrm{\pi r}}^{2}={\mathrm{\pi d}}^{2}/4[/latex]
Area of a sphere with radius [latex]r[/latex] [latex]A=4{\pi r}^{2}[/latex]
Volume of a sphere with radius [latex]r[/latex] [latex]V=\left(4/3\right)\left({\mathrm{\pi r}}^{3}\right)[/latex]

Footnotes

  1. 1 Stated values are according to the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty, www.physics.nist.gov/cuu (accessed May 18, 2012). Values in parentheses are the uncertainties in the last digits. Numbers without uncertainties are exact as defined.
  2. 2 Stated values are according to the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty, www.physics.nist.gov/cuu (accessed May 18, 2012). Values in parentheses are the uncertainties in the last digits. Numbers without uncertainties are exact as defined.

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