Units and Dimensions

Units and dimensional analysis

Base quantities (SI)
$[M], [L], [T], [A], [K], [$ mol $], [$ cd $]$
Common dimensions
$F : [M L T^{- 2}],$ $E : [M L^{2} T^{- 2}],$ $P : [M L^{2} T^{- 3}],$ $p : [M L T^{- 1}]$
$G : [M^{- 1} L^{3} T^{- 2}],$ $h : [M L^{2} T^{- 1}],$ pressure $: [M L^{- 1} T^{- 2}],$ $η : [M L^{- 1} T^{- 1}]$
Homogeneity
every term of a valid equation has the same dimensions
Changing units
$n_{2} = n_{1} (\frac{M _{1}}{M _{2}})^{a} (\frac{L _{1}}{L _{2}})^{b} (\frac{T _{1}}{T _{2}})^{c}$

Absolute and relative error
$Δ a_{mean} = \frac{1}{n} \sum ∣Δ a_{i} ∣,$ relative error $= \frac{Δ a}{a}$
Sum or difference
$Z = A \pm B \Rightarrow Δ Z = Δ A + Δ B$
Product, quotient, power
$Z = \frac{A ^{p} B ^{q}}{C ^{r}} \Rightarrow \frac{Δ Z}{Z} = p \frac{Δ A}{A} + q \frac{Δ B}{B} + r \frac{Δ C}{C}$
Significant figures
$\times, \div :$ least number of significant figures $;$ $+, - :$ least number of decimal places