Represent each of the following combinations of units in the correct SI form using an appropriate prefix: (a) 0.000431 kg, (b) 35.3(10³) N, and (c) 0.00532 km.
Statics of Rigid Bodies 14th Edition by RC Hibbeler, Problem 1-7
Solution:
Part A
\begin{align*}
0.000 \ 431 \ \text{kg} & = 0.431 \times 10^{-3} \ \text{kg}\\
& = 0.431\times 10^{-3} \times 10^3 \ \text{g} \\
& = 0.431 \ \text{g}
\end{align*}Part B
\begin{align*}
35.3\left( 10^3 \right) \ \text{N} & = 35.3 \ \text{kN}
\end{align*}Part C
\begin{align*}
0.00532 \ \text{km} & = 0.00532 \times 10^3 \ \text{m} \\
& = 5.32 \times 10^{-3} \times 10^3 \ \text{m} \\
& = 5.32 \ \text{m}
\end{align*}
![\displaystyle 4.70\:\text{slug/ft}^3\times \left[\frac{\left(1\:\text{ft}^3\right)\left(14.59\:\text{kg}\right)}{\left(0.3048\:\text{m}\right)^3\:\left(1\:\text{slug}\right)}\right]=2.42\:\text{Mg/m}^3](https://s0.wp.com/latex.php?latex=%5Cdisplaystyle+4.70%5C%3A%5Ctext%7Bslug%2Fft%7D%5E3%5Ctimes+%5Cleft%5B%5Cfrac%7B%5Cleft%281%5C%3A%5Ctext%7Bft%7D%5E3%5Cright%29%5Cleft%2814.59%5C%3A%5Ctext%7Bkg%7D%5Cright%29%7D%7B%5Cleft%280.3048%5C%3A%5Ctext%7Bm%7D%5Cright%29%5E3%5C%3A%5Cleft%281%5C%3A%5Ctext%7Bslug%7D%5Cright%29%7D%5Cright%5D%3D2.42%5C%3A%5Ctext%7BMg%2Fm%7D%5E3&bg=ffffff&fg=000000&s=1&c=20201002)
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