Soalan 3:
Tukarkan ukuran dalam sistem metrik berikut kepada unit yang diberikan dalam kurungan.
Nyatakan jawapan anda dalam bentuk piawai.
(a) 1 050 kilometer [meter]
(b) 216 gigabait [bait]
(c) 0.75 teraliter [liter]
(d) 95 mikrometer [meter]
(e) 123 nanometer [meter]
(f) 0.089 femtometer [meter]
Penyelesaian:
(a)
$$ \begin{aligned} &1050 \text { kilometer }\\ &\begin{aligned} & =1050 \times 10^3 \text { meter } \\ & =\left(1.05 \times 10^3\right) \times 10^3 \text { meter } \\ & =\left(1.05 \times 10^{3+3}\right) \text { meter } \quad \text { Use index law } a^m \times a^n=a^{m+n} \\ & =1.05 \times 10^6 \text { meter } \end{aligned} \end{aligned} $$
(b)
$$ \begin{aligned} 216 \text { gigabait } & =216 \times 10^9 \text { bait } \\ & =\left(2.16 \times 10^2\right) \times 10^9 \text { bait } \\ & =\left(2.16 \times 10^{2+9}\right) \text { bait } \\ & =2.16 \times 10^{11} \text { bait } \end{aligned} $$
(c)
$$ \begin{aligned} 0.75 \text { teraliter } & =0.75 \times 10^{12} \text { liter } \\ & =\left(7.5 \times 10^{-1}\right) \times 10^{12} \text { liter } \\ & =\left(7.5 \times 10^{-1+12}\right) \text { liter } \\ & =7.5 \times 10^{11} \text { liter } \end{aligned} $$
(d)
$$ \begin{aligned} 95 \text { mikrometer } & =95 \times 10^{-6} \text { meter } \\ & =\left(9.5 \times 10^1\right) \times 10^{-6} \text { meter } \\ & =\left(9.5 \times 10^{1+(-6)}\right) \text { meter } \\ & =9.5 \times 10^{1-6} \text { meter } \\ & =9.5 \times 10^{-5} \text { meter } \end{aligned} $$
(e)
$$ \begin{aligned} 123 \text { nanometer } & =123 \times 10^{-9} \text { meter } \\ & =\left(1.23 \times 10^2\right) \times 10^{-9} \text { meter } \\ & =\left(1.23 \times 10^{2+(-9)}\right) \text { meter } \\ & =1.23 \times 10^{2-9} \text { meter } \\ & =1.23 \times 10^{-7} \text { meter } \end{aligned} $$
(f)
$$ \begin{aligned} 0.089 \text { femtometer } & =0.089 \times 10^{-15} \text { meter } \\ & =\left(8.9 \times 10^{-2}\right) \times 10^{-15} \text { meter } \\ & =\left(8.9 \times 10^{-2+(-15)}\right) \text { meter } \\ & =8.9 \times 10^{-2-15} \text { meter } \\ & =8.9 \times 10^{-17} \text { meter } \end{aligned} $$
Tukarkan ukuran dalam sistem metrik berikut kepada unit yang diberikan dalam kurungan.
Nyatakan jawapan anda dalam bentuk piawai.
(a) 1 050 kilometer [meter]
(b) 216 gigabait [bait]
(c) 0.75 teraliter [liter]
(d) 95 mikrometer [meter]
(e) 123 nanometer [meter]
(f) 0.089 femtometer [meter]
Penyelesaian:
(a)
$$ \begin{aligned} &1050 \text { kilometer }\\ &\begin{aligned} & =1050 \times 10^3 \text { meter } \\ & =\left(1.05 \times 10^3\right) \times 10^3 \text { meter } \\ & =\left(1.05 \times 10^{3+3}\right) \text { meter } \quad \text { Use index law } a^m \times a^n=a^{m+n} \\ & =1.05 \times 10^6 \text { meter } \end{aligned} \end{aligned} $$
(b)
$$ \begin{aligned} 216 \text { gigabait } & =216 \times 10^9 \text { bait } \\ & =\left(2.16 \times 10^2\right) \times 10^9 \text { bait } \\ & =\left(2.16 \times 10^{2+9}\right) \text { bait } \\ & =2.16 \times 10^{11} \text { bait } \end{aligned} $$
(c)
$$ \begin{aligned} 0.75 \text { teraliter } & =0.75 \times 10^{12} \text { liter } \\ & =\left(7.5 \times 10^{-1}\right) \times 10^{12} \text { liter } \\ & =\left(7.5 \times 10^{-1+12}\right) \text { liter } \\ & =7.5 \times 10^{11} \text { liter } \end{aligned} $$
(d)
$$ \begin{aligned} 95 \text { mikrometer } & =95 \times 10^{-6} \text { meter } \\ & =\left(9.5 \times 10^1\right) \times 10^{-6} \text { meter } \\ & =\left(9.5 \times 10^{1+(-6)}\right) \text { meter } \\ & =9.5 \times 10^{1-6} \text { meter } \\ & =9.5 \times 10^{-5} \text { meter } \end{aligned} $$
(e)
$$ \begin{aligned} 123 \text { nanometer } & =123 \times 10^{-9} \text { meter } \\ & =\left(1.23 \times 10^2\right) \times 10^{-9} \text { meter } \\ & =\left(1.23 \times 10^{2+(-9)}\right) \text { meter } \\ & =1.23 \times 10^{2-9} \text { meter } \\ & =1.23 \times 10^{-7} \text { meter } \end{aligned} $$
(f)
$$ \begin{aligned} 0.089 \text { femtometer } & =0.089 \times 10^{-15} \text { meter } \\ & =\left(8.9 \times 10^{-2}\right) \times 10^{-15} \text { meter } \\ & =\left(8.9 \times 10^{-2+(-15)}\right) \text { meter } \\ & =8.9 \times 10^{-2-15} \text { meter } \\ & =8.9 \times 10^{-17} \text { meter } \end{aligned} $$