$\mathrm{0,000102}\cdot 10=\mathrm{0,00102}\backslash \; 0\{,\}000102\backslash cdot10=0\{,\}00102$

$\mathrm{0,00102}\cdot 10=\mathrm{0,0102}\backslash \; 0\{,\}00102\backslash cdot10=0\{,\}0102$

$\mathrm{0,0102}\cdot 10=\mathrm{0,102}\backslash \; 0\{,\}0102\backslash cdot10=0\{,\}102$

$\mathrm{0,102}\cdot 10=\mathrm{1,02}\backslash \; 0\{,\}102\backslash cdot10=1\{,\}02$

Du musst $\mathrm{0,000102}0\{,\}000102$ also $44$ mal mit $1010$ multiplizieren, damit du $\mathrm{1,02}1\{,\}02$ erhältst.

$10\cdot 10\cdot 10\cdot 10={10}^4\backslash \; 10\backslash cdot10\backslash cdot10\backslash cdot10=10^4$

$\mathrm{0,000102}\cdot {10}^4=\mathrm{1,02}\Rightarrow \mathrm{0,000102}={\displaystyle \frac{\mathrm{1,02}}{{10}^4}}=\mathrm{1,02}\cdot {\displaystyle \frac{1}{{10}^4}}\backslash \; 0\{,\}000102\backslash cdot10^4=1\{,\}02\backslash Rightarrow0\{,\}000102=\backslash dfrac\{1\{,\}02\}\{10^4\}=1\{,\}02\backslash cdot\backslash dfrac\{1\}\{10^4\}$

$\Rightarrow \mathrm{1,02}\cdot {10}^{-4}=\mathrm{0,000102}\backslash \; \backslash Rightarrow1\{,\}02\backslash cdot10^\{-4\}=0\{,\}000102\backslash qquad$zur Erinnerung:$\boxed{{\displaystyle \frac{1}{a^x}=a^{-x}}}\backslash quad\; \backslash boxed\{\backslash dfrac\{1\}\{a^x\}=a^\{-x\}\}$

Kreuze entsprechend an.