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question-how to Convert 10 joules into ergs using dimensional analysis??

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$\begin{array}{l} \text {we know, } 1 \text { Joule }=1 \ \mathrm{Kg} \ \mathrm{m}^{2} / \mathrm{s}^{2} \\ 1 \ \mathrm{erg}=1 \ \mathrm{g} \ \mathrm{cm}^{2} / \mathrm{s}^{2} \\\\ \text {So, } 1 \text { Joule }=1 \mathrm{Kg} \mathrm{m}^{2} / \mathrm{s}^{2} \\ =\{1000 \mathrm{g}\}\{100 \mathrm{cm}\}^{2} / \mathrm{s}^{2} \cdot[1 \mathrm{kg}=1000 \mathrm{g} \text { and } 1 \mathrm{m}=100 \mathrm{cm}] \\ =1000 \times 10000 \mathrm{g} \mathrm{cm}^{2} / \mathrm{s}^{2} \\ =1000000 \mathrm{erg} \\ \\ \text {Hence, } 1 \text { Joule }=10^{7} \ \mathrm{erg} \\ \text {So, } 10 \text { Joule }=10 \times 10^{7 } \ \mathrm{erg}=10^{8} \mathrm{erg} \end{array}$

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