$$420=3 \times { 10 }^{ 6 } \times { 10 }^{ -8 } \times 39 \times 12 \times N \times 4$$
$N = \frac{875}{117} = 7\frac{56}{117} \approx 7.478632479$
$$420=3\times 10^{-2}\times 39\times 12N\times 4$$
$$420=3\times \frac{1}{100}\times 39\times 12N\times 4$$
$$420=\frac{3}{100}\times 39\times 12N\times 4$$
$$420=\frac{117}{100}\times 12N\times 4$$
$$420=\frac{351}{25}N\times 4$$
$$420=\frac{1404}{25}N$$
$$\frac{1404}{25}N=420$$
$$N=420\times \frac{25}{1404}$$
$$N=\frac{875}{117}$$
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