Question

Solve: $\frac{4\times 22\times 6.67\times {10}^{-11}\times 6.4\times {10}^6\times 11\cdot 3\times {10}^3}{3\times 7}$

Answer 1

$\frac{4\times 22\times 6.67\times {10}^{-11}\times 6.4\times {10}^6\times 11.3\times {10}^3}{3\times 7}$

$=\frac{2^2\times 2\times 11\times 6.67\times {10}^{-11+6+3}\times 2^6\times 0.1\times 11.3}{3\times 7}$

$=\frac{2^{2+1+6}\times 11\times 6.67\times {10}^{-11+6+3}\times 0.1\times 11.3}{3\times 7}$

$=\frac{2^9\times 11\times 6.67\times {10}^{-2}\times {10}^{-1}\times 11.3}{3\times 7}$

$=\frac{2^9\times 11\times 6.67\times {10}^{-3}\times 11.3}{3\times 7}$

$=\frac{2^9\times {10}^{-3}\times 829.081}{21}=20213.784\times {10}^{-3}\approx 20.2138$