# How do you multiply 3.045*10^5 * 6.853*10^6?

Apr 3, 2015

Regroup the coefficients and the exponents together and multiply separately
$3.045 \cdot {10}^{5} \cdot 6.853 \cdot {10}^{6}$
$= \left(3.045 \times 6.853\right) \cdot \left({10}^{5} \cdot {10}^{6}\right)$

$3.045 \times 6.853 = 20.86738$
solve this by hand or use a calculator/spreadsheet

${10}^{5} \cdot {10}^{6} = {10}^{11}$
since ${b}^{p} \times {b}^{q} = {b}^{p + q}$

So
$3.045 \cdot {10}^{5} \cdot 6.853 \cdot {10}^{6}$
$= 20.86738 \cdot {10}^{11}$

or (if normalized)
$= 2.086738 \cdot {10}^{12}$