How do you calculate (5.3times10^-2) times (-2.06times10^9)?

Jun 26, 2016

-$1.0918 \times {10}^{8}$

Explanation:

This is done in the same way as you would multiply in algebra.

$3 {x}^{5} \times - 4 {x}^{-} 2$

This could be written as$\left(3 \times - 4\right) \times \left({x}^{5} \times {x}^{-} 2\right)$
Multiply the numbers,: $3 \times - 4 = - 12$
Multiply the variables by adding the indices.

${x}^{5} \times {x}^{-} 2 = {x}^{5 - 2} = {x}^{3}$

$3 {x}^{5} \times - 4 {x}^{-} 2 = - 12 {x}^{3}$

We can do the same with numbers in scientific notation:
$5.3 \times {10}^{-} 2 \times - 2.06 \times {10}^{9}$ can be written as:

$\left(5.3 \times - 2.06\right) \times \left({10}^{-} 2 \times {10}^{9}\right)$

Multiply the numbers,: $5.3 \times - 2.06 = - 10.918$

Multiply the powers by adding the indices.
${10}^{-} 2 \times {10}^{9} = {10}^{- 2 + 9} = {10}^{7}$

$5.3 \times {10}^{-} 2 \times - 2.06 \times {10}^{9} = - 10.918 \times {10}^{7}$

However, in standard form there must be only one digit before the decimal point.
$- 10.918 \times {10}^{7} = - 1.0918 \times {10}^{8}$