How do you evaluate (2.542times10^5)/(4.1times10^-10)?

Jul 20, 2017

See a solution process below:

Explanation:

First, rewrite the expression as:

$\left(\frac{2.542}{4.1}\right) \times \left({10}^{5} / {10}^{-} 10\right) \implies 0.62 \times \left({10}^{5} / {10}^{-} 10\right)$

Next, use this rule of exponents to evaluate the $10 s$ terms:

${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} - \textcolor{b l u e}{b}}$

$0.62 \times \left({10}^{\textcolor{red}{5}} / {10}^{\textcolor{b l u e}{- 10}}\right) \implies 0.62 \times {10}^{\textcolor{red}{5} - \textcolor{b l u e}{- 10}} \implies$

$0.62 \times {10}^{\textcolor{red}{5} + \textcolor{b l u e}{10}} \implies$

$0.62 \times {10}^{15}$

To write the result in scientific notation form we need to move the decimal point $1$ place to the right, therefore we need to subtract $1$ from the exponent for the 10 term:

$6.2 \times {10}^{14}$

If we want to right this in standard from we need to move the decimal point 14 places to the right:

$620 , 000 , 000 , 000 , 000$