# How do you calculate (7.8times10^7)/(1.0times10^4)?

Oct 22, 2016

$7.8 \times {10}^{3}$

#### Explanation:

In algebra we would simplify the following by dividing the numbers and subtracting the indices of like bases

(color(red)(12)color(blue)( x^11))/(color(red)(4)color(blue)(x^5))" " rarr(cancel12^3 xx x^11)/(cancel4 xx x^5

=$\textcolor{red}{3} \textcolor{b l u e}{\times {x}^{6}} \text{ } \left(11 - 5 = 6\right)$

=$3 {x}^{6}$

In scientific notation you do EXACTLY the same:
Divide the numbers and subtract the indices of like bases.

(color(red)(7.8)color(blue)( xx 10^7))/(color(red)(1.0)color(blue)( xx 10^4)

=$\textcolor{red}{7.8} \textcolor{b l u e}{\times {10}^{3}}$

=$7.8 \times {10}^{3}$