Question

How do yo simplify `\frac { ( 8.4\times 10^ { 3} ) } { ( 2\times 10^ { 5} ) }`?

Answer 1

`4.2 xx10^-2`

Explanation:

In algebra: `(color(red)(12)x^color(blue)(5))/(color(red)(4)x^color(blue)(9)) = color(red)(3)x^color(blue)(-4) = 3/x^4`

`rarr` divide the numbers and subtract the indices

In scientific notation we do exactly the same....

`\frac { ( color(red)(8.4)\times 10^ { color(blue)(3)} ) } { ( color(red)(2)\times 10^ { color(blue)(5)} ) } = color(red)(4.2) xx10^color(blue)(-2)`

`rarr` divide the numbers and subtract the indices.

However in scientific notation we keep the negative index of 10.