Question

How do you simplify `(2.135times10^5)/(3.5times10^12)`?

Answer 1

`6.1 xx 10^(-8)`

Explanation:

One way to go about this is to write the whole thing out, answer it, then simplify it:

`2.135 xx 10^5 = 213500`

`3.5 xx 10^12 = 3500000000000`

then you are able to do the calculation (use a calculator).The calculator gives the answer of

`0.000000061 = 6.1 xx 10^(-8)`

Hopefully this was helpful...

Answer 2

This is a sort of cheat method to make the numbers easier to deal with.

`6.1xx10^(-8)`

Explanation:

Given: `(2.135xx10^5)/(3.5xx10^12)`

but `2.135xx10^5` is the same as `2135xx10^2`
and `3.5xx10^12` is the same as `3500xx10^9`

and `10^2/10^9 = 10^2/(10^2xx10^7) =1/10^7`

`color(white)(.)`
`color(white)(.)`

So we now have:

`2135/3500xx1/10^(7)`

`(2135-:5)/(3500-:5)xx1/10^(7)" "=" "427/700xx1/10^7`

`" "=" "427/7xx1/10^9`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Using long division `427-:7` is:

`" "427`
`color(red)(60)xx7->ul(420) larr" subtract"`
`" "color(white)(42)7`
`color(white)(6)color(red)(1)xx7 ->ul(color(white)(42)7) larr" subtract"`
`" "0`

`427-:7" is: "color(red)(60+1)=61`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So `" "427/7xx1/10^9" "=" "61xx1/10^9" "=" "6.1xx1/10^8`

Which is the same as: `" "6.1xx10^(-8)`