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

2 Answers
Feb 16, 2017

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...

Feb 16, 2017

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)