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

2 Answers
Feb 16, 2017

Answer:

#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

Answer:

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)#