How do you simplify #(6.1times10^5)(2.4times10^4)#?

1 Answer
Dec 28, 2016

Answer:

#1.467xx10^10 larr" Scientific notation"#

Explanation:

#color(brown)("Breaking this down into a lot of detail so that you can see what is")# #color(brown)("happening.")#

#6.1# is the same as #61/10 -> 61xx1/10#

#2.4# is the same as #24/10->24xx1/10#

So #(6.1xx10^5)(2.4xx10^4) =6.1xx10^5xx2.4xx10^4#

#=61xx10^5/10xx24xx10^4/10#

#=61xx24xx10^5/10xx10^4/10#

#=61xx24xx10^4xx10^3#

#=61xx24xx10^7#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(white)(14)24#
#ul(color(white)(14)61) larr" multiply"#
#1440#
#ul(color(white)(14)24)larr" add"#
#1464#

So we now have:

#1464xx10^7#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#1467xx10^7#
#146.7xx10^8#
#14.67xx10^9#
#1.467xx10^10larr" this is the same format as in the question "#

#1.467xx10^10 larr" Scientific notation"#