How do you write #6(2.2 xx 10^10)# in standard notation?

1 Answer
Jim H
Mar 25, 2015

#6(2.2xx10^10)#

I can think of 2 ways to explain this. I'll explain a second one after I explain this one.

#6(2.2xx10^10)# can be written to clarify the multiplication:

#6(2.2xx10^10)=6xx2.2xx10^10=(6xx2.2)xx10^10#

Use your favorite multiplication method to get #6xx2.2=13.2#

So
#6(2.2xx10^10)=13.2xx10^10#

This answer is the correct number, but it is in neither standard notation nor scientific notation. We should choose one notation or the other. We'll use scientific notation.

#13.2xx10^10=1.32xx10^11#

(#13.2# move the decimal 10 right is the same as 1.32 move 11 to the right.

EDIT
On re-reading, I see that you did ask how to write this in standard notation: #13.2xx10^10=132,000,000,000#

.Second Edit
Using the usual rules for significant figures the answer should be #1.3xx10^11# or
#130,000,000,000#
(Like many mathematicians, I tend to carry more significatn figures than I have a right to.)

Second Description

If you chose to (if it is clearer to you) You could re-write both numbers in scientific notation to start with:

#6(2.2xx10^10)=(6xx10^0)(2.2xx10^10)#

#=(6xx2,2)xx(10^0xx10^10)#

#=13.2 xx 10^(0+10)#

#=13.2xx10^10#

#=1.32xx10^11#

Again keeping the correct significant figures: #1.3xx10^11#.

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