How do you write 6(2.2 xx 10^10)6(2.2×1010) in standard notation?

1 Answer
Mar 25, 2015

6(2.2xx10^10)6(2.2×1010)

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

6(2.2xx10^10)6(2.2×1010) can be written to clarify the multiplication:

6(2.2xx10^10)=6xx2.2xx10^10=(6xx2.2)xx10^106(2.2×1010)=6×2.2×1010=(6×2.2)×1010

Use your favorite multiplication method to get 6xx2.2=13.26×2.2=13.2

So
6(2.2xx10^10)=13.2xx10^106(2.2×1010)=13.2×1010

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=1.32xx10^1113.2×1010=1.32×1011

(13.213.2 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=132,000,000,00013.2×1010=132,000,000,000

.Second Edit
Using the usual rules for significant figures the answer should be 1.3xx10^111.3×1011 or
130,000,000,000130,000,000,000
(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)6(2.2×1010)=(6×100)(2.2×1010)

=(6xx2,2)xx(10^0xx10^10)=(6×2,2)×(100×1010)

=13.2 xx 10^(0+10)=13.2×100+10

=13.2xx10^10=13.2×1010

=1.32xx10^11=1.32×1011

Again keeping the correct significant figures: 1.3xx10^111.3×1011.