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

Mar 25, 2015

$6 \left(2.2 \times {10}^{10}\right)$

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

$6 \left(2.2 \times {10}^{10}\right)$ can be written to clarify the multiplication:

$6 \left(2.2 \times {10}^{10}\right) = 6 \times 2.2 \times {10}^{10} = \left(6 \times 2.2\right) \times {10}^{10}$

Use your favorite multiplication method to get $6 \times 2.2 = 13.2$

So
$6 \left(2.2 \times {10}^{10}\right) = 13.2 \times {10}^{10}$

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.

$13.2 \times {10}^{10} = 1.32 \times {10}^{11}$

($13.2$ 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: $13.2 \times {10}^{10} = 132 , 000 , 000 , 000$

.Second Edit
Using the usual rules for significant figures the answer should be $1.3 \times {10}^{11}$ 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:

$6 \left(2.2 \times {10}^{10}\right) = \left(6 \times {10}^{0}\right) \left(2.2 \times {10}^{10}\right)$

$= \left(6 \times 2 , 2\right) \times \left({10}^{0} \times {10}^{10}\right)$

$= 13.2 \times {10}^{0 + 10}$

$= 13.2 \times {10}^{10}$

$= 1.32 \times {10}^{11}$

Again keeping the correct significant figures: $1.3 \times {10}^{11}$.