Question

How do you simplify `(9 times 10^2)(2 times 10^10)`?

Answer 1

`1.8xx10^(13)`

Explanation:

Split it:

`9xx2color(white)("ddd")=color(white)("ddd")18color(white)("ddd") = color(white)("ddd")1.8xx10`

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`10^2xx10^10color(white)("ddd") = color(white)("ddd")10^(2+10)color(white)("ddd")=color(white)("ddd")10^(12)`

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Putting it all together

`1.8xx10xx10^12color(white)("d")=color(white)("d")1.8xx10^(13)`

Answer 2

`(9xx10^2)(2xx10^10)=color(blue)(18xx10^12)=color(green)(1.8xx10^13)`

Explanation:

`(9xx10^2)(2xx10^10)=9xx2xx10^2xx10^10`

`color(white)("XXXXXXXXXXX")=18xx10^12`

(or in standard scientific notation)
`color(white)("XXXXXXXXXXX")=1.8xx10^13`