How do you simplify $(9 \times 10^{2}) (2 \times 10^{10})$ $(9 times 10^2)(2 times 10^10)$ ?

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How do you simplify $(9 \times 10^{2}) (2 \times 10^{10})$ $(9 times 10^2)(2 times 10^10)$ ?

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Answer 1 · 2018-06-22T15:07:07

$1.8 \times 10^{13}$ $1.8xx10^(13)$

Explanation:

Split it:

$9 \times 2 ddd = ddd 18 ddd = ddd 1.8 \times 10$ $9xx2color(white)("ddd")=color(white)("ddd")18color(white)("ddd") = color(white)("ddd")1.8xx10$

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$10^{2} \times 10^{10} ddd = ddd 10^{2 + 10} ddd = ddd 10^{12}$ $10^2xx10^10color(white)("ddd") = color(white)("ddd")10^(2+10)color(white)("ddd")=color(white)("ddd")10^(12)$

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Putting it all together

$1.8 \times 10 \times 10^{12} d = d 1.8 \times 10^{13}$ $1.8xx10xx10^12color(white)("d")=color(white)("d")1.8xx10^(13)$

Answer 2 · 2018-06-22T15:07:52

$(9 \times 10^{2}) (2 \times 10^{10}) = 18 \times 10^{12} = 1.8 \times 10^{13}$ $(9xx10^2)(2xx10^10)=color(blue)(18xx10^12)=color(green)(1.8xx10^13)$

Explanation:

$(9 \times 10^{2}) (2 \times 10^{10}) = 9 \times 2 \times 10^{2} \times 10^{10}$ $(9xx10^2)(2xx10^10)=9xx2xx10^2xx10^10$

$XXXXXXXXXXX = 18 \times 10^{12}$ $color(white)("XXXXXXXXXXX")=18xx10^12$

(or in standard scientific notation)
$XXXXXXXXXXX = 1.8 \times 10^{13}$ $color(white)("XXXXXXXXXXX")=1.8xx10^13$

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